Introduction
in this work I advance a theory of the proposition
the proposition is a proposal – open to question –
open to doubt and uncertain
in the absence of proposal – of propositions – the reality
we face is unknown
we propose to make known –
our knowledge is proposal –
our knowledge is open to question – open to doubt – and is
uncertain
our reality is propositional
there are two modes of propositional activity
firstly – we critically evaluate propositions –
that is we put propositions to question – to doubt and we
explore their uncertainty
secondly – we play propositional games
propositional games are rule governed propositional actions
if you play a propositional game – you play in accordance
with the rules of the game
if you don’t play in accordance with the rules – there is no
game
in a propositional game – nothing is proposed – a game does
not propose – a game is played
and the game as played is not open to question – open to
doubt – or to be regarded as uncertain
in propositional life – we propose – and we play
in what follows I will explore and argue for this view of
the proposition in relation to the argument of the Tractatus
I will proceed by presenting the propositions of the Tractatus
– and follow each proposition with my response
Tractatus 1
1. The world is all that is the case.
what is the case is what is proposed –
the world – is what is proposed
a proposal is open to question – open to doubt – and
uncertain –
the world is open to question – open to doubt – and
uncertain
1.1. The world is the totality of facts, not things.
facts are proposals – things are proposals – the world is
proposal –
it makes no sense to speak of the totality of facts /
proposals –
propositional action is on-going and indeterminate
proposals – propositions – are open to question – open to
doubt – and are uncertain
1.11. The world is determined by the facts, and by there
being all the facts.
‘the world’ – is not
determined – the world is open – open to question – open to doubt – and
uncertain
‘facts’ – are
proposals – open to question – open to doubt – and uncertain
as to their being ‘all the facts’ –
it makes no logical sense to speak of ‘all the facts’ –
propositional action – the putting of proposals – of facts –
is on-going and indeterminate
what we deal with – is what is proposed – and
what is proposed – at any time and place
1.12. For the totality of facts determines what is the case,
and also what is not the
case.
there is no totality of facts – facts are proposals – and
propositional action is on-going – and indeterminate
what is proposed – is not determined –
what is proposed – is open – open to question – open to
doubt – and uncertain
what is the case – is what is proposed –
what is not the case – is what is not proposed –
1.13. The facts in logical space are the world.
facts are proposals – propositions –
what we deal with is propositions – and propositional
constructs
the notion of ‘logical space’ – is irrelevant to propositional
action
the world is propositional
1.2. The world divides into facts.
you can put the proposal that the world divides into facts /
propositions
this is just another proposal – open to question – open to
doubt – and uncertain
1.21. Each item can be the case or not the case while
everything else remains the
same.
‘each item’ – is – each proposal –
a proposal put is the case
and what is proposed – is open to question – open to doubt –
and uncertain
what is not the case – is that which is not proposed –
‘everything else remains the same’ –
‘everything else’ – is what is not proposed
Tractatus 2
2. What is the case – a fact – is the existence of states of
affairs.
a ‘fact’ is a proposal –
what is the case – is what is proposed –
‘the existence of a state of affairs’ is a proposal
2.01. A state of affairs (a state
of things) is a combination of objects (things).
a state of affairs – a state of things – is a proposal
–
a combination of objects (things) is a propositional
construct
2.011. It is essential to things that they should be
possible constituents of states of
affairs.
a ‘thing’ is a proposal –
‘a state of affairs’ is a propositional construct
‘a possible constituent of a state of affairs’ – is a
proposal –
a proposal – a propositional construct – is open to question
– open to doubt – and uncertain
propositional uncertainty is the ground of possibility
nothing is ‘essential’ in propositional logic
2.012. In logic nothing is accidental; if a thing can
occur in a state of affairs, the
possibility of the state of affairs must be written into the
thing.
logic is a rule governed propositional action
a rule governed propositional is a propositional game
the rules of a propositional game – as with any proposal /
proposition can be critically evaluated –
and this is indeed what happens in game construction –
however putting the rules of a propositional game to
question – to doubt – and exploring their uncertainty – is a different matter
to playing the game
in the game mode the propositions / rules are not questioned
– not put to doubt – or regarded as uncertain
if they are – there is no game
in a propositional game – you follow the rules of the game
a propositional analysis of a thing / proposal – is only
‘written into the thing’ – into the proposal – if that propositional analysis –
is proposed –
and any proposal put – is open to question – open to doubt –
and uncertain
2.0121. It would seem to be a sort of accident, that a
situation would fit a thing that
could already exist entirely on its own.
If things can occur in states of affairs, the possibility
must be in them from the
beginning.
(Nothing in the province of logic can be merely possible and
all possibilities are its
facts.)
Just as we are quite unable to imagine spatial objects
outside of space or temporal
objects outside of time, so too there is no object that we
can imagine excluded from
the possibility of combining with others.
If I can imagine objects combined in states of affairs, I cannot
imagine them excluded
from the possibility of such combinations.
‘It would seem to be a sort of accident, that a situation
would fit a thing that could
already exist entirely on its own.’ –
‘a thing existing entirely on its own’ – is that which is proposed
the proposition that one proposal (situation) fits another
proposal (thing) –
is open to question – open to doubt – is uncertain
‘If things can occur in states of affairs, the possibility
must be in them from the
beginning.’ –
what exists in a state of affairs is that which is proposed
any proposed relation between propositions – i.e. – ‘things
and ‘states of affairs’ – is open to question – open to doubt – is uncertain
the ground of possibility is uncertainty
the only ‘beginning’ – is the proposal – the action of
proposal
‘Nothing in the province of logic can be merely possible and
all possibilities are its
facts.’ –
logic is a rule governed propositional game – one among many
its possibilities are rule governed
‘Just as we are quite unable to imagine spatial objects
outside of space or temporal
objects outside of time, so too there is no object that we
can imagine excluded from
the possibility of combining with others.’ –
yes it is possible to combine any proposition – with any
other proposition –
but this is to make a trivial point –
‘If I can imagine objects combined in states of affairs, I
cannot imagine them
excluded from the possibility of such combinations.’ –
yes – you can
proposals combined in a propositional state of affairs – can
be put independently of a proposed state of affairs
2.0122. Things are independent in so far as they can occur
in all possible situations,
but this form of independence is a form of connection with
states of affairs, a form of
dependence. (It is impossible for words to appear in two
different roles: by themselves
and in propositions.)
proposals / propositions are proposed independently
propositional connections are proposals
words are proposals –
words can be proposed – independently of propositions in
which occur
words / proposals can be combined to form new proposals
2.0123. If I know an object I also know all its possible
occurrences in states of affairs.
(Everyone of these must be part of the nature of an object).
A new possibility cannot be discovered later.
I can’t know a proposal’s occurrence or use – in all
propositional contexts –
I know a propositions occurrence in the propositional
contexts that I use – or that I
have been introduced to
a propositional context is not part of a proposition
– it is a separate proposal – a separate propositional construct
a new proposal or new propositional context can always be
put
2.01231. If I am to know an object I need not know all its
external properties, I must
know all its internal properties.
all properties of an object / proposal – are proposals
separate and external to the object proposal –
there are no ‘internal’ properties
what I know is the proposals that I put – or that are put to
me
2.0124. If all objects are given, then at the same time all possible
states are also given.
what is given – is what is proposed
all proposals – all possible proposals – are not given
2.013. Each thing is, as it were, in a space of possible
states of affairs. This space I can imagine empty, but I cannot imagine the
thing without the space.
each thing /
proposal – is put – is proposed
‘a space of possible
states of affairs’ – is the unknown
the unknown is
propositionally empty
a proposal – a
proposition – is a response to – the unknown
every proposal –
every proposition – defies the unknown
2.0131. A spatial object must be situated in infinite space.
(A spatial point is an
argument place).
A speck in the visual field, though it need not be red, must
have some colour; it is, so
to speak, surrounded by colour-space. Notes must have some
pitch, objects of the
same touch, must have some degree of hardness, and
so.
if an object / proposal is described – defined – as
‘spatial’ – it will by definition be situated in space
as to whether the ‘space’ is infinite or not – that’s
another question
any proposal is an argument place – in that it is open to
question – open to doubt – and uncertain
and yes – a speck in the visual field will be coloured – if
the visual field is defined as coloured
and by definition – a note has pitch – and objects of the
same touch will have some degree of hardness
all we have here is a series of analytic definitions
analyticity is nothing more than propositional reassertion–
a spatial object – is a spatial object – a coloured object –
is a coloured object – hard objects are hard objects
reasserting a proposition has no logical value –
its only value is rhetorical
the idea is that reassertion establishes a proposition’s
truth –
and protects it from question – from doubt – and from
uncertainty
any such view of the proposition is logically corrupt and
pretentious
2.014. Objects contain the possibilities of all situations.
proposals / objects – are put – and put in propositional
contexts
‘all situations ‘ – are all propositional contexts –
to say that a proposal contains the possibilities of all
propositional contexts – is to say that a proposal – a proposition – contains
in some mystical sense – all propositions –
when I propose one thing – I do not propose everything –
to suggest that one proposition contains all propositions –
is preposterous and ridiculous
and the vanity of it is breathtaking
2.0141. The possibility of its occurring in states of
affairs is the form of an object.
the form of an object is the form of a proposal –
the form of a proposition – is a proposal of propositional
structure
the possibility of a proposal / object occurring in a state
of affairs – that is – in a propositional context – depends on the use of the
object / proposal –
it is a contingent matter
2.02. Objects are simple.
objects are proposals –
how we describe an object / proposal – i.e. as ‘simple’ – or
‘complex’ – will be a matter of propositional context
and any description is open to question – open to doubt and
uncertain
2.0201. Every statement about complexes can be resolved into
a statement about their
constituents and into the propositions that describe
complexes completely.
any analysis of any of any proposal – ‘ i.e. ‘complexes can
be resolved into a statement about their constituents’ – is a proposal –
any description is a proposal –
a proposal is open to question – open to doubt – and
uncertain
propositional uncertainty defies ‘completeness’ – and
renders it illogical
2.021 Objects make up the substance of the world that is why
they cannot be
composite.
objects are proposals
the world is propositional
any proposal regarding the ‘substance of the world’ – is
open to question –
there is no ‘cannot be’ – given propositional uncertainty
a composite description of the substance of the world – is
as valid as any other proposed description –
and may well serve a purpose –
such a description – as with any other – is open to question
– open to doubt – and is uncertain
2.0211. If the world had no substance, then whether a
proposition had sense would
depend on whether another proposition is true.
that the world has substance – is a proposal
that the world has no substance – is a proposal –
these proposals are open to question – open to doubt – and
uncertain
the sense of a proposition – is open to question – open to
doubt – and is uncertain
a proposition is true – if it is assented to – for whatever
reason
a proposition is false – if dissented from – for any reason
–
any proposal of assent or any proposal of dissent – is open to question – open to doubt – and
is uncertain
2.0212. In that case we could not sketch any picture of the
world.
a picture of the world – is a proposal –
a proposal open to question – open to doubt – and uncertain
‘in that case’ – the picture sketched – would be of a world
with no substance –
whatever that would amount to
and whatever that amounted to – would be a proposal – open
to question – open to doubt – and uncertain
2.022. It is obvious that an imagined world, however
different it may be from the real
one, must have something – a form – in common with
it.
this proposal can always be put – and is open to question
what do you say to an artist who says his picture (proposal)
has nothing in common with the world of common experience?
the point is – there can be – there is – question – doubt – uncertainty –
the ‘obvious argument’ – is really just rhetoric
logically speaking – any proposal – is open to question –
open to doubt – and uncertain
logically speaking – nothing is ‘obvious’ – if ‘obvious’
means – beyond question
2.023. Objects are what constitutes this unalterable form.
objects are proposals –
‘form’ is a proposal of propositional structure –
a proposal – open to question – open to doubt – and uncertain
there is no unalterable form / propositional structure
2.0231. The substance of the world can only determine
a form, and not any material
properties. For it is only by means of propositions that
material properties are
represented – only by the configuration of objects that they
are produced.
‘the substance of the world’ – is a proposal
a form is a proposal of propositional structure
– a form is proposed –
the world is propositional –
a ‘material property’ – is a proposal
it is only by means of proposal that material properties
exist –
what exists is what is proposed
the ‘configuration of objects’ – is a proposal
2.0232. In a manner of speaking objects are colourless.
in a manner of speaking proposals / propositions are
colourless
2.0233. If two objects have the same logical form, the only
distinction between them,
apart from their external properties, is that they are
different.
an object is a proposal –
logical form is a proposal of propositional structure
two object / proposals – which it is proposed have the same
propositional structure –
will be different at least in terms of their provenance –
i.e. where and when – they were proposed –
they will be contingently different
2.02331. Either a thing has properties that nothing else
has, in which case we can
immediately use a description to distinguish it from the
others and refer to it; or, on
the other hand, there are several things that have the whole
set of properties in
common, in which case it is quite impossible to indicate one
of them.
For if there is nothing to distinguish a thing, I cannot
distinguish it, since otherwise it
would be distinguished after all.
if you have two things / two proposals –
you have two separate proposals to begin with –
the question is –
apart from the fact that they are separate – what
distinguishes them?
if one thing / proposal has properties / descriptions that
are not applied to the other
those descriptions can be used to distinguish it from the
other
if on the other hand those descriptions do not
distinguish one from the other
the question remains how they are to be distinguished?
perhaps other descriptions will do the job
any proposal of distinction will be open to question – open
to doubt – and uncertain
what distinguishes one thing / proposal from another – is
open to question – open to doubt – and is uncertain
2.024. Substance is what subsists independently of what is
the case.
what is independent of what is the case – that is of – what
is proposed –
is the unknown
2.025. It is form and content.
form is a proposal of propositional structure
a proposition’s content – is what is proposed
form and content are propositional characterizations
form and content do not exist outside of the propositional
context
2.0251. Space, time and colour (being coloured) are forms of
objects.
space – time – and colour – are descriptions – proposals of
propositional context – that are applied to the proposal of objects
2.026. There must be objects if the world is to have an
unaltered form.
the proposal of objects – is open to question – open to
doubt – is uncertain
form is a proposal of propositional structure
any such proposal is open to question – open to doubt – and
is uncertain –
our world is propositional – it is not ‘unaltered’ – it is
uncertain
2.027 Objects, the unalterable, and the subsistent are one
in the same.
objects are propositions – proposals – open to question –
open to doubt – and uncertain
in that logically speaking – any proposition is uncertain –
it is not ‘unalterable’
what exists in the absence of proposal – of propositions –
is the unknown
2.0271. Objects are what is unalterable and subsistent;
their configuration is what is
changing and unstable.
‘objects’ are proposals – propositions – open to question –
open to doubt – and uncertain
any proposed configuration of objects – is open to question
– open to doubt – and is uncertain
what comes off as unalterable and subsistent – is
philosophical prejudice
2.0272. The configuration of objects produces states of
affairs.
a configuration of proposals is a state of affairs
2.03. In a state of affairs objects fit into one another
like the links of a chain.
in a propositional construct proposals / objects are placed
in relation to proposals –
and their relation is a proposal – open to question – open
to doubt – and uncertain
2.031 In a state of affairs objects stand in a determinate
relation to one another.
the relation of one proposition – one object / proposal – to
another – is open to question – open to doubt – and is uncertain
2.032. The determinate way in which objects are connected in
a state of affairs is the
structure of the state of affairs.
the relation of objects / propositions in a proposed state
of affairs – logically speaking –
is indeterminate –
that is – open to question – open to doubt – and uncertain
2.033. Form is the possibility of structure.
form is a proposal of structure
2.034. The structure of a fact consists of the structures of
states of affairs.
a ‘fact’ is a generally accepted proposal – within some
propositional context
a ‘fact’ can be structured – that is propositionally
structured
a ‘state of affairs’ – is a proposal – a proposition made up
of other propositions – a proposition that can be analysed into other
propositions and their relations
if the structure of a fact consists of the structures of
states of affairs –
there is not much point talking about ‘facts’ and ‘states of affairs’ – for in terms
of structure – they amount to the same thing
and in that case – best to just speak of propositional
structures
propositional structures – open to question – open to doubt
– and uncertain
2.04. The totality of existing states of affairs is the
world.
the totality of existing states of affairs – would be the
totality of proposals – of propositions put –
however – it is pointless to talk of a ‘totality’ of
propositions – propositional action is on-going
‘the world’ – is a proposal
2.05. The totality of existing states of affairs also
determines which states of affairs do
not exist.
that which does not exist – is that which is not proposed
2.06.The existence and non-existence of states of affairs is
a reality.
(We also call the existence of states of affairs a positive
fact, and their non-existence a
negative fact.)
a state of affairs exists – if it is proposed
reality is that
which is proposed –
that which is not proposed – is not there – is not a
reality
there are no ‘negative facts’ –
a ‘negative fact’ would have to be ‘a proposal that is not
proposed’ – which is an absurdity
reality is what is proposed
2.061. States of affairs are independent of each other.
a ‘state of affairs’ is a proposal –
one proposal is contingently independent of another
two proposals can be related via a third proposal etc.
2.062. From the existence or non-existence of one state of
affairs it is impossible to
infer the existence or non-existence of another.
it is possible to infer from the existence of one proposed
state of affairs – to another
the inference is a relational proposal
.
there is no inference / proposal from a non-existent state
of affairs / proposal
2.063. The sum total of reality is the world.
the world is not a sum total
reality is what is proposed –
reality is propositional –
and propositional action is on-going
2.1. We picture facts to ourselves.
a picture is a proposal – a proposal of
representation
i.e. – that one proposition or set of propositions
represents another proposition or set propositions
we propose facts to ourselves – and to others
do we picture facts?
firstly a fact is a proposal – a generally accepted proposal
do we propose that facts / proposals – represent – other proposals – other propositions?
yes – you can put that one proposition or set of proposals /
‘facts’ – represent another proposition or set of other propositions
however at the same time not all proposals of facts are
picture proposals – representation proposals
a fact may simply be proposed in a declarative statement –
i.e. ‘the Mona Lisa is in the Louvre’ – might be proposed as
a fact
and not all propositional action is ‘representational’ –
we may i.e. propose to modify or even oppose another
proposition –
representation – is one mode of propositional action
–
and just what representation amounts to – is open to
question – open to doubt – and uncertain
2.11. A picture presents a situation in logical space, the
existence and non-existence of states of affairs.
a picture is a proposal – a representative proposal
as to – ‘a situation in logical space’ –
the representative proposal – is the situation
this notion of ‘logical space’ is superfluous –
what is logically relevant is that a proposition is put
– and is open to question – open to doubt – and is uncertain –
packaging up a proposition with ‘logical space’ – is
unnecessary and irrelevant
we do not have pictures / representational proposals of
non-existent states of affairs
if a state of affairs is proposed – it exists
an existing state of affairs – is a proposal
if a state of affairs is not proposed – it doesn’t exist
what does not exist – is what is not proposed
2.12. A picture is a model of reality.
a picture is a proposal – a representative proposal
‘a model of reality’ – is a proposal – a representative
proposal
reality is what is proposed – reality is a proposal
reality is open to question – open to doubt – and uncertain
2.13. In a picture objects have the elements of the picture
corresponding to them.
you can propose an elemental analysis here –
this is where it is proposed that the picture – the
representative proposal – is to be understood as elemental –
and that therefore the object proposal – is to be construed
elementally
what you have here is an elemental analysis – an elemental
argument
these proposals –
the elemental proposal – and the proposal of the correspondence of the elements
– are open to question – open to doubt – and uncertain
not all pictures are
construed elementally
2.131. In a picture the elements of the picture are the
representatives of objects
if you run with an elemental analysis – that is a proposal –
that is the argument
it is a proposal – open to question – open to doubt – and
uncertain
the fact is you can have a representative proposal that is
not elemental –
that is not construed in terms of elements
2.14. What constitutes a picture is that its elements are
related to one another in a
determinate way.
a picture is a proposal of representation –
what constitutes a picture – is open to question – open to
doubt – and uncertain
picture / proposals can be given an elemental analysis –
from a logical point of view – how the elements are related
is open to question – open to doubt – and uncertain
and if the picture / representative proposal – is not given
an elemental / determinate analysis – does it cease to be a picture?
2.141. A picture is a fact.
a ‘picture’ is a proposal – a representative proposal
a ‘fact’ is a proposal –
you can describe a picture – a relational / representative
proposal as a fact –
in any case this picture / ‘fact’ – as with any proposal –
is open to question – open to doubt – and uncertain
2.15. The fact that the elements of a picture are related to
one another in a determinate
way represents that things are related to one another in the
same way.
Let us call this connection of its elements the structure of
the picture, and let us call
the possibility of this structure the pictorial form of the
picture.
you can propose an
elemental / determinate relation of representation between propositions – i.e.
between a painting – and its subject –
you will adopt this proposal if it suits your purpose
this proposal is
open to question – open to doubt – and uncertain –
and it should be
understood is that is not the final word on representation
representation – is
open to question – open to interpretation
the point being that
not all proposals of representation – will be – or need be –
elemental and
determinate –
what if the proposal
is that the picture – the relational representative proposal – depicts a
non-elemental – indeterminate relation?
does it cease to be
a picture?
as to this notion of ‘pictorial form’ – it is nothing other
than the representative proposal –
nothing other than the picture
2.151. Pictorial form is the possibility that things are
related to one another in the
same way as the elements of a picture.
‘pictorial form’ –
just is the representative proposal – that is the picture
an elemental analysis
is not essential to representation
representation is
open to question – open to doubt – and uncertain
2.1511. That is how a picture is attached to reality;
it reaches right out to it.
a representational proposal is put –
just what that representation amounts to is open to question
this ‘reaching out’ can only be the putting of the
representational proposal
the picture – the proposal of representation – is a
reality –
it is not something other than reality – it is reality
our reality is propositional
2.1512. It is laid against reality like a measure.
a proposition – is not laid against reality – it is reality –
propositions are related to propositions –
and relations between propositions – are proposed –
our reality is a reality of propositions and propositional
relations
2.15121. Only the end points of the graduating lines
actually touch the object that is to
be measured.
we can do without the quasi-mathematical and
quasi-geometrical imagery here
propositions are put in relation to propositions –
and any relation proposed – is open to question – open to
doubt – and is uncertain
2.1513. So a picture conceived in this way, also includes
the pictorial relationship,
which makes it into the picture.
the pictorial relationship is not ‘included in’ the picture
–
this ‘pictorial relationship’ – the relational /
representative proposal – is the picture
2.1514. The pictorial relationship consists of the
correlations of the picture's elements
with things.
the picture is the representative proposal –
the elemental correlation – is a secondary proposal
the elemental proposal – and the proposed elemental
correlation – is open to question – open to doubt – and uncertain
not all pictures / representations are proposed in terms of
an elemental analysis – or an elemental correlation
2.1515. The correlations are, as it were, the feelers of the
picture's elements, with
which the picture touches reality.
the ‘correlations’ are relational proposals – relational
propositions
the relational proposals – are ‘feelers’ – only in the sense
that they are open to question – open to doubt – and uncertain
we don’t ‘touch’ reality – we propose reality
2.16. If a fact is to be a picture, it must have something
in common with what it
depicts.
if a ‘fact’ – a proposal – is to be a picture – the fact
will be a representative proposal
what is common to the picture and what it represents – if
indeed there is a proposed commonality –
is open to question – open to doubt and uncertain
‘commonality’ – is open to question – open to doubt – and
uncertain
2.161. There must be something identical in a picture and
what it depicts, to enable
the one to be a picture after all.
if you consider abstract art – there is always a question of
just what it represents
identity doesn’t seem to be in the picture at all – or
necessary to it
and the more general issue is just what representation
amounts to –
yes you can propose identity – but does it hold in all
proposals of representation?
there is no ‘must’ here – no necessity – the matter is
better understood in terms of –
uncertainty
2.17. What a picture must have common with reality, in order
to be able to depict it –
correctly or incorrectly – in the way it does, is its
pictorial form.
‘pictorial form’ is nothing other than the proposal of
representation – that is to say –
the picture
once this is recognized this notion of ‘pictorial form’ –
will be seen to be unnecessary and irrelevant
2.171. A picture can depict any reality whose form it has.
A spatial picture can depict anything spatial, a coloured
one anything coloured, etc.
a picture / proposal
may depict a subject – a proposal (a reality) – whose propositional structure
it is proposed it has –
or it may not depict
that structure
a picture may
propose / depict a different structure altogether –
we see this i.e. in
abstract art – in theoretical science – and in philosophy
if the picture / proposal is described as spatial – then
what it represents will be described as spatial
if the picture / proposal is described as coloured – then
what it represents will be described as coloured –
what we have here are analytic definitions –
a spatial picture – depicts anything spatial – a coloured
picture – depicts anything coloured
analyticity is nothing more than propositional reassertion–
a spatial object – is a spatial object – a coloured object –
is a coloured object
reasserting a proposition has no logical value –
its only value is rhetorical
the issue is just what description to give the picture /
proposal –
and that is open – open to question – open to doubt – and is
– regardless of any decision on description – uncertain
2.172. A picture cannot however depict its pictorial form:
it displays it
the picture is a representative proposal –
pictorial form just is
the representative proposal – that is the picture
the proposal is the depiction – is the display
2.173. A picture represents its subject from a position
outside of it. (Its standpoint is
representational form). That is why a picture represents its
subject correctly or
incorrectly.
a picture is a representative proposal
and yes – it represents its subject / proposal from outside
of it –
a correct representation is a proposal of representation –
that is assented to – for whatever reason
an incorrect representation is a proposal of representation
– that is dissented from – for whatever reason
any proposal of assent or dissent – is open to question –
open to doubt – and uncertain
2.174. A picture cannot, however, place itself outside its
representational form.
what is called the ‘representational form’ here – just is
the relation of representation – that is the picture
and yes – a picture proposal – is not outside itself
2.18. What any picture, of whatever form, must have in
common with reality, in order
to be able to depict it – correctly or incorrectly – in any
way at all, is logical form, i.e.
the form of reality.
our reality is propositional
a picture is a proposal of representation
a picture – a proposal of representation – is a
reality
the form or structure of reality –
is open to question – open to doubt – and uncertain
2.181. A picture whose pictorial form is logical is called a
logical picture.
any form – that is – any proposed propositional structure –
is logical – if it is held open to question – open to doubt – and regarded as –
uncertain
2.182. Every picture is at the same time a logical
one. (On the other hand, not every
picture is, for example, a spatial one)
every proposition – every picture / proposition – described
as ‘spatial’ – or – given some other description – is – from a logical point of view –
open to question – open to doubt – and uncertain
2.19. Logical pictures can depict the world.
logical pictures are proposals – open to question – open to
doubt and uncertain –
any proposal can be described as logical picture –
and any proposal can be described as a depiction of the
world – of reality
2.2. A picture has logico-pictorial form in common with what
it depicts.
a logico-pictorial form – is a proposal of propositional
structure – open to question – open to doubt – and uncertain
what a picture represents is another proposal or set of
proposals
a picture can – but need not – have a common ‘logical
pictorial form’ – that is a common structure – to what it represents –
we need only consider i.e. –
abstract art – quantum physics – or various philosophical theories – to
see the point here
in any case just what representation amounts to – is open to
question – open to doubt – and uncertain
it is not a fixed concept
2.201. A picture depicts reality by representing a
possibility of existence and non-
existence of states of affairs.
the picture is the depiction –
a picture – a representational proposal – is reality
what is proposed – exists
what is not proposed – is non-existent –
we don’t have pictures of what doesn’t exist
2.202. A picture represents a possible situation in logical
space.
a picture does not represent a possible
situation in logical space
a picture – is a representative proposal –
a picture is a reality – is actual
the notion of ‘logical space’ here – is irrelevant –
it’s not in the picture
2.203. A picture contains the possibility of the situation
that it represents.
a picture is the situation proposed
what is proposed is a representation
2.21. A picture agrees with reality or it fails to agree; it
is correct or incorrect, true or
false.
a picture is a proposal – a representative proposal
reality is propositional – a picture / proposal is a reality
a proposal is true – if it is affirmed for whatever reason – false if it is denied –
for whatever reason
a representational proposal
– is true – if it is affirmed – false – if it is denied
any proposal of affirmation or denial – is like the proposal
– the picture – in question – open to question – open to doubt – and uncertain
2.22. What a picture represents it represents independently
of its truth or falsity, by
means of its pictorial form.
a picture – is a representative proposal
what a picture represents – and how it represents – is open
to question – open to doubt – and uncertain
a proposal of representation is true – if it is assented to
– false if it is dissented from
any proposal of assent or dissent is independent of the
proposal of representation
any proposal of assent or dissent – is open to question –
open to doubt – and is uncertain
a proposal put – exists – regardless of whether it is
affirmed or denied
2.221. What a picture represents is its sense.
the picture is a proposal – a proposition –
the picture is a representational proposal
the ‘sense’ of a proposition – is open to question – open to
doubt – and is uncertain
the sense of a picture – a representative proposal – is open
to question – open to doubt – and is uncertain
2.222. The agreement or disagreement of its sense with
reality constitutes its truth or
falsity.
the agreement or disagreement of its sense with reality –
is the question of the agreement or disagreement of the
sense of one proposal (the picture) – with the sense of another (what it
represents)
any proposed relation of agreement or disagreement between
proposals – is open to question – open to doubt – and is uncertain
truth and falsity – are the propositional actions of
affirmation and denial –
if it is proposed that that the picture / proposal
represents a reality (another proposal) –
and this is agreed to – the proposed relation will be deemed
true
if it is proposed that the picture / proposal represents a
reality (another proposal) – and this is denied the proposed relation will be
deemed false –
any propositional action of agreement or disagreement – is
open to question – open to doubt and uncertain
2.223. In order to tell whether a picture is true or false
we must compare it with
reality.
the relation between a picture and what it represents –
is open to question – open to doubt – and uncertain
any comparison – is open to question – open to doubt – and
uncertain
whether the picture is true or false –
is the question of
whether a proposed relation i.e. agreement – is affirmed – for whatever
reason – or denied – for whatever reason –
any proposal of affirmation – or any proposal of denial – is
open to question – open to doubt – and is uncertain –
it should be noted too – that just what ‘agreement’ amounts
to – and just what ‘disagreement’ amounts to – is open to question – open to
doubt and is uncertain
2.224. It is impossible to tell from the picture alone
whether it is true or false.
yes –
whether a picture is true or false – depends on whether the
representative proposal that has been put – is affirmed – or denied
2.225. There are no pictures that are true a priori.
a picture is a proposal – a representative proposal
a proposal is open to question – open to doubt – and
uncertain
if by ‘true a priori’ – is meant that a proposal – a proposition is beyond question – beyond doubt
– and certain
logically speaking – there are no a ‘true a priori’
propositions –
there are no pictures that are true a priori
the ‘true a priori’ tag – is a mark of logical ignorance .
Tractatus 3
3. A logical picture of facts is a thought
a picture is a proposal – a representational proposal
a picture of facts – will be a proposal representing facts
as to logical –
the picture / proposal – will be logical –
if it is held open to question – open to doubt – and
regarded as uncertain
now do we call this ‘logical picture of facts’ – this
proposal that represents facts – a ‘thought’?
this strikes me as a definition from Wittgenstein –
as it were a starting point from which he will argue
there is nothing against this – it is a proposal –
and a proposal – open to question – open to doubt – and
uncertain
just why he regards a picture of facts – a thought – and
what exactly this amounts to –
he is yet to explained
3.01. The totality of true thoughts is a picture of the
world.
any representative proposal / any propositional picture –
can be described as a picture of the world
a proposal is true – if assented to
logically speaking – a thought – is a proposal –
a proposal open to question – open to doubt – and uncertain
a ‘totality’ – is definitive –
propositional action is on-going – is indefinite
3.02. A thought contains the possibility of the situation of
which it is the thought.
What is thinkable is possible too.
a proposal can be described as a ‘thought’
a proposal can be described a ‘situation’
here we have a proposal described as a ‘thought’ – and
further described as a ‘situation’ –
this proposal / thought – is – the proposal /
situation –
a thought does not contain the possibility of which
it is a thought –
‘containing the possibility of which it is a thought’ – is
metaphysical mumbo-jumbo
a proposal is an actuality –
what is thinkable – is what is proposed –
any proposal – any proposition –
is open to question – open to doubt – is uncertain
3.03. Thought can never be of anything illogical, since, if
it were, we should have to
think illogically.
a proposal – a thought – that is not held open to question –
not held open to doubt –
and regarded as certain – is illogical
uncritical thinking is illogical
we can – we do – think and act – illogically
3.031. It used to be said that God could create anything
except what would be contrary to the laws of logic. – The truth is that we
could not say what an 'illogical' world would look like.
our proposals – our propositions – are the world
an ‘illogical’ world is the world of uncritical and
pretentious propositions
we all know what that looks like
3.032. It is impossible to represent in language anything
that 'contradicts logic' as it is
in geometry to represent by its co-ordinates a figure that
contradicts the laws of space,
or to give the co-ordinates of a point that does not exist.
language as proposal – contradicts logic – if it is
uncritical and pretentious
the laws of space – as with any set of proposals are open to
question – open to doubt – and uncertain
a point that does not exist – is a proposal that is not
proposed –
to pretend such a proposal – is to corrupt
propositional logic –
3.0321.Though a state of affairs that would contravene the
laws of physics can be
represented by us spatially, one that would contravene the
laws of geometry cannot.
geometry is a rule governed propositional game
3.04. If a thought were correct a priori, it would be a
thought whose possibility
ensured its truth.
so called a priori truth – in so far as it is not open to
question – not open to doubt – and is regarded as certain – is illogical
such a proposal – is a corruption of the proposal – of
propositional logic
such a proposal is better termed a prejudice
3.05. A priori knowledge that a thought was true would be
possible only if its truth
were recognizable from the thought itself (without anything
to compare it with).
a proposition itself – is neither true nor false
the truth or falsity of any claim to knowledge – of any
proposal – of any thought –
is a matter of assent or dissent –
and proposals of assent and proposals of dissent – are open
to question – open to doubt – and uncertain
whether or not there is anything to compare a proposal to –
to compare a thought to – is logically irrelevant –
what is logically relevant – is that a proposal is
recognized as being open to question –
open to doubt – and uncertain
if by ‘a priori knowledge’ – is meant – proposals /
propositions – not open to question – not open to doubt – and certain –
so called ‘a priori knowledge’ is illogical
the better term here is ‘a priori prejudice’
3.1. In a proposition a thought finds an expression that can
be perceived by the
senses.
a proposal made public – i.e. spoken or written – can be
perceived by the senses –
a proposal – not made public – a proposal / thought not expressed – will not
be perceived by the senses
3.11. We use the perceptible sign of the proposition (spoken
or written, etc.) as a
projection of a possible situation.
The method of projection is to think of the sense of the
proposition.
the perceptible sign of the proposition – is the
proposition –
a proposal is an actual situation – not a possible
situation
the ‘method of projection’ – is proposal
the sense of the proposition – is open to question – open to
doubt – and is uncertain
3.12. I call the sign with which we express a thought a propositional
sign. – And a
proposition is a propositional sign in its projective
relation to the world.
the propositional sign is the proposal – is the proposition
the world is propositional
a proposition’s ‘projective relation to the world’ – is its
proposed relation to other propositions
3.13. A proposition includes all that the projection
includes, but not what is projected.
Therefore, though what is projected is not itself included,
its possibility is.
A proposition therefore, does not actually contain its
sense, but does contain the
possibility of expressing it.
('The content of the proposition' means the contents of a
proposition that has sense).
A proposition contains the form, but not the content, of its
sense.
the proposition is what is proposed
there is no ‘projection’ – just what is proposed –-
a proposal – a proposition is actual – not possible
what is ‘possible’ – is pre-propositional
the sense of a
proposition – logically speaking – is a separate proposal – to the subject
proposition – a proposal put in relation to the subject proposition –
the content of a proposition – is what is proposed –
and what is proposed is open to question – open to doubt –
and uncertain
the form of a proposition – is a proposed structure of the
proposition –
a proposal – open to question – open to doubt – and
uncertain
3.14. What constitutes a propositional sign is that in it
its elements (the words) stand
in a determinate relation to one another.
A propositional sign is a fact.
what constitutes a propositional sign – is open to question
– open to doubt and uncertain
this elemental / determinist characterization is one view –
and to adopt this view – may have some pragmatic value –
some pragmatic use – in a particular context
however it is not the only view possible
i.e. – one may think of – and use – the proposition as it
where as a whole – without any elemental analysis –
and this I would suggest is how propositions by and large
are regarded in common everyday usage
in a word game – where the idea is to construct propositions
– out of a limited number of words – the relation of the words may well be
regarded as indeterminate – even after a proposition is constructed –
and when we are stuck for a word – and try different words
to finish a sentence – do we regard the exercise of ‘constructing a
proposition’ – to be determinate?
isn’t it rather that the resulting proposition is an outcome
of indeterminacy? –
and where the proposition’s ‘construction’ if you want to
call it that – is seen to be –
uncertain?
any so called ‘determinate’ view of the proposition – of
language – will only get a start in a defined propositional context
and even there – questions can always be raised – doubts can
emerge – uncertainties can be explored
a propositional sign can be described as a fact – can be
regarded as a fact
3.141. A proposition is not a blend of words. – (Just as a
theme in music is not a blend
of notes).
a proposition could be described – as a blend of words –
just as a theme in music could be described as a blend of notes
the proposition – the nature of the proposition – is open –
open to question – open to doubt – and open to
interpretation .
3.142. Only facts can express a sense, a set of names
cannot.
facts are proposals –
sense is a proposal – open to question – open to doubt – and
uncertain
names are proposals –
names can and do express sense –
the sense of a name – is open to question – open to doubt –
and uncertain
3.143. Although a propositional sign is a fact, this is
obstructed by the usual form of
expression in writing or print.
For in a printed proposition, for example, no essential
difference is apparent between
a propositional sign and a word.
(That is what made for Frege to call a proposition a
composite name).
a fact is a proposal –
any form of expression is a proposal –
there is no essential difference between a propositional
sign and a word
the propositional sign is a proposal – a word is a proposal
–
a proposal is open to question – open to doubt – and
uncertain
3.1431. The essence of a propositional sign is very clearly
seen if we imagine one
composed of spatial objects (such as tables, chairs, and
books) instead of written signs
Then the spatial arrangement of these things will express
the sense of a proposition
imagining spatial objects – is proposing objects – and
proposing a relation between them
a relation – described as – proposed as – ‘spatial’
whether written or not we are dealing with proposals –
propositions –
the sense of any proposal / proposition – is open to
question – open to doubt – and uncertain
3.1432. Instead of, ‘The complex sign "aRb"
says a stands in relation to b in the relation
R', we ought to put, 'That "a"
stands to "b" in a certain relation says that aRb'.
we have the proposal "aRb" –
this proposal – as with any proposal – is open to
interpretation –
the propositional analysis – ‘a stands in relation to
b in the relation R' – is one interpretative proposal of "aRb"
'That "a" stands to "b"
in a certain relation says that aRb' – is another
the difference between – ‘a stands in relation to b’
and ‘That a stands to b in a certain relation’ – if
anything – comes down to a difference of emphasis or a difference of
presentation
the difference is rhetorical – not logical
3.144. Situations can be described but not given names.
(Names are like points; propositions like arrows – they have
sense.)
a propositional situation can be given a name –
propositional situations are named
take for example the propositional situations of the weather
patterns – el nino and la nina
names are proposals – and proposals can be variously
interpreted and described
the sense of any proposal – of any proposition – is open to
question
3.2. In a proposition a thought can be expressed in such a
way that elements of the
propositional sign correspond to the objects of thought.
a thought is a proposal – is a proposition
a proposition can be given an elemental analysis –
and it can be proposed that the elements of one proposition
– of one propositional sign correspond to the elements in another
these propositions – the relational proposition – and the
subject propositions – are open to question – open to doubt – and are uncertain
3.201. I call such elements 'simple signs', and such a
proposition 'completely
analysed'.
you can call your elements ‘simple signs’ – and you
can call such a proposal – ‘completely analysed’ – if it suits your
purposes
logically speaking though – no proposition is completely
analysed
a proposition is open – open to question – open to doubt –
open to analysis – and uncertain
a so called ‘completely analysed’ proposition – is a
logically dead proposition
you can – for whatever reason – decide to stop the logical
actions of question and doubt –
at best this is a pragmatic decision – the point of which is
to proceed – to get on with it
at worst it is an ignorant and pretentious decision – that
is a turning away from critical analysis – a turning away from logic
any propositional decision is open to question – to doubt –
and is uncertain
3.202. The simple signs employed in propositions are called
names.
a proposal can be analysed – can be described in terms of
simple signs – and you can call these simple signs names
and this analytical proposal of simple signs as names – is
logically speaking – open to question – open to doubt – and is uncertain
3.203. A name means an object. The object is its meaning. ('A'
is the same sign as 'A'.)
a name proposal – is an identifying proposal –
the proposal that ‘a name means an object’ – is to propose a
relation between a name proposal – and an object proposal
it is to say that the name proposal identifies the object
proposal –
the relational proposal – the name proposal – and the object
proposal – are open to question – open to doubt – and uncertain
‘the object is its meaning’ –
is to propose that the object proposal – is identified by
the name proposal –
this may or may not be the case – but it is the proposal
“A’ is the same sign as ‘A” – is to posit ‘A’
as ‘A’ – which is pointless
repetition does not elucidate anything –
to suggest that it does – is just pretentious rhetoric
3.21. The configuration of objects in a situation
corresponds to the configuration of
simple signs in the propositional sign.
the configuration of objects is a proposal – a propositional
construction – and is the propositional situation
that there is a correspondence between this proposal – and
the proposal of a configuration of simple signs – is a proposal – a relational
proposal
these proposals are open to question – open to doubt – and
uncertain
3.22. In a proposition a name is the representative of an
object.
a name in a proposition is a proposal –
an object is a proposal
that a name proposal represents an object proposal – is a
proposal –
a proposal open to question – open to doubt and uncertain
3.221. Objects can only be named. Signs are their
representatives. I can only speak
about them: I cannot put them into words.
Propositions can only say how things are,
not what they are.
we propose in relation to proposals –
object proposals – can be named – and they can be described
–
it can be proposed that propositions / signs represent
object proposals –
speaking about object proposals – is – proposing in relation
to them – is – putting them into words
‘things’ are proposals –
I can propose how things / propositions are – and I can
propose – what they are
and any proposal put – is open to question – open to doubt –
and is uncertain
3.23. The requirement that simple signs be possible is the
requirement that sense be
determinate.
sense – the sense of a proposition – from a logical point of
view – is open to question – open to doubt – and uncertain
logically speaking – sense is indeterminate
simple signs – as with any other propositional construct –
are open to question – open to doubt and uncertain
3.24. A proposition about a complex stands in an internal
relation to a proposition
about a constituent of the complex.
A complex can be given by its description, which will be
right or wrong. A
proposition that mentions a complex will not be non-sensical
if the complex does not
exist, but simply false.
When a propositional element signifies a complex, this can
be seen from an
indeterminateness in the propositions in which it occurs. In
such cases we know that
the proposition leaves something undetermined. (In fact the
notation for generality
contains a prototype.)
The contraction of a symbol for a complex into a simple
symbol can be expressed in a
definition.
a proposition about
a complex – and a proposition about a constituent of the complex – are two
different and separate propositions –
to say that one is
internal to the other – that one is ‘in’ the other – is to confuse them
a relation between
propositions is a proposal – separate to the two propositions in question –
the relation is an external proposal
a propositional
description – is not right or wrong – it is open to question – open to doubt –
and is uncertain –
you can proceed with
a description – or not – in either case your decision is logically uncertain –
and any reasons you
have for proceeding or not – are open to question
a proposition – a
proposal concerning a non-existent propositional complex – is a ridiculous
notion
a proposition exists
if it is proposed
if it is not
proposed – it’s not there – it doesn’t exist
an element – is an
element of a complex – by definition
and an element
signifying a complex – will leave unsaid – what is left of the complex
and yes proposing a
symbol for a complex is really a matter of definition
even so – such a
definition is open to question
3.25. A proposition has one and only one complete analysis.
the idea that a proposal – a proposition has one and only
one complete analysis – is illogical – and pretentious
regardless of any proposed analysis – a proposition is
logically speaking – open –
open to question –
open to doubt – and uncertain –
3.251. What a proposition expresses it expresses in a
determinate manner, which can
be set out clearly: a proposition is articulate.
what is proposed is open to question –
any determination of what is proposed – is a proposal –
a proposal – open to question – open to doubt and uncertain
a clear presentation – is open to question
a proposition is articulate
3.26. A name cannot be dissected any further by means of a
definition: it is a primitive sign.
a name is a sign –
is a proposal
a proposal / name –
is open to question – open to doubt – and uncertain –
a definition – is a
proposal – open to question – open to doubt – and uncertain
if by ‘primitive sign’ is meant a proposal – that is not
open to question – open to doubt – and certain
there is no primitive sign
3.261. Every sign that has a definition signifies via
the signs that serve to define it;
and the definitions point the way.
Two signs cannot signify in the same manner if one is
primitive and the other is
defined by means of primitive signs. Names cannot be
anatomized by means of
definitions.
(Nor can any sign that has a meaning independently and on
its own.)
if a sign – (a proposal) – is defined – in terms of other
proposals (signs) – it is transformed by the signs (proposals) that define it
what way a proposed definitions points – is open to question
a sign that is not propositionally transformed – will be different
to one that is
what one sign signifies relative to another is open to
question –
there are no ‘primitive’ signs
any sign is open to question – open to doubt – and uncertain
a name is a proposal – open to question – open to doubt –
and uncertain
a definition is a proposal – open to question – open to
doubt – and uncertain
a name can be defined –
a defining proposal can be put to a name –
i.e. – this name means this in this context
signs are given meaning –
that is to say meaning is proposed
no sign has a meaning ‘independently and on its own’
any proposed meaning of any sign is open to question – open
to doubt – and is uncertain
3.262. What signs fail to express, their application shows.
What signs slur over, their
application says clearly.
what a sign expresses is open to question – open to doubt
and uncertain
the application of a sign is open to question – open to
doubt and uncertain
3.263. The meanings of primitive signs can be explained by
means of elucidations.
Elucidations are propositions that contain primitive signs.
So they can only be
understood if the meanings of those signs are already known.
so called ‘primitive signs’ are proposals – open to question
– open to doubt – and uncertain
any elucidation of a proposal / sign – is propositional
an elucidating proposition refers to the proposal / sign –
to be elucidated
the meaning of the sign – before and after any propositional
elucidation – is open to question – open to doubt and uncertain
what is known – is what is proposed –
what is proposed – is open to question – open to doubt and
uncertain
3.3. Only propositions have sense; only in the nexus of a
proposition does a name
have meaning.
there is nothing other than proposal
sense is a proposal – a name is a proposal – meaning is a
proposal
a name can have meaning as a stand alone proposition –
or ‘in the nexus of a proposition’ –
that is a sign in a proposal
any proposal – is open to question – open to doubt – and is
uncertain
3.31. I call any part of the proposition that characterizes
its sense an expression (a
symbol).
(A proposition is itself an expression.)
Everything essential to their sense that propositions can
have in common with one
another is an expression.
An expression is the mark of form and content.
any characterization of sense – is a proposal –
a proposal – put in relation to the proposition in
question
‘a proposition in itself’ – is a proposal –
any proposal of sense – is open to question
there is nothing ‘essential’ any proposal of sense
what propositions have in common with one another is that
they are open to question – open to doubt – and uncertain
an expression is a proposal – if it is a mark of form
(structure) and content – it is proposed as a mark of form (structure)
and content
and as such – open to question – open to doubt – and
uncertain
3.311. An expression presupposes the forms of all the
propositions in which it can
occur. It is the common characteristic mark of a class of
propositions.
an expression – a proposal – occurs where it does
occur – where it is proposed
an expression – a proposal – does not presuppose
where it can occur
an expression / proposal – is not the common
characteristic mark of a class of propositions –
unless it is proposed as such
3.312. It is therefore presented by means of the general
form of the propositions that
it characterizes.
In fact, in this form the expression will be constant
and everything else variable.
‘It is therefore presented by means of the general form of
the propositions that
it characterizes.’ –
the form of a proposition – is its proposed propositional
structure –
as to ‘general form’ –
a proposition is a proposal – and any proposal of a
‘general structure’ – a structure common to all propositions – is open to
question – open to doubt – and uncertain
an expression / proposal – put as a characterization of
other propositions – is a proposal – open to question – open to doubt – and
uncertain
‘In fact, in this form the expression will be constant
and everything else variable.’
a proposed characterization – will be ‘constant’ – so long
as the proposal is adhered to
as to ‘everything else is variable’ –
presumably that means that the class of propositions – that
this proposal of characterization is put in relation to – is variable
what is being proposed here – is a propositional game
3.313. Thus an expression is presented by means of a
variable whose values are the
propositions that contain the expression.
(in the limiting case the variable becomes a constant, the
expression becomes a
proposition.)
I call such a variable a 'propositional variable'.
it is not that an expression becomes a proposition –
when a variable becomes a constant
the expression is a proposition – to begin with –
however it is played
what you have here – is two different – propositional
games
game one – the expression / proposal / proposition – as a
variable
game two – the expression / proposal / proposition – as a
constant
3.314. An expression has meaning only in a proposition. All
variables can be
constructed as propositional variables.
(Even variable names)
an expression is a proposal – is a proposition
–
we can simply drop this notion of ‘expression’ – it is a
logical redundancy
a variable is a propositional game –
variable names – is a variable game
3.315. If we turn a constituent of a proposition into a
variable, there is a class of
propositions all of which are values of the resulting
variable proposition. In general,
this class too will be dependent on the meaning that our
arbitrary conventions have
given to parts of the original proposition. But if all the
signs in it that have arbitrarily
determined meanings are turned into variables, we shall
still get a class of this kind.
This one, however, is not dependent on any convention, but
solely on the nature of the
proposition. It corresponds to a logical form – a logical
prototype.
there are two modes of propositional activity –
the critical or logical mode – and the game mode
in the critical mode – propositions are put to question –
put to doubt – and their uncertainty – explored –
in the game mode – propositions and propositional structures
are rule governed
if you play the game – you play in accordance with the rules
proposed –
if you don’t play in accordance with the rules – you don’t
play the game
a propositional game – as played is not open to question –
open to doubt – or uncertain
the game is not questioned – it is played
Wittgenstein begins by saying –
‘If we turn a constituent of a proposition into a variable,
there is a class of propositions all of which are values of the resulting
variable proposition.’
here he is proposing a propositional game – the
variable game
the first move in this game is to turn a ‘constituent’ of a
proposition – into a variable –
Wittgenstein is using the definition of the variable
commonly used in formal logic –
the ‘variable’ – as ‘the unspecified member of a class or
set’
(in propositional logic the letters p – q –
and r – are conventionally used as propositional variables – in
predicate logic – the letters x – y – an z – are used as
variables)
and a rule of Wittgenstein’s ‘variable game’ – is that there
is a class of propositions all of which are values of the resulting variable
proposition
‘In general, this class too will be dependent on the meaning
that our arbitrary conventions have given to parts of the original proposition.’
‘our arbitrary conventions’ – whatever they may be – will be
operating rules of this variable game
‘But if all the signs in it that have arbitrarily determined
meanings are turned into variables, we shall still get a class of this kind’ –
this is to say that if all the signs in the game are turned
into variables – we still have this variable game
‘This one, however, is not dependent on any convention, but
solely on the nature of the proposition. It corresponds to a logical form – a logical
prototype.’
‘a logical form’ – is
a proposed propositional
structure –
there are no ‘logical prototypes’ – there are different
logical forms – that is different propositional / game structures – and there
are different propositional games –
in practise propositional games – if they are generally
accepted propositional practises – are conventions –
rule governed conventions
3.316. What values a propositional variable may take is
something that is stipulated.
The stipulation of values is the variable.
a propositional game – is a rule governed propositional
action
‘What values a propositional variable may take is something
that is stipulated.’
the values – are the rules adopted for the game
‘the stipulation of values is the variable’ – is the
variable game
3.317. To stipulate values for a propositional variable is to
give the propositions
whose common characteristic the variable is.
The stipulation is the description of those propositions.
The stipulation will therefore be concerned only with
symbols, not with their
meaning.
And the only thing essential to the stipulation is that
it is merely a description of
symbols and states nothing about what is signified.
How the description of the proposition is produced is not
essential
to stipulate values for a propositional variable – is to give the rule for the variable game
the rule of a propositional game – determines the
propositions to be played
the stipulation is the rule of the game –
the rule of the game does not ‘describe’ the game
propositions – it determines the game propositions – and the possibilities of
their play
the rule of the game determines the play of the symbols –
their ‘meaning’ – in the game – is not relevant
the rule of the game defines the symbols and determines the play of the symbols –
a game does not signify – a game is played
if the proposition is a game proposition – that is to say –
rule governed –
‘description’ of it – is effectively irrelevant to the game
–
what is essential to the game – is that the proposition –
the play of the proposition – is rule governed
if it is not rule governed – it is not a game proposition
3.318. Like Frege and Russell I construe a proposition as a
function of the expressions
contained in it.
the proposition is not a function of the expressions
contained in it –
a proposition is a proposal –
we can regard the proposition critically – as open to
question – open to doubt – and uncertain
or we can regard the proposition as rule governed – as a
token in a propositional game
a functional
analysis of the proposition – transform the proposition into a game
that is – a
rule-governed propositional play
like Frege and
Russell – Wittgenstein is a game designer and a game player
you can design
whatever propositional game you like – and play it to your heart’s content
on the other hand –
‘logic’ – properly understood – is the critical activity – of question – of
doubt – and the exploration of uncertainty
3.32. A sign is what can be perceived of a symbol.
a sign is / can be – what is perceived of a symbol – if it
is so proposed
3.321. So the one and the same sign (written or spoken,
etc.) can be common to two
different symbols – in which case they will signify in
different ways.
two different symbols will signify differently –
and this will be the case whether or not the one and the
same sign is said to be common to two different symbols –
if the sign is – prime facie –‘common’ to different symbols
– it will – in different symbols – have a different significance –
it will – as it were – be transformed by the symbol
it will in different symbols – signify differently –
effectively – despite appearances – it will be a different
sign – from one symbol to another
the symbol – relative to the sign is best understood as the
propositional context of the sign –
we have the one sign functioning in different propositional
contexts
in different contexts signs will have different
signification
and once this is understood – in formal language – a
difference in notation should be indicated – should be signed
3.322. Our use of the same sign to signify two different
objects can never indicate a
common characteristic of the two, if we use it with two
different modes of
signification. For the sign, of course is arbitrary.
So we could choose two different
signs instead, and then what would be left in common on the
signifying side?
the use of the one sign / proposal – to signify different
object / proposals – doesn’t work –
it is either logical laziness – or the two object / proposals – are not
different –
the mode of signification is how the sign is expressed – and
how the sign is expressed – just is the sign expressed
different modes – different signs
and in formal propositional language – in formal logical
games – we should use different sign / proposals to indicate different object /
proposals
what would be left in common on the signifying side?
signs – open to question – open to doubt – and uncertain
3.323. In every day language it very frequently happens that
the same word has
different modes of signification – and so belongs to
different symbols – or that two
words that have different modes of signification are
employed in propositions in what
is superficially the same way.
Thus the word 'is' figures as the copula, as a sign for
identity, and as an expression for
existence; 'exist' figures as an intransitive verb like
'go', and 'identical' as an adjective;
we speak of something, but also of something's
happening.
(In the proposition, 'Green is green' – where the first word
is the proper name of a
person and the last an adjective – these words do not merely
have different meanings:
they are different symbols).
where the same word has different modes of signification –
we understand the difference if we understand the different propositional
contexts / symbols in which the word is being used –
different symbols are different propositional contexts –
and where two words that have different modes of
signification are employed in propositions in what is superficially the same
way –
you either understand the different propositional contexts
of use – or you find different words
outside of a rule-governed / game propositional context –
propositional use is never clear-cut or uncontroversial –
all non-game propositional use is open to question – open to
doubt – and uncertain
we live and in and deal with propositional uncertainty
‘(In the proposition, 'Green is green' – where the first
word is the proper name of a
person and the last an adjective – these words do not merely
have different meanings:
they are different symbols).’
these words in standard usage – have different meanings and
can be analysed in terms of different symbols
a symbol represents a propositional context – different
symbols – different propositional contexts
3.324. In this way the most fundamental confusions are
easily produced (the whole of
philosophy is full of them).
if you understand that a proposition – outside of a rule
governed / game context – is open to question – open to doubt and uncertain –
there is no room for confusion –
what we face and what we deal with is uncertainty
3.325. In order to avoid such errors we must make use of a
sign-language that
excludes them by not using the same sign for different
symbols and by not using in a
superficially similar way signs that have different modes of
signification: that is to say
a sign-language that is governed by logical grammar –
by logical syntax.
(The conceptual notation of Frege and Russell is such a
language, though it is true, it
fails to exclude all mistakes.)
the use of a sign-language that excludes the use of the same
sign for different symbols – makes obvious sense –
a sign-language that doesn’t do this – is a failure
a sign-language
governed by ‘logical syntax’ – is rule-governed – a rule governed language – a game language
‘logical syntax’ –
here – is a game language – and its accompanied set of rules
strictly speaking
there are no mistakes in a game – or in a game language
if the rules are
inadequate or faulty – there is no game to begin with
also – one game may
be more comprehensive – more wide-ranging than another –
and if so – this
will be determined by the rules –
and here we will be
dealing with different games
the conceptual
notation of Frege and Russell – is a different
game – to that proposed by Wittgenstein
3.326. In order to recognize a symbol with its sign we must
observe how it is used
with a sense.
the use of a symbol with its sign – in a formal language is
rule governed
which is to say – has nothing to do with questions of sense
3.327. A sign does not determine a logical form unless it is
taken together with its
logico-syntactical employment.
a sign is a representative of logical form – of a proposed
logical structure
its logico-syntactical employment is the rule governed
application of structure – in a propositional game
3.328. If a sign is useless, it is meaningless. That
is the point of Occam's maxim.
(If everything behaves as if a sign had meaning, then it
does have meaning.)
if a sign has no use – no rule governed application – no
game application – yes – it is useless –
this has nothing to do with Occam or his razor
3.33. In logical syntax the meaning of a sign should never
play a role. It must be
possible to establish a logical syntax without mentioning
the meaning of a sign: only
the description of expressions may be presupposed.
in logical syntax – signs are rule governed
in rule governed propositional games – meaning is not in the
picture
the point of a rule governed propositional game – is its play
the establishment of logical syntax is the establishment of
a game language –
what it presupposes is – the rules of the game
propositional rules are the instruments of propositional
play –
if you want to play – you set up the rules
3.331. From this observation we turn to Russell's 'theory of
types'. It can be seen that
Russell must be wrong, because he had to mention the meaning
of signs when
establishing the rules for them.
Russell confused propositional logic – with propositional
game playing
3.332. No proposition can make a statement about itself,
because a propositional sign
cannot be contained in itself.
propositions are proposals – but propositions do no not
propose –
propositions are proposed by human beings
a proposition about a proposition – is a separate
proposition –
a separate proposal –
the theory of types is a proposal of propositional relation
– a proposal of propositional structure –
as with any proposal – it is open to question – open to
doubt – and is uncertain –
and as with any proposal – its value is a question of its
utility –
and utility is a matter – open to question
3.333 The reason why a function cannot be its own argument
is that the sign for a function already contains the prototype of its argument,
and it cannot contain itself.
For let us suppose that the function F(fx) could be
its own argument: in that case there would be a proposition ‘F(F(fx))’,
in which the outer function F and the inner function F must have different
meanings, since the inner one has the form f(fx)
and the outer has the form y(f(fx)). Only
the letter ‘F’ is common to the two functions, but the letter by itself
signifies nothing.
This immediately becomes clear if instead of ‘F(Fu)’
we write ‘($f): F(fu). fu =
Fu’.
That disposes of Russell’s paradox.
a function is a propositional game –
the rule of the game is that for any given first term –
there is exactly one second term
the constituent(s) of the first term are called the
argument(s) of the function – and of the second term the value of the function
the function game – can be analysed into the components –
‘argument’ and ‘value’ –
seen this way the ‘argument’ is a component of the function
– not the function itself –
and the sign for the function is not a component of itself
it makes no sense to speak of a proposition – or a
propositional game – or for that matter – anything else – containing itself
a propositional game – is a rule governed propositional play
–
it doesn’t ‘contain’ anything – it has no ‘self’
the so called ‘outer function F’ and ‘the inner
function F’ are either two different functions – or the one function reasserted
–
if they are different functions – then they should be
distinguished in the notation i.e. F and F¢
if they are one in the same – then the reassertion is
logically irrelevant –
and the notation F(F(fx)) – is a confused mess
3.334. The rules of logical syntax must go without saying,
once we know how each
individual sign signifies.
how we know how each individual sign signifies – is rule
governed –
and the rules must be stated – if there is to be a game
3.34. A proposition possesses essential and accidental
features.
Accidental features are those that result from the
particular way in which the
propositional sign is produced. Essential features are those
without which the
proposition could not express its sense.
a proposition is a proposal – open to question – open to
doubt – and uncertain
any proposed feature of a proposition – is open to question
–
the sense of a proposition – is open to question – open to
doubt – and is uncertain
3.341. So what is essential in a proposition is what all
propositions that can express
the same sense have in common.
And similarly, in general, what is essential in a symbol is
what all symbols that can
serve the same purpose have in common
the sense of a proposition – is open to question – open to doubt
– and is uncertain
what propositions have in common – is logical uncertainty
in a game context – what is ‘essential’ in a symbol – is
that it is rule-governed
3.3411. So one could say that the real name of an object was
what all symbols that
signified it have in common. Thus, one by one, all kinds of
composition would prove
to be unessential to a name.
the ‘real name’ of an object / proposition – is whatever
name it is given
there is nothing essential to a name
3.342. Although there is something arbitrary in our
notations, this much is not
arbitrary – that when we have determined one thing
arbitrarily, something else is
necessarily the case. (This derives from the essence
of notation.)
any proposal – or any aspect of any proposal – is open to
question – open to doubt – and is uncertain
there are entrenched propositional practises – and
rule-governed propositional games –
necessity is a propositional game – a rule governed game
notation – has no essence
3.3421. A particular mode of signifying may be unimportant
but it is always important that it is a possible mode of signifying. And
it is generally so in philosophy: again and again the individual case turns out
to be unimportant, but the possibility of each case discloses something about the
essence of the world.
any mode of signifying is valid –
what is important – or unimportant – is a question of propositional
/ philosophical fashion
in the absence of proposal – our world is unknown
any proposal put – makes known –
our world is propositional –
‘the world’ – is what is proposed –
what is proposed – is open to question – open to doubt – and
is uncertain –
the world has no essence
3.343. Definitions are rules for translating from one
language into another. Any
correct sign-language must be translatable into any other in
accordance with such
rules; it is this they all have in common.
translation is a definition game – a rule governed
propositional game
that is to say – to achieve a translation – you follow the
rules proposed –
if you don’t follow the rules – you don’t translate
and yes what different sign games have in common is these
translation rules
you can of course engage in the logical activity of question
– of doubt – and of exploring the uncertainty of the proposed rules of
translation
doing this though – is not playing the game –
it is not translating
3.344. What signifies in a symbol is what is common to all
the symbols that the rules of logical syntax allow us to substitute for it.
yes – the symbol represents a rule governed propositional
game –
if the game is a ‘logical syntax game ‘ then the game is
governed by the rules of logical syntax
the rules of logical syntax determine symbolic substitution
you can question the rules of logical syntax – but this is a
logical activity –
it is not playing the substitution game
3.3441. For instance, we can express what is common to all
notations for truth
functions in the following way: they have in common that,
for example, the notation
that uses '~p' ('not p') and 'pvq' ('p
or q') can be substitutes for any of them.
(This serves to characterize the way in which something
general can be disclosed by
the possibility of a specific notion.)
truth functional analysis is a rule governed sign-game
– a rule governed propositional game
there are substitution rules in this game
if you play such a rule governed game – you play according
to the rules –
if you don’t follow the rules – you don’t play the
game –
‘something general can be disclosed by the possibility of a specific notation’ –
the ‘something general’ that is disclosed – is the game –
the rule governed propositional game
3.3442. Nor does analysis resolve the sign for a complex in
an arbitrary way, so that it
would have a different resolution every time that it was
incorporated in a different
proposition.
analysis here is rule governed and is integral to the game –
as played
3.4. A proposition determines a place in logical space. The
existence of this logical
space is guaranteed by the mere existence of the
constituents – by the existence of the
proposition with sense.
we can talk about propositions – without the notion of
logical space
I think that the notion of logical space – is an unnecessary
underpinning of propositional action –
however – if it has its use – it has its use –
but the use is rhetorical – not logical
3.41 The propositional sign with logical co-ordinates – that
is the logical place.
the propositional sign with logical co-ordinates – is a
proposal
3.411. In geometry and logic alike a place is a possibility;
something can exist in it.
a place is a proposal
3.42. A proposition can determine only one place in logical
space: nevertheless the
whole of logical space must already be given by it.
(Otherwise negation, logical sum, logical product, etc.,
would introduce more and
more elements – in co-ordination.)
(The logical scaffolding surrounding a picture determines
logical space. The force of a proposition reaches through logical space.)
this ‘whole of logical space’ idea – just strikes me as
mystical –
as little more than rhetorical packaging
what is given by a proposal – by a proposition – is open to
question – open to doubt and uncertain
negation – logical sum – logical product – are rule governed
propositional actions –
propositional games
propositions exist and function in proposed propositional
contexts – structures – and in propositional games
3.5. A propositional sign, applied and thought out, is a
thought.
a propositional sign – applied – is a proposal – applied
the proposal – is open to question – open to interpretation
– open to description –
its application – is open to question – open to doubt – and
uncertain
a proposal can be described as a thought
Tractatus 4
4. A thought is a proposition with sense.
a proposition is a proposal – open to question – open to
doubt – and uncertain
a proposition can be described as a thought – as a thought
with sense
this description – this
proposal – is open to question – open to doubt – and uncertain
different descriptions of propositions – suit different
purposes
4.001. The totality of propositions is language.
language is proposal
4.002. Man possesses the ability to construct languages
capable of expressing every
sense, without having any idea how each word has meaning or
what its meaning is –
just as people speak without knowing how the individual
sounds are produced.
Everyday language is a part of the human organism and is no
less complicated than it.
It is not humanly possible to gather immediately from it
what the logic of language is.
Language disguises thought. So much so, that from the
outward form of the clothing it
is impossible to infer the form of the thought beneath it;
because the outward form of
the clothing is not designed to reveal the form of the body,
but for entirely different
purposes.
The tacit conventions on which the understanding of everyday
language depends are
enormously complicated.
human beings propose – propose in relation to the unknown
sense is a proposal – open to question – open to doubt – and
uncertain
‘every sense’ is only the sense that is
proposed
meaning is open to question – open to doubt – and uncertain
and any proposal of propositional use – is open to question
– open to doubt – and
uncertain
how anything is produced – is open to question – to doubt –
is uncertain
the nature of human organism – as science demonstrates – is
open to question – open to doubt – and is uncertain
any so called ‘logic of language’ – is a proposal – open to
question – open to doubt – and uncertain
‘thought’ can be a description of language –
language disguises nothing – language is not a disguise
language is proposal – open to question – open to doubt –
and uncertain –
there are no hidden realities – there is only what is proposed
what is proposed – is what there is
how language works – is worked
out in its use –
any analysis of how language works – is open to question –
open to doubt – and is uncertain
the ‘enormous complication’ – is propositional uncertainty
4.003. Most of the propositions and questions to be found in
philosophical works are
not false but nonsensical. Consequently we cannot give any
answer to questions of
this kind, but can only point out that they are nonsensical.
Most of the propositions
and questions of philosophers arise from our failure to
understand the logic of our
language.
(They belong to the same class of question whether the good
is more or less identical
than the beautiful.)
And it is not surprising that the deepest problems are in
fact not problems at all.
propositions to be found in philosophical works are neither
true – false – or nonsensical – they are uncertain
any question – any doubt – is logically valid
the proposals and propositions of philosophers are no
different to the proposals and questions of anyone else – they are open to
question – open to doubt and uncertain
whether the good is more or less identical to the beautiful
– is a fair enough question –
any response to this question will be a proposal – itself
open to question
a ‘philosophical problem’ is no different to any other
problem to which there are different answers or responses
any proposal – so called philosophical or not – is open to
question – open to doubt and uncertain
4.0031. All philosophy is a 'critique of language' (though
not in Mauthner's sense). It
was Russell who performed the service of showing that the
apparent logical form of a
proposition need not be its real one.
a philosophical proposition –
whether it is designed as a ‘critique of language’ – or not
–
is a proposal of knowledge –
that is a proposal – in response to the unknown –
and as with any proposal –
it is open to question – open to doubt – and is uncertain
the ‘logical form of a proposition’ – is a proposal of
propositional structure –
any such proposal – Russell’s included – is open to question
– open to doubt – and is uncertain
4.01. A proposition is a picture of reality.
A proposition is a model of reality as we imagine it.
a proposition is a proposal – open to question – open
to doubt – and uncertain
‘a picture of reality’ – is a proposal
any description of a proposition – i.e. as a ‘picture of
reality’ – as ‘a model of reality as we imagine it’ – is open to question – to
doubt – and is uncertain –
4.011. At first sight a proposition – one set out on the
printed page, for example – does
not seem to be a picture of the reality with which it is
concerned. But neither do
written notes seem at first sight to be a picture of a piece
of music, nor our phonetic
notation (the alphabet) to be a picture of our speech.
And yet these sign-languages prove to be pictures, even in
the ordinary sense, of what
they represent.
a proposition on a printed page – written notes in a piece
of music – and phonetic notation – are proposals
these proposals can
be variously described – i.e. as ‘pictures’ – as ‘forms’ – whatever
any proposal or any description of a proposal – is open to
question – open to doubt and is uncertain
4.012. It is obvious that a proposition of the form 'aRb'
strikes us as a picture. In this
case the sign is obviously a likeness of what is signified.
the sign is a proposal – open to question –
the proposition it signifies – is open to question
asserting that such and such is obvious – is just rhetoric
4.013. And if we penetrate to the essence of this pictorial
character, we see that it is
not impaired by apparent irregularities (such as the
use of # and ♭in musical
notation).
For even these irregularities depict what they are intended
to express; only they do it
in a particular way.
any sign is a proposal –
how it is interpreted – is open to question
4.014. A gramophone record, the musical idea, the written
notes, and the soundwaves,
all stand to one another in the same internal relation of
depicting that holds between
language and the world.
They are all constructed according to a common logical
pattern.
Like the two youths in the fairy tale, their two horses, and
their lilies. They are in a
certain sense one.
a gramophone record – the musical idea – the written notes –
the soundwaves – are proposals – different proposals – different propositions
if a relation between these proposals – is proposed – it is
a separate proposition – and a proposition external to the subject propositions
and any proposed propositional construction – or
propositional pattern – is a separate and external proposal –
‘they are in a certain sense one’ –
unless you want to get mystical here – the best you can say
is that the different propositions are related to one another in terms of a proposed
‘logical pattern’
and this relational proposal – as with any proposal – any
proposition – is open to question – open to doubt – and is – logically speaking
– uncertain
4.0141. There is a general rule by means of which the musician
can obtain the
symphony from the score, and which makes it possible to
derive the symphony from
the groove on the gramophone record, and, using the first
rule, to derive the score
again. That is what constitutes the inner similarity between
these things which seem to
be constructed in such entirely different ways. And that law
is the law of projection
which projects the symphony into the language of musical
notation. It is the rule for
translating this language into the language of gramophone
records.
rules can be put to relate different proposals – different
propositional constructions
the relation between the constructions mentioned – is
rule-governed – and as such the relation is external to the constructions
this ‘law of projection’ – is a description of the rule that
relates the different propositional constructions
however it should be noted that just what this rule – this
‘law of projection’ – amounts to – as it is presented here by Wittgenstein – is
quite vague
translation when rule-governed is a language-game
a rule governed propositional activity is a propositional game
4.015. The possibility of all imagery, of all our pictorial
modes of expression, is
contained in the logic of depiction.
the possibility of
all imagery – of all our pictorial modes of expression – is contained in – the
logic of the proposal –
imagery is proposal –
depiction is a form of proposal
the proposal is open to question – open to doubt – and
uncertain
4.016. In order to understand the essential nature of a
proposition, we should consider
the hieroglyphic script, which depicts the facts that it
describes.
And alphabetic script developed out of it without losing
what was essential to
depiction.
depiction – is proposal –
and the proposal here is that the hieroglyphic script
depicts the facts / proposals that it is proposed the script represents –
and that – if you like – is the proposal of the hieroglyphic
script
however I think it is a bit of a stretch to say that the
alphabetic script – in terms of depiction – is in the same boat as the
hieroglyphic script
you can put that any script is a depiction – i.e. signs
propose /represent –
but this is no more than to say that a sign – signs
in any case – logically speaking – any proposed depiction –
as with any other kind of proposal – is open to question – open to doubt – and
is uncertain
4.02. We can see this from the fact that we understand the
sense of a propositional
sign without its having been explained to us.
a sign is a proposal – its sense is open to question – open
to doubt and uncertain –
understanding sense is recognizing and dealing with –
propositional uncertainty
4.021. A proposition is a picture of reality: for if I
understand a proposition, I know
the situation that it represents. And I understand the
proposition without having had
its sense explained to me.
a proposition is a proposal – open to question – open to
doubt – and uncertain
a proposition proposes a situation –
what I ‘know’ – is what is proposed
understanding a proposition – is recognizing propositional
uncertainty –
the sense of a proposition – whether explained or not – is
uncertain
4.022. A proposition shows its sense.
A proposition shows how things stand if it is
true. And it says that they do so stand.
what a proposition shows is open to question – open to doubt
– and is uncertain
the truth or falsity of a proposition is a question of
assent to the proposition – or dissent from it
‘that they do so stand’ – is the proposal –
a proposal – open to question – open to doubt – and
uncertain
4.023. A proposition must restrict reality to two
alternatives: yes or no.
In order to do that, it must describe reality completely.
A proposition is a description of a state of affairs.
Just as a description of an object describes it by giving
its external properties, so a
proposition describes reality by its internal properties.
A proposition constructs a world with the help of a logical
scaffolding, so that one can
actually see from the proposition how everything stands
logically if it is true.
One can draw inferences from a false proposition.
our reality is propositional – open to question – open to
doubt – and uncertain
you can respond yes or no to a proposition –
or you can –– withhold judgment –
the proposition is not restricted to two alternatives
logically speaking the proposition – propositional reality –
is open – open to question – to doubt – and therefore – incomplete
a proposition is a proposed state of affairs –
as to reality’s ‘internal properties’ –
reality in the absence of proposal – is unknown
we make reality ‘known’ – with our proposals
our reality is propositional
a property is a proposed characterization – of a proposition
the property – the propositional characterization – is
external to the subject proposition
what you have then – is two propositions – the subject
proposition – and the property / characterization proposition – put in relation to each other –
a relational proposition will express the proposed relation
–
and it is to this relational proposition that our focus will
be directed – in the first place
a proposition – proposes the world
any propositional construction – is a proposal
‘logical scaffolding’ – is a proposal
‘how everything stands’ – is open to question – open
to doubt – and uncertain
a proposition is true – if it is affirmed – if it is
assented to
an inference is a relational proposal
you can ‘draw inferences’ from a proposition that you reject
–
any such inference – is a proposal – and as with the subject
propositions – is open to question – open to doubt – and uncertain
4.024. To understand the proposition means to know what is
the case if it is true.
(One can understand it, therefore, without knowing whether
it is true.)
It is understood by anyone who understands its constituents.
to understand the proposition is to recognise that it is
open to question – open to doubt and uncertain – understanding – is logical
one can understand a proposition – a proposal – without
affirming or denying it
you can understand a proposition – a proposal – without it
being analysed in terms of ‘constituents’
a theory of the ‘propositional constituents’ – is a proposal
– open to question – open to doubt and uncertain
4.025. When translating one language into another, we do not
proceed by translating
each proposition of the one into a proposition
of the other, but merely by translating the constituents of propositions.
(And the dictionary translates not only substantives, but
also verbs, adjectives and
conjunctions, etc.; and it treats then all the same way.)
breaking a proposition up into constituents – is a method of
translation
the dictionary analysis is a form of constituent analysis
however language users with a high degree of natural
facility in both languages may well translate – as it were – directly – without
a constituent analysis
we assume accurate translation for pragmatic reasons
nevertheless any translation – however it is proposed – or
however it happens – is open to question – open to doubt – and is uncertain –
we can of course adopt a rule-governed approach to
translation –
and in that case translation becomes a language-game
4.026. The meanings of simple signs (words) must be
explained to us if we are to
understand them.
With propositions, however, we make ourselves understood.
yes – meanings of simple signs (words) are proposed –
any proposal is an understanding – open to question – open
to doubt and uncertain –
and yes – we propose understandings of ourselves
4.027. It belongs to the essence of a proposition that it
should be able to communicate
a new sense to us.
the proposition is open to question – open – to doubt – and
uncertain
the uncertainty of propositional reality – is the source of
all propositional novelty and creativity
4.03. A proposition must use old expressions to communicate
a new sense.
A proposition communicates a sense to us, and so it must be essentially
be connected
with the situation.
And the connection is precisely that it is its logical
picture.
A proposition states something only in so far as it is a
picture.
a ‘new sense’ is a proposal – it will come out of question –
and doubt – and uncertainty – in relation to a proposal already put
a situation is a proposal – and open to question
a proposition will be a response to proposed situation –
the connection between a proposition and a proposed
situation – will be open to question – open to doubt – and uncertain
there is no ‘essential’ connection
the two proposals – the two propositions – are connected
logically – in that they are open to question – open to doubt and uncertain
any proposed connection is uncertain
uncertainty is the logical picture
what a proposition states – is open to question – open to
doubt – and uncertain
4.031. In a proposition a situation is, as it were,
constructed by way of experiment.
Instead of, 'This proposition has such and such a sense', we
can say simply, 'This
proposition represents such and such a situation'.
a situation is proposal –
and as with any experiment – open to question – open to
doubt – and uncertain
'This proposition represents such and such a situation' –
the proposition – the proposal – is the situation
in the absence of proposal – there is no situation
in the absence of proposal – what we face is the unknown
4.0311. One name stands for one thing, another for another
thing, and they are
combined with one another. In this way the whole group –
like a tableau vivant –
presents a state of affairs.
the ‘one thing’ – and the ‘another thing’ – are proposals –
unidentified proposals
a name is a proposal of identification
the unidentified proposals are identified by name proposals
combining identifying proposals – presents a new proposal –
which can be described as a ‘state of affairs’ –
‘a state of affairs’ – is a proposal – open to question –
open to doubt – and uncertain
4.0312 The possibility of propositions is based on the
principle that objects have signs
as their representatives.
My fundamental idea is that the 'logical constants' are not
representatives; that there
can be no representatives of the logic of facts.
‘objects’ here – are proposals –
signs are proposals put in relation to object proposals
logical constants are proposals of propositional structure –
this so called ‘logic of facts’ – is an analysis of
propositions – a propositional analysis of
propositions
and as such – is a
proposal –
and as with any proposal
– is representative
and any such proposal –
is open to question – open to doubt – and is uncertain
4.032. It is only in so far as a proposition is logically
articulated that it is a picture of a
situation.
(Even the proposition, 'Ambulo', is composite: for its stem
with a different ending
yields a different sense, and so does its ending with a
different stem)
a proposition – a proposal – is an articulation
any so called ‘logical articulation’ of a proposition –
is a proposal in relation to the proposition –
an analysis of it – if you like –
you can describe such an analysis as a ‘picture’ –
such analytical proposals and descriptive proposals – are
open to question – open to doubt – and uncertain
as to ‘ambulo’ –
its stem with a different ending – is different proposition
its ending with a different stem – is a different
proposition
4.04 In a proposition there must be exactly as many
distinguishable parts as in the
situation it represents.
The two must possess the same logical (mathematical)
multiplicity. (Compare Hertz's
Mechanics on dynamical models.)
a situation is a proposal – is a proposition
a proposition can be interpreted in any number of ways
an analytical proposal – i.e. a proposal of distinguishable
parts – is an interpretation of the original proposal
there is no correspondence between the original proposition
– and its analytical interpretation
they are different proposals – different propositions
and the idea is that the second proposition – the analytical
proposition – remakes and replaces the first proposition
this interpretive proposal
– as with the original proposal – is open to question – open to doubt
and is uncertain
‘the same logical (mathematical) multiplicity’ – is an
analytical proposal –
a proposal – open to question
4.041. This mathematical multiplicity, of course, cannot
itself be the subject of
depiction. One cannot get away from it when depicting.
a proposal of mathematical multiplicity can be depicted –
that is proposed – in any number of propositional contexts
if you get away from what you are depicting – you are not
depicting it –
however any depiction / proposal – is open to question –
open to doubt and uncertain
4.0411. If, for example, we wanted to express what we now
write as '(x).fx' by putting
an affix in front of 'fx' – for instance by writing 'Gen.
fx' – it would not be adequate: we
should not know what was being generalized. If we wanted to
signalize it with an
affix ‘ g ’ –for instance by writing 'f(xg)' – that would not be adequate either: we
should
not know the scope of the generality sign.
If we were to try to do it by introducing a mark into the
argument places – for instance
by writing
'G, G). F(G,G)'
– it would not be adequate: we should not be able to
establish the identity of variables.
And so on.
All these modes of signifying are inadequate because they
lack the necessary
mathematical multiplicity.
all that is being asserted here is that a notation that does
not propose mathematical multiplicity – will not signifying mathematical
multiplicity
4.0412. For the same reason the idealist's appeal to
'spatial spectacles' is inadequate to
explain the seeing of spatial relations, because it cannot
explain the multiplicity of
these relations
the multiplicity of spatial relations is a proposal
how this proposal is interpreted – explained – is open to
question – open to doubt – and uncertain – whether you are an idealist or not
4.05. Reality is compared with propositions.
reality is propositional – reality is that which is proposed
in the absence of proposal – reality is unknown
propositions are responses to propositions
4.06. A proposition can be true or false only in virtue of
being a picture of reality.
a proposal – be it further described as a ‘picture of
reality’ – or not –
is true – if it is affirmed – for whatever reason –
and false – if it is denied – for whatever reason –
any proposal of affirmation or denial – as with the proposal
affirmed or denied – is
open to question – open to doubt – and uncertain
4.061. It must not be overlooked that a proposition has a
sense that is independent of
the facts: otherwise one can easily suppose that true and
false are relations of equal
status between signs and what they signify.
In that case one could say, for example, that ‘p’ signified
in the true way what ‘~p’
signified in a false way, etc.
a proposition – and
the facts –
the ‘facts’ are a
proposition – are a proposal
what we have here is
two proposals – two propositions – one (the proposition) – put in relation to
the other (the facts)
it is a fair enough
initial assumption that two different and independent propositions have
different and independent senses –
however the sense of
a proposition – is open to question – open to doubt – and uncertain
so it might well be
argued subsequently that different and independent as they are – the two
propositions have the same sense
this is a
possibility
a true proposition
is a proposition affirmed – for whatever reason
a false proposition
– is a proposition denied – for whatever reason
any proposed
signification – can be affirmed or it can be denied – and in that sense –
affirmation and denial are ‘equal’ responses to a proposition
what 'p' signifies – where ‘p’ is affirmed is
that ‘p’ will be proceeded with
what ‘~p’ signifies – is that ‘p’ will
not be proceeded with
note –
in standard logical notation ‘p’ is both the
proposition put – and the proposition affirmed
‘p’ proposed – needs to be distinguished from ‘p’
affirmed –
for the proposition affirmed – is a separate propositional action to the
proposition put
it would be better if the proposition affirmed was signified
as i.e. ‘+p’ – and ‘p’ – left as the proposition put
this would bring the notation for the proposition affirmed (‘+p’ ) in
line with the notation for the
proposition denied (‘~p’ )–
4.062. Can we not make ourselves understood with false
propositions just as we have
done up to now with true ones? – So long as it is known that
they are meant to be
false. – No! For a proposition is true if we use it to say
that things stand in a certain
way, and they do; and if by ‘p’ we mean ‘~p’ and
things stand as we mean that they do,
then, constructed in the new way, ‘p’ is true and not
false.
a true proposition is a proposition affirmed
a false proposition is a proposition denied
if ‘p’ is affirmed – we assert that we will proceed
with the proposition
if ‘p’ is denied (‘~p’) – we assert that we will not proceed with the
proposition
when we deny a proposition – when we do not accept a
proposition – we make ourselves
understood – in terms of what we will not proceed with –
we will not proceed with ‘p’
4.0621. But it is important that the signs ‘p’ and ‘~p’
can say the same thing. For it
shows that nothing in reality corresponds to the sign ‘~’.
The occurrence of negation in a proposition is not enough to
characterize its sense
(~~p = p).
The propositions ‘p’ and ‘~p’ have opposite
sense, but there corresponds to them one
and the same reality.
‘p’ and ‘~p’– do not say the same thing
–
the sign ‘~’ indicates the negation of ‘p'– the
denial of ‘p’ – the non-acceptance of ‘p’ – as a propositional
reality
negation does not occur in a proposition –
negation is a basic response to the
proposition – indicated by the sign ‘~’
(~~p = p) – is a (logical) sign game
‘p’ and ‘~p’ – indicate two basic responses to
‘p’ – affirmation – and denial
the sense of a proposition – is open to question to doubt –
and is uncertain
we can respond negatively or positively to a proposition
regardless of its sense
(we can also – not affirm – or not deny – but rather
withhold judgment – regarding the matter as uncertain – the middle is not
excluded)
different basic responses to the proposition – indicate
different propositional realities
if ‘p’ is in your picture of reality – but not in
mine – denied in mine –
then we operate with two different propositional realities
4.063. An analogy to illustrate the concept of truth:
imagine a black spot on white
paper: you can describe the shape of the spot by saying, for
each point on the sheet,
whether it is black or white. To the fact that a point is
black there corresponds a
positive fact, and to the fact that a point is white (not
black), a negative fact. If I
designate a point on a sheet (a truth value according to
Frege) then this corresponds to
the supposition that is put forward for judgement, etc. etc.
But in order to be able to say a point is black or white, I
must first know when a point
is called black, when white: in order to be able to say. “‘p”
is true (or false)’, I must
have determined in what circumstances I call ‘p’ true,
and in so doing I determine the
sense of the proposition.
Now the point where the simile breaks down is this: we can
indicate a point on the
paper even if we do not know what black or white are, but if
a proposition has no
sense, nothing corresponds to it, since it does not
designate a thing (a truth value)
which might have properties called ‘false’ or ‘true’. The
verb of a proposition is not ‘is
true’ or ‘is false’, as Frege thought: rather that which ‘is
true’ must already contain the
verb.
this black spot / positive fact – white spot / negative fact
– is simply a propositional game – it has nothing to do with truth or falsity
a point is called black – when I call it black – a point is
called white – when I call it white
p is true – when I affirm p –
when I affirm p – is – the circumstance of
affirmation
I will have a sense of p when I affirm p –
however my sense of p – is open to question – open to
doubt – and uncertain
a proposition with no sense?
a proposition with no sense – is not a proposal – not a proposition
a response to a proposition – can be – ‘is true’ – ‘is
false’
the proposition does not ‘already contain the verb’ –
the proposition in itself – is neither true nor false –
truth and falsity – are propositional responses to a
proposition
a proposition is true – if affirmed – for whatever reason –
under whatever circumstances
false – if dissented from – for whatever reason – under
whatever circumstances
any proposal of affirmation – or any proposal of denial – is
open to question – open to doubt – and uncertain
4.064. Every proposition must already have a sense:
it cannot be given a sense by
affirmation. Indeed its sense is just what is affirmed. And
the same applies to
negation. etc.
a proposal is a proposal of sense –
even though the sense of the proposal – is open to question
– open to doubt – and is uncertain
sense is not given by affirmation
affirmation is a response to the proposition – to its
perceived sense –
and the same applies to negation
4.0641. One could say that negation must be related to the
logical place determined by
the negated proposition.
The negating proposition determines a logical place different
from that of the negated
proposition.
The negating proposition determines a logical place with the
help of the logical place
of the negated proposition. For it describes it as lying
outside the latter's logical place.
The negated proposition can be negated again, and this in
itself shows that what is
negated is already a proposition, and not merely something
that is preliminary to a
proposition.
negation is a propositional response to a subject proposition –
a propositional action
performed on a subject proposition –
not the name of a logical place
any so called ‘logical space’ – is a proposal – a proposal
open to question – open to doubt – and uncertain –
a proposal that can be affirmed or denied
furthermore this notion of ‘logical place’ – is unnecessary
propositional packaging –
unnecessary and logically irrelevant
4.1. Propositions represent the existence and non-existence
of states of affairs.
a proposition – a proposal – can be described as a state of
affairs
that which is proposed – exists – as a proposal – open to
question – open to doubt and uncertain
a non-existent state of affairs is a state of affairs that
is not proposed –
if it is proposed – what you have is a corruption of the
proposal
4.11. The totality of true propositions is the whole of
natural science (or the whole
corpus of the natural sciences).
there is no totality of propositions –
the putting of proposals – is open ended – is on-going
true propositions are propositions affirmed –
affirmation or denial of propositions is a contingent matter
– open to question –
propositions – regardless of the description they are given
– i.e. ‘of natural science’ – are open to question – open to doubt – and
uncertain
4.111. Philosophy is not one of the natural sciences.
(The word 'philosophy' must mean something whose place is
above or below the
natural sciences, not beside them)
the propositions of philosophy – as with the propositions of
the natural science – are open to question – open to doubt – and uncertain
any proposal – any proposition – is open to question – open
to doubt – and is uncertain
philosophical proposition are on the same level as any other
proposition
there is no ‘above’ or ‘below’ – in propositional logic
4.112. Philosophy aims at the logical clarification of
thoughts.
Philosophy is not a body of doctrine but an activity.
A philosophical work consists essentially of elucidations.
Philosophy does not result in ‘philosophical propositions’,
but rather in the clarification of propositions
Without philosophy thoughts are, as it were, cloudy and
indistinct: its task is to make clear and to give them sharp boundaries.
what the propositional activity described as ‘philosophy’
aims at – is open to question – open to doubt and uncertain
what philosophy is – is open to question
a philosophical work consists of proposals
there are ‘philosophical propositions’ – what they result in
– is open to question
proposals / thoughts – are open to question – open to doubt
and are uncertain
philosophy is not the palace guard
4.1121. Psychology is no more closely related to philosophy
than any other natural
science.
Theory of knowledge is the philosophy of psychology.
Does not my study of sign language correspond to the study
of thought process, which
philosophers used to consider so essential to the philosophy
of logic? Only in most
cases they got entangled in unessential psychological
investigations, and with my
method too there is an analogous risk.
the propositions of psychology – philosophy and other
natural sciences – are related to each other – if a relation is proposed
any proposal – any proposition – however it is described or
categorized – is open to question – open to doubt and is uncertain
how theory of knowledge is described – is open to question –
you can describe a study of sign language as the study of
thought processes
this description – this proposal – is as with any other
proposal – is open to question – open to doubt – and is uncertain
4.1122. Darwin's
theory has no more to do with philosophy than any other hypothesis
in natural science.
the relation of Darwin’s
theory to philosophy or any other hypothesis of natural science –
is open to question – open to doubt – and is uncertain
4.113. Philosophy sets limits to the much disputed sphere of
the natural science.
philosophical propositions and the propositions of natural
science – are proposals – open to question – open to doubt and uncertain
I don’t think it makes sense to speak of any limit to the
propositional activity of question – of doubt – and the exploration of
uncertainty – in natural science –
or indeed in any other sphere of propositional activity
4.114. It must set limits to what can be thought; and in
doing so, what cannot be
thought.
It must set limits to what cannot be thought by working
outwards through what can be
thought.
what can be thought – is what is proposed – and what
is proposed – is open to question – open to doubt – and is uncertain
what cannot be thought / proposed – is not thought /
proposed
4.115. It will signify what cannot be said, by presenting
clearly what can be said.
what cannot be said – is not said –
what can be said – what can be proposed – is what is said
– what is proposed –
presentation is not a logical issue – presentation – is
rightly seen as a rhetorical matter
clarity – as with any other concept – any other proposal –
is open to question
4.116. Everything that can be thought at all can be thought
clearly. Everything that can
be put into words can be put clearly.
the notion of clarity – is open to question – open to doubt
– and is – itself – uncertain
and for all practical purposes – clarity is in the eye of
the beholder
4.12. Propositions can represent the whole of reality, but
they cannot represent what
they must have is common with reality in order to able to
represent it – logical form.
In order to be able to represent logical form, we should
have to be able to station
ourselves with propositions somewhere outside logic, that is
to say outside the world.
our reality is propositional – propositions are our reality
–
as to ‘the whole of reality’ –
propositional activity is on-going –
reality is on-going –
and best seen as propositional action – as propositional
activity
what propositions have in common – is that they are open to
question – open to doubt – and uncertain
logical form is a proposal of propositional structure –
proposal is representation
we ‘represent’ a proposal of logical form – by proposing
it –
there is no logical form / structure – unless it is proposed
– that is represented
logical form as the relation between propositional reality
and some extra-propositional reality – is a false concept –
Wittgenstein’s notion of logical form is mystical – at best
his idea is that logical form is that which could only be
known from outside of reality
there is no ‘outside of the world’ –
there is no outside of propositional reality
4.121. Propositions cannot represent logical form; it is
mirrored in them.
What finds its reflection in language, language cannot
represent.
What expresses itself in language, we cannot express
by means of language.
Propositions show the logical form of reality.
They display it.
‘logical form’ – is a proposal of propositional structure –
a proposition interpreted in terms of a proposal of logical
structure – can be said to represent that proposal of logical structure
‘logical form’ is not something outside of language – that
is mirrored in language
logical form is a proposal in language
language is proposal – it is not reflection –
what language represents – is what language proposes
what expresses itself in language – is a proposal – and a
proposal is expressed by means of language
reality is propositional – and we have proposals of logical
structure
a display is a proposal
any proposal of logical form – of logical structure – is
open to question – open to doubt –
and is uncertain
4.1211. Thus one proposition 'fa' shows that the
object a occupies in its sense, two
propositions 'fa' and 'ga' show that the same
object is mentioned in both of them.
If two propositions contradict one another, then their
structure shows it; the same is
true if one of them follows from the other. And so on.
‘fa’ – is a proposal – in a rule-governed sign-game –
there is no point to ‘fa’ – outside of a game context
what it ‘shows’ depends on the rules of the game –
in ‘fa’ and ‘ga’ – ‘a’ is mentioned in
both –
the rule of the game – whatever the game is – determines the
role of ‘a’
there is no sense in a sign game – there is just the rules
of the game and the playing of the game in accordance with the rules
contradiction – is a
rule governed propositional game –
the rule of the game
determines the structure of the game –
and the play of the
game is determined by its structure
likewise with the
‘follow on’ game –
the rule of the game
determines the structure of the game –
and the play of the
game is determined by its structure
4.1212. What can be shown, cannot be said.
what can be shown – is what can be proposed – what
can be proposed – is what can be said
4.1213. Now, too, we understand our feeling that once we
have a sign-language in
which everything is all right, we already have a correct
logical point of view.
‘every thing is all right’ – because what you have here is a
rule governed sign-game –
if you play the game – you play in accordance with
the rules
yes – you can put the rules to question – to doubt – and
explore their uncertainty –
but that is logical analysis – it is not playing the
game
in the propositional game – ‘everything is all right’ –
because nothing is put to question –
nothing is put to doubt – there is no uncertainty – if you
follow the rules
if you don’t follow the rules – you don’t play the game
without the rules – there is no game
4.122. In a certain sense we can talk about formal
properties of objects and states of
affairs, or in the case of facts, about structural
properties: and in the same sense about
formal relations and structural relations.
(Instead of 'structural property' I also say 'internal
property'; instead of 'structural
relation', 'internal relation'.
I introduce these expressions in order to indicate the
source of the confusion between
internal relations and relations proper (external
relations), which is very widespread
among philosophers.)
It is impossible, however, to assert by means of
propositions that such internal
properties and relations obtain; rather, this makes itself
manifest in the propositions
that represent the relevant states of affairs and are
concerned with the relevant objects.
all relations are proposals –
a relation / proposal
is external to the propositions it proposes to relate
propositions do not have an interior
relations do not inhere
there are no internal relations –
what makes itself ‘manifest’ here –
is the failure to understand propositional logic –
and there is more than just a hint too –
of a surrender to mysticism
4.1221. An internal property of a fact can also be called a
feature of that fact (in the
sense in which we speak of facial features, for example).
a fact – is a proposal – a proposition that has gained
acceptance –
a ‘property’ – a propositional characterization
there is no ‘internal property of a fact’ –
any proposed characterization of a fact – is a separate
proposal – to the proposal of the proposition / fact –
and any such characterization is a proposal – external to the fact / proposal –
what you then have is two propositions – the subject
proposition – and the property proposition – put – in relation to each other –
via a third proposal
the relating proposition – will likely be the initial focus
we are so adept at proposal – at propositional action – that
we often fail to see that the proposition we are dealing with – is not a simple
proposal – but is actually a propositional complex –
any relational proposal – is a propositional complex
4.123. A property is internal if it is unthinkable that its
object should not possess it.
(This shade of blue and that one stand, eo ipso, in the
internal relation of lighter to
darker. It is unthinkable that these two should not
stand in this relation)
(Here the shifting use of the word 'object' corresponds to
the shifting use of the words
'property' and 'relation'.)
a property is a propositional characterization put in
relation to an object-proposal –
the two proposals are external to each other –
the relational proposal is external to the subject
propositions
the object-proposal – without any propositional
characterization – is unknown
any proposed properties – are open to question – open to
doubt and uncertain
we are not dealing with ‘unthinkable’ here – we are dealing
with uncertainty
once you characterize the colours in terms of shade – then
the further characterization of their relation in terms of lighter and darker –
is no more than the original characterization restated and refined in different
terms
it is not that it is unthinkable that these two – lighter
and darker – should not stand in this relation – it is rather that this
relation is what is proposed –
colour propositions can be characterized and related in any
number of ways
as to ‘object’ – ‘property’ – and ‘relation’ –
what we have is different proposals – in different configurations
what we deal with is not ‘shifting use’ – rather
propositional uncertainty
4.124. The existence of an internal property of a possible
situation is not expressed by
means of a proposition: rather it expresses itself in the
proposition representing the
situation, by means of an internal property of that
proposition.
It would be just as non-sensical to assert that a
proposition had a formal property as to
deny it.
if ‘the existence of
an internal property of a possible situation’ is not expressed by a
proposition – it is not there
‘rather it expresses
itself in the proposition representing the situation, by means of an internal
property of the proposition’
this is a circular
argument – the internal property – is internal –
it is the conclusion
– stated as the argument for the conclusion
the proposition does
not have an interior
properties do not inhere
–
properties are proposed
– are put as characterizations of object propositions
properties are
proposals – external propositions
at best – what this
shows is that Wittgenstein’s theory of the proposition collapses into
mysticism
‘It would be just as non-sensical to assert that a
proposition had a formal property as to deny it.’
a formal property – a characterization – is a proposal put
in relation to a proposition
and of course a proposition can exist without such a
characterization
if such a formal property / proposal is put – it is open to
question – open to doubt – and uncertain
and just as such a proposal can be affirmed – it can be
denied
4.1241. It is
impossible to distinguish forms from one another by saying that one has this
property and another that property: for this presupposes that it makes sense to
ascribe either property to either form.
it is not impossible to distinguish forms – proposed
propositional structures – by proposing that one has this property /
characterization – and another that property / characterization
any form – propositional structure – can be further
characterized – by means of a property / characterization
and any such proposal – is open to question – open to doubt
– and uncertain
4.125. The existence of an internal relation between
possible situations expresses
itself in language by means of an internal relation between
the propositions
representing them.
the ‘argument’ here
is that internal relations are expressed by means of internal relations
this no argument –
it simply the assertion of internal relations
a relation between
propositions is a proposal with respect to the propositions in question
the proposal of a
relation – is external the subject propositions –
the relation is
external
propositions – of
whatever kind – are external to each other
4.1251. Here we have the answer to the vexed question
'whether all relations are
internal or external'.
all relations are proposals
and all relational proposals are external to the proposals
that are related
all relations are external –
there are no ‘internal’ relations
4.1252 I call a series that is ordered by an internal relation a series of forms.
The order of the number-series is not governed by an
external relation but by an internal relation.
The same is true of the series of propositions
‘aRb’,
‘($x): aRx. xRb’,
‘($x,y): aRx. xRy. yRb’,
and so forth.
(If b stands in one of these relations to a, I
call b a successor of a.)
an ordered series is a propositional game
the relation that orders the series is a rule
the number series is a rule governed propositional game
the rule governing the series – is external to the numbers
numbers do not order themselves
in a series of propositions such as –
‘aRb’,
‘($x): aRx. xRb’,
‘($x,y): aRx. xRy. yRb’,
and so forth.
we have a rule governed game
the rule governing this game is separate and external to the
propositions in question
propositions do not order themselves
(If b stands in one of these relations to a, I
call b a successor of a.)
the rule then – is that b is a successor to a
this rule – is separate and external to a and b
4.126. We can now talk about formal concepts, in the same
sense that we can speak of
formal properties.
(I introduce this expression in order to exhibit the source
of the confusion between
formal concepts and concepts proper, which pervades the
whole of traditional logic.)
When something falls under a formal concept as one of its
objects, this cannot be
expressed by means of a proposition. Instead it is shown in
the very sign for this
proposition. (A name shows that it signifies an object, a
sign for a number that it
signifies a number, etc.)
Formal concepts cannot, in fact, be represented by means of
a function, as concepts
proper can.
For their characteristics, formal properties, are not
expressed by means of functions.
The expression for a formal property is a feature of certain
symbols.
So the sign for the characteristics of a formal concept is a
distinctive feature of all
symbols whose meanings fall under the concept.
So the expression for a formal concept is a propositional
variable in which this
distinctive feature alone is a constant.
a formal concept is a proposal in a formal language – a
formal property – a proposal in a formal language
when ‘something’ falls under a formal concept / proposal –
as one of its ‘objects’ –
that ‘something’ – that ‘object’ – is a proposal –
a sign is a proposal – is a proposition
the sign for the proposition – is the proposition –
a name is a proposal that identifies a proposal – i.e. –
‘that man is …’ –
a number is a proposal – a proposition / sign – in a sign
game – a calculation game
a sign-game is a rule governed propositional action
the formal concept and the function are different proposals
the formal property is a proposal put in relation to certain
symbols – to characterize those symbols –
the function is a rule governed propositional operation –
the rule is that for
any given first term (the argument of the function) – there is exactly one
second term (the value of the function) –
e.g. multiplication
of numbers by a constant is a function i.e. 5x = y –
here x stands for an
argument – y for the value of the function –
a function is a propositional game
you can propose that the sign is a distinctive
feature of all the symbols that fall under the concept / proposal
here we have a proposal put in relation to a proposals – a
natural propositional action
if the expression – that is the use of the formal
concept / proposal – is not a propositional variable – the formal concept will
have limited function – will have limited propositional value – limited
propositional use
you can propose
the rule that the sign for the characteristics of a formal
concept is a distinctive feature of all symbols whose meanings fall under the
concept
and you can propose the rule that the expression for
a formal concept is a propositional variable in which this distinctive feature
alone is a constant
this is really all about establishing the architecture of a
formal language – and the games played in that formal language
4.127. The propositional variable signifies the formal
concept, and its values signify
the objects that fall under the concept.
you can
propose that the propositional variable signifies a formal concept –
and that its values
signify the objects / proposals that fall under the concept –
and adopt this
proposal as a rule for the relation between the propositional variable
and the formal concept in the propositional game
the idea here is
that that the propositional variable expresses the formal concept – that it
gives it function
here we are dealing
with the establishing of a rule governed propositional game
4.1271. Every variable is a sign for a formal concept.
For every variable represents a constant form that all its
values posses, and this can be
regarded as a formal property of those values.
could we operate
with ‘variables’ without this notion of formal concept?
yes – but that is
not the game that is here being proposed –
and could we operate
with ‘variables’ without the notion of a formal property of its values?
yes – but such is
not be the game that is here being proposed
we are dealing here
with game theory and game construction
Wittgenstein is
proposing a formal language – and the rules that establish the games in that
language
alternative
proposals – alternative formal languages – and alternative formal language
games – are always possible
4.1272. Thus the variable name 'x' is the proper sign
for the pseudo-concept object.
Wherever the 'object' ('thing', etc.) is correctly used, it
is expressed in conceptual
notation by a variable name.
For example, in the proposition, 'There are 2 objects
which.....', it is expressed by
'($x,y).....'.
Wherever it is used in a different way, that is as a proper
concept-word, nonsensical,
pseudo-propositions are the result.
So one cannot say, for example, 'There are objects' as one
might say, 'There are
books'. And it is just as impossible to say, 'There are 100
objects', or, 'There are 
objects'.
objects'.
And it is nonsensical to speak of the total number of
objects.
The same applies to the words 'complex', 'fact' 'function',
'number' etc.
They all signify formal concepts, and are represented in
conceptual notation by
variables, not by functions or classes (as Frege and Russell
believed).
'I is a number', 'there is only one zero', and all similar
expressions are nonsensical.
(It is just nonsensical to say, 'There is only one 1' as it
would be to say, '2+ 2 at 3
0'clock equals 4').
‘Thus the variable name 'x' is the proper sign for
the pseudo-concept object.’
Wittgenstein here
puts the rule that the variable name ‘x’ is the proper sign for ‘object’
– in his formal language game
he goes on to say –
‘Wherever it is used in a different way, that is as a proper
concept-word, nonsensical,
pseudo-propositions are the result’
‘in a different way’ – can only mean here – in the non-game context –
Wittgenstein confuses the propositional game – rule governed
propositional actions – with non-game propositions – proposals – open to
question – open to doubt – and uncertain –
and he is arguing that propositional games – and his in
particular – are the correct and proper form and use of the proposition
the reality is – yes – we play games – rule governed
propositional actions – but we also put propositions to question – to doubt –
and explore their uncertainty –
the fact of matter – the empirical fact of the matter
– is that game playing is just one mode
of propositional use – it is not the full propositional story –
and to suggest that it is – is a good example of
philosophical myopia –
and to argue that the game mode should be
regarded as the only correct form and use of the proposition – is simply
pretentious
Wittgenstein’s argument is that non-game propositions –
proposals – are pseudo-propositions and senseless
there are no ‘nonsensical pseudo propositions’ –
a proposition – however it is used – however it is described
and analysed – is a proposal – open to question – open to doubt – and
uncertain
‘So one cannot say, for example, ‘There are objects’, as one
might say’, There are books’. And it is just as impossible to say, ‘There are
100 objects’, or ‘'there are objects'.
objects'.
in Wittgenstein’s propositional game the rule is that
you can’t say ‘there are 100 objects' or
'there are objects'.
objects'.
and that’s fair enough – he can set whatever rules he likes
for his game
however outside of Wittgenstein’s propositional game –
outside of the game mode of propositional use – ‘object’ and ‘number’ –
are proposals – open to question – uncertain – and open to interpretation
outside of Wittgenstein’s game context – of course you can
say – ‘there are 100 objects’
and in set theory – another rule governed propositional game
– you can say 'there are objects'
objects'
‘And it is nonsensical to speak of the total number of
objects.’
this is a rule in Wittgenstein’s game
in anther game – where the ‘total number of objects’ – is
set at a finite number – I see no problem
outside of the game context – in the logical mode – the
total number of objects – is the total number of object / proposals –
the total number of propositions
propositional action is on-going – and is therefore –
indeterminate –
and so in the non-game context – in the logical mode –
we can’t know the ‘total’ number of objects / propositions
‘The same applies to the words ‘complex’, ‘fact’,
‘function’, ‘number’ etc.’
in Wittgenstein’s proposal for his formal language – its
rules – and its games – yes – they all signify formal concepts and are
represented in notation by variables –
but outside of Wittgenstein’s formal logic game context –
they are proposals – open to question – open to doubt – and uncertain
and the formal logic games of Frege and Russell – are
constructed differently
Wittgenstein here compounds his confusion of propositional
games – rule-governed propositional actions – with proposals – propositions –
open to question – open to doubt – and uncertain – by comparing games –
comparing his game with those of Frege and Russell –
different games – different rules – different plays –
different games are not comparable
one game – or one game’s rules are not inferior or superior
– or faulty – relative to another game – or another game’s rules
they are just different – different games
in saying – 'I is a number' – 'there is only one zero' – ‘there is only one
1’ and '2 + 2 at 3 o’clock equals 4’
– are nonsensical –
all Wittgenstein is saying is that these proposals – do not
have a place in his formal language – its rules – and its games
outside of that context – they are genuine proposals – open
to question – open to doubt – and uncertain
'2 + 2 at 3 o'clock equals 4’ – might well be a line in a
surrealist poem
4.12721. A formal concept is given immediately any object
falls under it is given. It is
not possible therefore, to introduce as primitive ideas
objects belonging to a formal
concept and the formal concept itself. So it is
impossible for example, to introduce as
primitive ideas both the concept of a function and specific
functions, as Russell does;
or the concept of a number and particular numbers.
Wittgenstein here
outlines his game plan –
and makes the point
that in terms of his formal game – its concepts and operations –
‘it is not possible’
to introduce ‘as primitive ideas both
the concept of the function and specific functions – or the concept of number
and particular numbers as Russell does’
‘it is not possible’
– is perhaps a little theatrical –
what we are dealing
with here is different game plans
Russell’s conception
is a different structure to Wittgenstein’s –
different conceptions
of language games – rule governed propositional constructions –
are not in conflict
– they are different – different games
there is no argument
between dominoes and chess
4.1273. If we want to express in conceptual notation the
general proposition, 'b is a
successor of a', then we require an expression for
the general term of the series of
forms
aRb,
($x) :aRx.xRb,
($x,y) :aRx.aRy.yRb.
.... .
In order to express the general term of a series of forms,
we must use a variable,
because the concept 'term of that series of forms' is a formal
concept. (This is what
Frege and Russell overlooked: consequently the way in which
they want to express
general propositions like the one above is incorrect; it
contains a vicious circle.)
We determine the general term of a series of forms by giving
its first term and the
general form of the operation that produces the next term
out of the proposition that
precedes it.
what we have with –
aRb,
($x) :aRx.xRb,
($x,y) :aRx.aRy.yRb.
.... .
is a propositional game
the ‘general term of the series of forms’ – is the game rule
now Wittgenstein says is that in order to express ‘the
general term of the series’ – the game rule – we must use a variable – because
– in his terms – the concept of term of the series is a formal concept –
all this amount to is – the game rule and its application
the general term for of the operation that produces the next
term out of the proposition that precedes it –
is the rule governed operation or action
as to Wittgenstein’s criticism of Frege and Russell – that
their theory involves a vicious circle
as with Wittgenstein’s view – what we are dealing with in
the end – is a rule – a rule for a propositional game –
a rule is a rule – whether its so called ‘ground’ is a
vicious circle or not
the point is you play the game in accordance with the rule –
or you don’t play the game –
and you can always play another game – another game with
different rules
the ground or argument for the rule – is effectively
irrelevant
there are different games – different variations of games –
with different rules
to have one game as an argument against another is like
taking the rules of tennis and applying them to hockey – and arguing that
therefore – hockey is deficient – or that it can’t be played
there is no argument to be had here
if you wish to argue the toss – then you step out of the
game context –
but again – if you step out of the propositional game
context here – what are you arguing about?
the root cause of this problem is that Wittgenstein – and
Frege and Russell – think that a propositional rule governed game in a formal
language – must have application – must have relevance – in the non-game
propositional context
and the fundamental problem here is that they have got the
proposition wrong
the proposition – is not a rule-governed expression in some
arbitrary game plan –
but is in fact a proposal – open to question – open to doubt
and uncertain
we can play games with propositions – or we can critically
evaluate them
we do both – however – propositional game playing –
important as it is in our propositional life – is not the main game – is not
the critical analysis of propositions
4.1274. To ask whether a formal concept exists is
nonsensical. For no proposition can
be the answer to such a question.
(So, for example, the question, 'Are there unanalysable
subject-predicate
propositions?' cannot be asked.)
if a proposition is put – the proposition exists
this ‘formal concept’ – is a proposal – is a proposition
the proposal – is the answer
whether you accept that answer or not – is open to question
– open to doubt – and is uncertain
the question – ‘are
there unanalysable subject-predicate propositions?’ – can be asked
it is
asked – by Wittgenstein – in Tractatus 4.1274
4.128. Logical forms are without number.
Hence there are no pre-eminent numbers in logic, and hence
there is no possibility of
philosophical monism or dualism, etc.
a logical form – a propositional form – is a proposal of
propositional structure
a number is a mark in an ordered series – representing a
point in the ordered series –
an ordered series is a game – a number – a token in the game
a proposal of propositional structure – does not involve
game tokens –
as to pre-eminent numbers –
philosophical monism is a proposal – as is philosophical
dualism –
these proposals are open to question – open to doubt – and
uncertain
they are not only possible – they are actual philosophical
proposals – actual philosophical traditions
the idea of one substance as against two – or more – really
just references mathematics –
the notion of a number as an extra-propositional reality –
is illogical rubbish
the best you can say for it is that it has a poetic value
4.2. The sense of a proposition is its agreement and
disagreement with possibilities of
existence and non-existence of states of affairs.
the sense of a proposition – is open to question – open to
doubt and uncertain – whether a relation of agreement with another proposal – a
state of affairs – is affirmed or denied
what exists is what is proposed –
and what is proposed is open to question – open to doubt and
uncertain
what does not exist is not proposed
4.21. The simplest kind of proposition, an elementary
proposition asserts the existence
of a state of affairs.
the proposal – the proposition – however described – i.e. as
‘simple’ – ‘elementary’ – ‘complex’ – is
a state of affairs –
that which is proposed – exists
a proposal – a proposition – is open to question – open to
doubt – and uncertain
4.211. It is a sign of a proposition's being elementary that
there can be no elementary
proposition contradicting it.
if by ‘elementary proposition’ – is meant a proposition that
cannot be put to question – that cannot be put to doubt – that is certain –
there are no elementary propositions
a proposition is a
proposal – open to question – open to doubt – and uncertain
a proposal – whether
described as ‘elementary’ or not – can be contradicted
4.22. An elementary proposition consists of names. It is a
nexus, a concatenation, of
names.
if you construct a proposition that consists of names – that
construction – that proposal – as with any propositional construction – as with
any proposal –
is open to question – open to doubt – and is uncertain
4.221. It is obvious that the analysis of propositions must
bring us to elementary
propositions which consist of names in immediate
combination.
This raises the question of how such combinations into
propositions comes about.
to give a logical analysis of a proposition – is to put it
to question – to put it to doubt – to explore its uncertainty
to pre-empt any such analysis by assuming the conclusion of
the analysis (‘it is obvious that…) – is to proceed illogically
so called ‘elementary propositions’ – ‘propositions that
consist of names in immediate combination’ – can be proposed – can be
constructed
any such proposal – any such construction – is open to
question – open to doubt – is uncertain
4.2211. Even if the world is infinitely complex, so that every
fact consists of infinitely
many states of affairs and every state of affairs is
composed of infinitely many objects,
there would still have to be objects and states of affairs.
‘objects’ and ‘states of affairs’ – are proposals – open to
question – open to doubt – and uncertain
‘there would still have to be objects and states of affairs’
–
whether or not these proposals continue to be used
– is open to question – open to doubt – and is uncertain
4.23. It is only in the nexus of an elementary proposition
that a name occurs in a
proposition.
if elementary
propositions consist of names (4.22) – and propositions are to be analysed into
elementary propositions (4.221) – then a name occurs in a proposition because
the proposition consists of names
what we have here is
an analytical proposal – an analysis of the proposition –
all very well – if
such an analysis suits one’s purpose – and is useful – but that’s it
the logical reality
is –
a proposition is a
proposal –
and any proposal –
analytical or not – is open to question – open to doubt – and is uncertain
4.24. Names are the simple symbols: I indicate them by
single letters ('x','y','z').
I write elementary propositions as functions of names so
that they have the form 'fx',
'f(x,y)', etc.
Or I indicate them by the letters 'p', 'q', 'r'.
the elementary proposition proposal is here translated into
a formal language – a game language –
and here Wittgenstein is putting a game view of the
proposition –
the proposition as a function of names –
the proposition as the game of names
4.241. When I use two signs with the same meaning, I express
this by putting the sign
' = ' between them.
So 'a = b' means that sign 'b' can be
substituted for the sign 'a'.
(If I use an equation to introduce a new sign 'b',
laying down that it shall serve as a
substitute for a sign 'a' that is already known,
then, like Russell, I write the equation -
definition – in the form 'a = b Def.' A definition is
a rule dealing with signs.)
and here we have a rule for the formal game
4.242. Expressions of the form 'a = b' are,
therefore, mere representational devises.
They state nothing about the meaning of the signs 'a'
and 'b'.
expressions of the form 'a = b' – ‘mere
representation devises’ – state nothing about the meaning of the signs ‘a’
and ‘b’ –
and are plays in a formal game
4.243. Can we understand two names without knowing whether
they signify the same
thing or two different things? – Can we understand a
proposition in which two names
occur without knowing whether their meaning is the same or
different?
Suppose I know the meaning of the English word and of a
German word that means
the same: then it is impossible for me to be unaware that
they do mean the same; I
must be capable of translating each into the other.
Expressions like 'a = a' and those derived from them
are neither elementary
propositions nor is there any other way in which they have
sense. (This will become
evident later).
logically speaking – understanding a proposition – is
understanding that the proposition – is a proposal – open to question – open to
doubt – and uncertain –
it is recognizing the that terms of any proposal – are open
to question
and this is the case whether or not you ‘know’ that two
names signify the same thing or not –
even with a translation – the terms are open to question –
the translation is open to question –
as to – 'a = a' –
to propose that ‘a’ can be substituted for ‘a’
– is a misuse of the ‘=’ sign – a misuse of the notion of substitution –
in short there is no ‘substitution’ –
however 'a = a' – could well represent the result –
the conclusion – of a propositional game
4.25. If an elementary proposition is true, the state of
affairs exists: if an elementary proposition is false, the state of affairs does
not exist.
if a proposition – so called ‘elementary’ or not – is put –
the state of affairs is proposed – the state of affairs
exists –
a proposal is true if it is assented to – false if it is
dissented from
a proposal put – exists – and what is proposed – exists –
whether or not it is affirmed or denied
a proposition – is a proposal – open to question – open to
doubt – and uncertain
a proposal of assent – or a proposal of dissent – is open to
question – open to doubt –
and is uncertain
4.26. If all true elementary propositions are given, the
result is a complete description of
the world. The world is completely described by giving all
elementary propositions,
and adding which of them are true and which are false.
all propositions – are never ‘given’ – propositional
action is on-going
truth or falsity is
the question of assent or denial
so called
‘elementary propositions’ are really philosophical constructions –
nevertheless – they
are logically speaking no different to any other proposal – open to question –
open to doubt – and uncertain
there is no such
thing as a ‘complete description’ –
any description is a
proposal – and is open to question – open to doubt – and uncertain
therefore –
logically speaking – incomplete
the world is open to
question – open to doubt – and is uncertain
n n
4.27. For n state of affairs, there are Kn = Ʃ (
)
v=0 v
possibilities of
existence and non-existence.
Of these states of affairs any combination can exist and the
remainder not exist.
that which is proposed – exists –
any such proposal is open to question – open to doubt – and
uncertain
that which is not proposed – does not exist
propositions come and go
4.28. There correspond to these combinations the same number
of possibilities of
truth – and falsity – for n elementary propositions.
here is a rule of the truth function game
4.3. Truth possibilities of elementary propositions mean
possibilities of existence and
non-existence of states of affairs.
a state of affairs is a proposal – a proposition – whether ‘elementary’
– or not –
if such a proposal is put – that state of affairs – as
proposed – exists
and exists – regardless of whether it is assented to – or
dissented from
any such proposal is open to question – open to doubt – and
is uncertain
4.31. We can represent truth-possibilities by schemata of
the following kind ('T' means
'true', 'F' means false; the rows of 'T's' and
'F's' under the row of elementary
propositions symbolize their truth-possibilities in a way
that can be easily
understood):
p q r
T T T
F T T p q
T F T T T p
T T F , F T ', T .
F F T T F F
F T F F F
T F F
F F F
T and F respectively – represent the propositional actions
of assent and dissent
the rows of T’s and
F’s under the rows of propositions represent the possible combinations of
assent and dissent
the above schema – is a representation of possibilities of
the truth value plays in truth functional games
4.4. A proposition is an expression of agreement and
disagreement with truth-
possibilities of elementary propositions
this is a truth
functional analysis of the proposition –
truth-functional
analysis of the proposition is a propositional game
4.41. Truth possibilities of elementary propositions are the
conditions of the truth or
falsity of propositions.
this is a rule of the truth-functional game
4.411. It immediately strikes one as probable that the
introduction of elementary
propositions provides the basis for understanding all other
kinds of proposition.
Indeed the understanding of general proposition palpably
depends on the
understanding of elementary propositions.
how we understand a proposition – is open to question – open
to doubt – and is uncertain
and any proposal of understanding – i.e. – the elementary
analysis – is valid –
and open to question – open to doubt – and uncertain
4.42. For n elementary propositions there are Kn
Ʃ ( Kn) = Ln
K= 0 K
ways in which a proposition can agree and disagree with
their truth-possibilities
the ‘truth possibilities’ of a game proposition – whether
categorized as ‘elementary’ or not – are ‘true’ and ‘false’ –
that is game being proposed here
4.43. We can express agreement with truth possibilities by
correlating the mark 'T'
(true) with them in the schema.
The absence of this mark means disagreement.
ok – here we have a protocol proposal – a protocol rule for
this truth function game
4.431. The expression of agreement and disagreement with the
truth possibilities of
elementary propositions expresses the truth conditions of a
proposition.
A proposition is the expression of its truth conditions.
(Thus Frege was right to use the term as a starting point
when he explained the signs
of his conceptual notation. But the explanation of the
concept of truth that Frege gives
is mistaken: if 'the true' and 'the false' were really
objects, and were the arguments in
~p etc., then Frege's method of determining the sense
of '~p' would leave it absolutely
undetermined.)
a proposal – a proposition – can be affirmed or denied –
and yes you can break a proposition up into components –
affirm or deny the components – and calculate the truth value of the
proposition in accordance with the rules
of truth functional analysis –
this is to play a
propositional game – the truth functional game
however – any
decision on the truth value of the components – or the truth value of the
proposition – is logically speaking – open to question – open to doubt – and
uncertain
if you play the
truth functional analysis game – and play in accordance with its rules then
there is no question – no doubt – no uncertainty –
the rules determine
the outcome of the game –
you play the game in
accordance with the rules – or you don’t play
a proposition is a
proposal – open to question – open to doubt – and uncertain
there is no ‘the
true’ and ‘the false’ –
a true proposition
is a proposal – assented to
a false proposition
– a proposal – dissented from
assent and dissent
are proposals –
open to question –
open to doubt – and uncertain
4.44. The sign that results from correlating the mark 'T'
with truth-possibilities is a
propositional sign.
correlating the mark 'T' with the truth-possibilities
is a game play
the sign that results from correlating the mark 'T'
with the truth possibilities is a game sign
4.441. It is clear that a complex of the signs 'F'
and 'T' has no object (or complex of
objects) corresponding to it, just as there is none
corresponding to the horizontal and
vertical lines or to the brackets. – There are no 'logical
objects'.
Of course the same applies to all signs that express what
the schemata of 'T's' and 'F's'
express.
a truth function game is rule governed
T and F in the truth-function game – are rule
governed game plays
4.442. For example, the following is a propositional sign:
'p q '
T T T
F T T
T F
F F T.
(Frege's 'judgement-stroke' '/-' is logically quite
meaningless: in the works of Frege
(and Russell) it simply indicates that these authors hold
the propositions marked with
this sign to be true. Thus '/-' is no more a component part
of a proposition than is, for
instance, the proposition's number. It is quite impossible
for a proposition to state that
it itself is true.)
If the order of the truth-possibilities in a schema is fixed
once and for all by a
combinatory rule, then the last column by itself will be an
expression of the truth-
conditions. If we now write this column as a row, the
propositional sign will become
'(TT-T) (p,q)'
or more explicitly
'(TTFT) (p,q)'.
(The number of places in the left hand pair of brackets is
determined by the number of
terms in the right-hand pair).
Frege and Russell’s judgment stroke – is a sign in a different
game
from the point of view of Wittgenstein’s game – it is
unnecessary and confusing
different propositional games – with different rules – are
not comparable
Wittgenstein wants an argument – but there is no argument
here–
you play one game or you play the other
‘If the order of the truth-possibilities in a schema is
fixed once and for all by a
combinatory rule, then the last column by itself will be an
expression of the truth-
conditions.’
Wittgenstein makes clear here that his game is rule-governed
4.45. For n elementary propositions there are Ln possible
groups of truth conditions.
The groups of truth-conditions that are obtainable from the
truth possibilities of a
given number of elementary propositions can be arranged in a
series.
yes – you can propose this schema – these rules – this game
4.46. Among the possible groups of truth conditions there are
two extreme cases.
In one of these cases the proposition is true for all the
truth possibilities of the
elementary propositions. We say that the truth conditions
are tautological.
In the second case the proposition is false for all the
truth-possibilities; the truth
conditions are contradictory
In the first case we call the proposition a tautology; in
the second, a contradiction.
the truth or falsity of a proposition – is not a matter of
propositional construction
a proposition is true – if it is assented to – false if
dissented from
a propositional game is a rule governed propositional action
a propositional game is neither true or false –
you play the game – according to its rule – or you don’t
play –
the tautology and the contradictions are propositional games
–
they are rule governed constructions
in the game of truth functional analysis – there is no
question as to whether the tautology is true – the rule of the game determines
that it is
and the rule is that the contradiction is false
the tautology and the contradiction are rule governed
definitions of true and false – of assent and dissent – in the truth functional
analysis game
4.461. Propositions show what they say: tautologies and
contradictions show that they
say nothing.
A tautology has no truth conditions, since it is
unconditionally true: and a
contradiction is true on no condition.
Tautologies and contradictions lack sense.
(Like a point from which two arrows go out in opposite
directions to one another.)
(For example, I know nothing about the weather when I know
it is either raining or
not raining.)
the tautology game and the contradiction game are played in
certain propositional games
the question of sense does not apply to games – to
propositional games –
games are rule governed propositional actions – you follow
the rules – you play the game – or you don’t
4.4611. Tautologies and contradictions are not, however,
nonsensical. They are part of
the symbolism, much as '0' is part of the symbolism of
arithmetic.
tautologies and contradictions are rule governed
propositional / sign games
games are without sense
games have rules – not sense
this much we can say –
in so far as playing games – is a natural propositional
activity or behaviour of human beings –
that is to say – it
is just what we do –
playing games ‘makes sense’ to us
4.462. Tautologies and contradictions are not pictures of
reality. They do not represent
any possible situations. For the former admit all
possible situations and the latter
none.
In a tautology the conditions of agreement with the world –
the representational
relations – cancel one another, so that it does not stand in
any representational relation
to reality.
reality is propositional –
propositions are open to question – open to doubt – and
uncertain
tautologies and contradictions – are propositional games
the question is then – in what propositional context these
propositional games have function and use?
i.e. – I would have thought that it is pretty clear that the
tautology and the contradiction games function in truth-functional analysis
propositional games are played – they have function in our
reality – our propositional reality –
and in so far as they are played – they picture or reflect our
reality
4.463. The truth conditions of a proposition determine the
range that it leaves open to
the facts.
(A proposition, a picture, or a model is, in the negative
sense, like a solid body that
restricts the freedom of movement of others, and, in the
positive sense, like a space
bounded by solid substance in which there is room for a
body.)
A tautology leaves open to reality the whole – the infinite
whole – of logical space: a
contradiction fills the whole of logical space leaving no
point of it for reality. Thus
neither of them can determine reality in any way.
‘the facts’ – are proposals – are propositions
the truth conditions of a proposition are the grounds given
for assent or denial of the proposition –
any decision of assent or dissent – is open to question –
open to doubt – and is uncertain
a proposition is a proposal – open to question – open to
doubt – and uncertain
the tautology is a game that defines true – defines assent –
in truth-functional games
the contradiction is a propositional game – that defines
false – defines dissent – in truth-
functional games
a proposition – a proposal – does not determine
reality – it proposes reality –
a propositional game is a structured use of propositions –
the point of which is play
4.464. A tautology’s truth is certain, a proposition’s
possible, a contradiction’s impossible.
(Certain, possible, impossible: here we have the first
indication of the scale that we need in the theory of probability.)
a tautology is a sign game within the truth functional
analysis game
it is defined as certain – defined as – always true
the contradiction is a sign game in the truth functional
analysis game
the truth functional analysis game defines the contradiction
construction – as always false
‘true’ and ‘false’ – in propositional games – are rules of
play
a game is neither true or false
the game is played or it is not –
a game is not certain – or impossible –
a game is a rule governed play
a proposition is not a game – a proposition is a proposal –
a proposal is open to question – open to doubt – and
uncertain
a proposition is true – if assented to
a proposition is false – if dissented from
probability theory – is a game theory –
probability is a calculation game –
a game – grounded in propositional uncertainty
4.465. The logical product of a tautology and a proposition
says the same thing as the
proposition. This product therefore is identical with the
proposition. For it is
impossible to alter what is essential to a symbol without
altering its sense.
if as Wittgenstein holds – the tautology says nothing – then
if you add it to a proposition
the ‘product’ – adds nothing –
the play of – or use of – a propositional game – has no
baring on the logical status of a proposition – it’s a sideshow – a logically
irrelevant sideshow
4.466. What corresponds to a determinate logical combination
of signs is a
determinate logical combination of their meanings. It is
only to the uncombined signs
that absolutely any combination corresponds.
In other words, propositions that are true for every
situation cannot be combinations
of signs at all, since if they were, only determinate
combinations of objects could
correspond to them.
(And what is not a logical combination has no combination of
objects corresponding
to it.)
Tautology and contradiction are limiting cases – indeed the
disintegration – of the
combination of signs.
any sign – or any combination of signs – and any proposed
meaning – is open to question – open to doubt – and uncertain
a proposition is true – if assented to –
‘every situation’ is in effect – every proposition
we cannot know ‘every situation’ – every proposition –
and it is therefore pointless and ridiculous to talk of
assent to – or dissent from – ‘every situation’
‘objects’ – are proposals – propositions
‘a determinate combination of objects’ – is a proposal – a
proposition – open to question – open to doubt and uncertain
‘a logical combination’ – of signs – is a proposal –
‘what is not a logical combination of signs’ – is a
combination of signs that has no propositional reference –
hard to imagine why such a combination would ever be put
the tautology and the contradiction are propositional games
–
they are truth value definition games in truth functional
analysis
4.4661. Admittedly the signs are all still combined with one
another even in
tautologies and contradictions – i.e. – they stand in a
certain relation to one another:
but these relations have no meaning, the are not essential
to the symbol
the point is that a symbol – is a proposal – a proposition –
open to question – open to interpretation
representing a symbol in terms of a combination of signs –
is to translate the symbol into a formulation – for a particular use
any such translation – is a proposal – open to question
the meaning of a sign or a combination of signs – is open to
question – open to doubt – and uncertain
there is nothing essential
to a proposition – to a symbol –
any symbol – any proposition – is open to question – open to
doubt – and uncertain
where symbols or signs function as propositional games –
their meaning and use is rule governed
of course any rule governed propositional action is open to
question – open to doubt – and is from a logical point of view – uncertain
however logical assessment and analysis – is not to be
confused with propositional game playing
4.5. It now seems possible to give the most general
propositional form: that is, to give
a description of the propositions of any sign
language whatsoever in such a way that
every possible sense can be expressed by a symbol satisfying
the description, and
every symbol satisfying the description can express a sense,
provided that the meaning
of the names is suitably chosen.
It is clear that only what is essential to the most
general propositional form may be
included in its description – for otherwise it would not be
the most general
propositional form.
The existence of a general propositional form is proved by
the fact that there cannot
be a proposition whose form could not have been foreseen
(i.e. constructed). The
general form of the proposition is: This is how things
stand.
the most general propositional form –
would be the most general propositional structure
any proposal of a general propositional structure – is open
to question – open to doubt – and is uncertain
the idea that ‘every possible sense can be expressed by a
symbol’ –
is simply to say that we can propose the sense of a
proposition in the form of a symbol
the sense of a proposition – whatever its form – is open to
question – any symbol is open to question – names are open to question
‘what is essential to the most general propositional form
may be included in its description …’
if by ‘essential’ is meant some final characterization of
the proposition – then we are in the realm of epistemological delusion –
we propose those descriptions – and work with those
descriptions that we regard as functional and useful
any description of the proposition – and any use of any
description – logically speaking – is open to question – open to doubt and
uncertain
‘there cannot be a proposition whose form could not have been
foreseen (i.e. constructed)’ –
the form of a proposition is not a question of foresight
what we deal with is what is proposed
‘this is how things stand’ – is to say – ‘this is what is
proposed’
4.51. Suppose that I am given all elementary
propositions: Then I can ask what
propositions I can construct out of them. And there I have
all propositions, and that
fixes the limits.
a so called ‘elementary proposition’ – is an analysis
of a proposition – an analysis which like the subject proposition – is open to
question – open to doubt – and uncertain
the notion of all propositions – all proposals
– ‘elementary’ – or not – is fanciful
we work with what is proposed –
we don’t know – we don’t work with ‘all’ – so called –
‘elementary propositions’
and what is proposed – whenever and wherever – it is
proposed – is the limit of our propositional action –
you can construct propositional games –
you could construct a game whose basis is ‘any’ elementary
proposition –
and this I think is the game Wittgenstein has in mind
4.52. Propositions comprise all that follows from the
totality of all elementary
propositions (and, of course, from its being the totality
of them all). (Thus, in a certain
sense, it could be said that all propositions are
generalizations of elementary
propositions.)
propositions are not constructions of elementary
propositions –
propositions are proposals
an elementary proposition – is the result of a particular
analysis of the proposal – the
proposition –
the proposition exists – before the analysis of the
proposition –
however any analysis of the proposition – will produce
further proposals – further propositions
a so called ‘elementary proposition’ – is a proposal –
propositions – however analysed – however classified –
however described –
are open to question – open to doubt – and uncertain
we don’t know this ‘totality of all elementary
propositions’ –
we don’t actually deal with – a ‘totality of all elementary propositions’ –
propositions do not comprise all that follows from
the totality of all elementary
propositions –
this idea of a totality of propositions – elementary or not
– is in the true sense of the word ‘fanciful’ –
and this idea of a ‘totality of all propositions’ – has no
bearing on propositional action
has no bearing on the propositions we put and we use –
it is logically speaking – a completely irrelevant notion
we don’t put – ‘a totality of elementary propositions’ – to
question – to doubt –
what we put to question and doubt are the propositions we
propose – and the propositions put to us
this ‘all propositions are generalizations of elementary
propositions’ – is at best a propositional game –
that is – a rule governed propositional action –
a rule governed propositional action – is not a logical
activity –
it is a game activity – an activity of play –
it is not the logical activity of question – of doubt – of
dealing with propositional uncertainty
and if presented as such – it is misunderstood – and
misrepresented
4.53. The general propositional form is a variable.
any proposal regarding – the general propositional form – is
open to question – open to doubt – and is uncertain
Tractatus 5
5. A proposition is a truth function of elementary
propositions.
(An elementary proposition is a truth function of itself.)
a proposition is not a truth function of elementary
propositions
a proposition is not a truth function
a proposition is a proposal – open to question – open
to doubt – and uncertain
truth functional analysis – is a propositional game
a propositional game is a rule governed propositional action
game propositions – and games – as played – are not
put to question –
if by elementary proposition – is meant a proposal that
cannot be further analysed – that is not open to question – not open to doubt –
and not uncertain –
then there are no elementary propositions
a proposition is not a truth function of itself
a proposition may function in a truth functional game
–
but it is not a truth functional game –
it is a token in a truth functional game
5.01. Elementary propositions are the truth-arguments of
propositions.
if by elementary proposition is meant a proposition that is
not open to question – not open to doubt – and not uncertain
there are no elementary propositions
so the question becomes – are propositions truth arguments
of propositions?
a proposition – is a proposal – open to question – open to
doubt – and uncertain
the truth of a proposition – is a matter of assent or
dissent
any proposal of assent or dissent – is open to question –
open to doubt – and uncertain
it is here that argument is relevant
5.02. The arguments of functions are readily confused with
the affixes of names. For
both arguments and affixes enable me to recognize the
meaning of the signs
containing them.
For example, when Russell writes '+c', the 'c'
is an affix which indicates that the sign
as a whole is the addition-sign for cardinal numbers. But
the use of this sign is the
result of arbitrary convention and it would be quite
possible to choose a simple sign
instead of '+c'; in '~p', however, 'p'
is not an affix but an argument: the sense of '~p'
cannot be understood unless the sense of 'p'
has been understood already. (In the name
Julius Caesar 'Julius' is an affix. An affix is already part
of a description of the object
to whose name we attach it: e.g. the Caesar of the
Julian gens.)
If I am not mistaken, Frege's theory about the meaning of
propositions and functions
is based on the confusion between an argument and its affix.
Frege regarded the
propositions of logic as names, and their arguments as the
affixes of those names.
the propositions of logic – of formal logic – are rule
governed propositions – game propositions – game tokens
how they are termed – how they are presented – is a question
of game and rule definition
different games – different rules – different definitions –
and different conventions
5.1. Truth functions can be arranged in series.
That is the foundation of the theory of probability.
truth functional analysis is a propositional game –
the foundation of the theory of probability – of the
probability game – is propositional uncertainty
5.101. The truth functions of a given number of elementary
propositions can always
be set out in a schema of the following kind:
(TTTT) (p,q) Tautology (If p then p and if q then q.) (p É q. q
É q)
(FTTT) (p,q) In words: Not both p and q. (~(p.q)
(TFTT) (p,q) " " : If q then p. (q É p)
(TTFT) (p,q) " " : If p then q. (p É q)
(TTTF) (p,q) " " : p or q. (p v q)
(FFTT) (p,q) " " : Not q. (~q)
(FTFT) (p,q) " " : Not p. (~p)
(FTTF) (p,q) " " : p or q, but not both. (p. ~q: v : q. ~p)
(TFFT) (p,q) " " : If p then q, and if q then p. (p = q)
(TFTF) (p,q) " " : p
(TTFF) (p,q) " " : q
(FFFT) (p,q) " " : neither p nor q. (~p. -q or p/q)
(FFTF) (p,q) " " : p and not q. (p. ~q)
(FTFF) (p,q) " " : q and not p. (q. ~p)
(TFFF) (p,q) " " : q and p. (q . p)
(FFFF) (p,q)
Contradiction (p and not p, and q and not q.) (p. ~p . q. ~q)
I will give the name truth-grounds of a proposition to those
truth-possibilities of its
truth-arguments that make it true.
here we have the rules of the truth functional analysis game
T and F are truth function possibilities –
their possible combinations are truth functional games
the truth grounds of a proposition – are the reasons given
for its assent – or dissent –
the truth arguments are the arguments for the truth grounds
the truth grounds and the truth arguments of a proposition –
are open to question – open to doubt – and uncertain
we are not dealing with propositions here –
Wittgenstein’s above schema is a game plan
the ‘propositions’ in this game ‘p’ and ‘q’ –
are game tokens –
the game schema above sets out the different games that can
be played with different combinations of T and F as applied to ‘p’
and ‘q’ –
these games – have nothing to do with the truth grounds of
propositions or the truth arguments for propositions
the schema lays out the truth possibilities as applied to
the game tokens –
any application of these truth functional games – is
just the playing of these games –
formal logic – is formal game
5.11. If all the truth grounds that are common to a number
of propositions are at the
same time truth-grounds of a certain proposition, then we
say that the truth of that
proposition follows from the truth of the others.
this is a truth function game rule
5.12. In particular, the truth of a proposition 'p'
follows from the truth of another
proposition ‘q’ if all the truth-grounds of the
latter are truth grounds of the former.
that ‘p’ ‘follows from’ ‘q’ – is a
propositional game – a rule governed propositional action
the game is the ‘follows on’ game –
where the rule is that the all the truth grounds of the
latter are the truth grounds of the former
if that rule is not followed – there is no game
in non-game propositional activity – there is no ‘follows
on’ –
the truth grounds of
a proposition – are the grounds or reasons for assent to that proposition – or
the grounds or reasons for dissent from it
there is no automatic ‘follow on’ with respect to assent or
dissent –
‘p’ and ‘q’ and their relationship – is open
to question – open to doubt and uncertain
grounds of assent are proposals in relation to the
propositions
the proposition as such is neither true nor false
the truth or falsity of a proposition is not a
characteristic of the proposition –
the truth of a proposition is a proposal – a decision – with
respect to that proposition –
with ‘p’ and ‘q’ – what you have is two
different propositions – and two separate propositional actions of assent –
any proposal of assent or dissent is open to question – open
to question – open to doubt – and uncertain
that it is argued that they share the same grounds – is
actually logically irrelevant –
however such a proposal can form the basis – or the rule –
for a language game – a formal logic game
5.121. The truth grounds of one are contained in the other: p
follows from q
in non-game propositional activity – where the proposition –
the proposal – is open to question – open to doubt – and uncertain –
the grounds of one are not contained in the other –
the truth grounds of p are proposed – the truth
grounds of q are proposed –
the grounds of assent – are separate proposals – to the
propositions in question
and as such are open to question – open to doubt – and
uncertain
where it is proposed that they do correspond –
you have a separate relating proposal – open to question –
open to doubt – and uncertain
p does not ‘follow from’ q – if by
‘follow from’ is meant that there is an internal relation between p and q
there are no ‘internal’ propositional relations –
any relation is a proposal and as such is external
and separate to the propositions in question
that propositions have common grounds of assent – is a
proposal external to the propositions in question
on the other hand – in a game context – in a rule governed
propositional action –
that he truth grounds of one are contained in the other – is
a game rule
the game is the ‘follows from’ game
we can play this and other games –
and we play such games for various reasons –
i.e. they can provide a sense of order – structure – and
coherence – to our propositional practice – to our propositional reality
5.122. If p follows from q, the sense of 'p'
is contained in the sense of 'q'
you can play a language game where the rule is that the
sense of ‘p’ is contained in the sense of ‘q’
in the ‘follow on game’ – the ‘sense’ of the proposition –
is determined – is rule governed
in non-game propositional activity – p and q
can be related via a proposal – by a proposition –
the proposal of a relation – is separate to and external to p
and q
just as p and q are separate and external to
each other
the logical reality is that any proposed relation between p
and q – is open to question – open to doubt and is uncertain
just as the sense of any proposition – is open to question –
open to doubt and is uncertain
5.123. If a god creates a world in which certain
propositions are true, then by that very
act he also creates a world in which all the propositions
that follow from them come
true. And similarly he could not create a world in which the
proposition 'p' was true
without creating all its objects.
propositions are not created true – propositions are
proposals – open to question – open to doubt – and uncertain
propositions are decided on – they are assented to (T)
– or dissented from (F) –
and the propositional actions of assent or dissent – are
like the proposition assented to or dissented from – open to question – open to
doubt – and uncertain
a proposition is not inherently related to another
proposition –
propositional relations are proposed
and truth is not some inherent property of a proposition –
that magically transfers from one proposition to another
a true proposition is a proposition assented to –
any proposal is open to question – open to doubt – and
uncertain –
we can and do construct propositional games – like the
‘follow on’ game –
you do not ask if a game is true or false – you simply play
it – according to its rules
you can question its rules – however questioning its rules –
is not playing the game –
the questioning of rules – is a logical activity
if you play – you play according to the rules proposed
the propositional game provides relief from the logical
activity of question – doubt – and uncertainty
and logical activity provides relief from – play
5.124. A proposition affirms every proposition that follows
from it.
propositions do not affirm themselves –
the truth or a falsity of a proposition is not a
property of the proposition
affirmation is the decision to accept a proposal – to
proceed with it
affirmation is a propositional action in relation to a
proposition
propositional follow on – is a propositional game
propositional games are neither true or false
propositional games are not affirmed or denied –
a propositional game is played – or it is not played
141.
5.1241. 'p . q' is one of the propositions that
affirm 'p' and at the same time one of the
propositions that affirms q.
The two propositions are opposed to each other if there is
no proposition with a
sense, that affirms them both.
Every proposition that contradicts another negates it.
if the context is that of the propositional game – i.e. – a
truth function game – the above can be regarded as rules for that game
outside of that context the matter is not so straightforward
‘p . q’ is a proposal –
‘p . q’ – is a proposal – a proposal that relates ‘p’
and ‘q’ –
‘p . q’ neither affirms or denies ‘p’ or affirms or denies ‘q’ –
it proposes ‘p . q’ –
affirmation is a propositional action – external to the
proposition(s) in question
it is the decision to accept the proposition – the decision
to proceed with the proposition
if ‘p. q’ is affirmed – is agreed to – then ‘p. q’
just is – the affirmation of ‘p’
– and – the affirmation of ‘q’
two propositions are opposed to each other?
if I say – ‘that fabric is green’ – and you say ‘no, it’s
blue’ –
our propositions are opposed to each other –
if we further discuss the matter – and come up with the
proposition – ‘the fabric is blue-green’ –
then we have put a proposal that recognizes that our
original propositions are open to question – open to doubt – and uncertain
the third proposal –‘the fabric is blue-green’ – is no less
uncertain – but it is a way forward
negation –
‘every proposition that contradicts another negates it’?
in the proposition ‘p . ~p’ – we have a
contradiction
‘p’ – asserted – is a proposal –
‘~p’ – is not a proposition – rather a
dissention from – or the signification of a dissention from ‘p’
this conflict – is represented as – ‘p . ~p’
however there is only one proposition in ‘p . ~p’ – and that is ‘p’
‘~p’ is not a proposal
‘negation’ – is the representation (‘~’) – of
dissent from
where a proposition is ‘negated’ it is denied –
in a denial – the proposition is rejected –
in a rejection – nothing is proposed
5.13 When the truth of one proposition follows from the
truth of others we can see
this from the structure of the propositions.
if so it is clear that what we are dealing with is a
propositional game –
where the rule just is that the structure of the
propositions shows that one proposition follows from others –
whether the proposition is actually affirmed or not – is
irrelevant to the game
the game just is that the truth of one follows from the
truth of others
what we are talking about really is not the structure of the
propositions involved – but rather the rule of the game – that is to say – the
structure of the game –
the ‘follows from’ game
5.131. If the truth of one proposition follows from the
truth of others, this finds
expression in relations in which the forms of the
propositions stand to one another;
nor is it necessary for us to set up these relations between
them, by combining them
with one another in a single proposition; on the contrary,
the relations are internal, and
their existence is an immediate result of the existence of
the propositions.
if the truth of one game proposition follows from the truth
of others – this is an expression of the rule of the propositional game
– the ‘follows from’ game
outside of the game context – in a logical / critical
context – the matter is entirely different
relations between propositions are external – external propositions –
there are no ‘internal’ relations
a relation is a proposal – is a proposition – that relates
separate and different propositions
a relation – by definition – does not subsist – or cannot
exist – in a proposition
these external relations / propositions – exist – if they
are proposed
5.1311. When we infer q from p v q and ~p,
the relation between the propositional
forms of 'p v q' and '~p' is masked, in this
case, by our mode of signifying. But if
instead of 'p v q' we write for example, 'p\q.\
.p\q', and instead of '~p', 'p\p' (p\q =
neither p nor q), then the inner connection
becomes obvious.
(The possibility of inference from (x). fx to fa
shows that the symbol (x). fx has
generality in it.)
there is no ‘inner connection’ revealed
what you have here – is different variations of the one game
–
this internality argument – and ‘inner connection’ business
– is just mystical rubbish –
it is not propositional logic
a sign does not have generality – in it
a sign can represent a generality game –
that is – a rule
governed propositional game
5.132. If p follows from q, I can make an
inference from q to p, deduce p from q.
The nature of the inference can be gathered only from the
two propositions.
They themselves are the only possible justification of the
law of inference.
'Laws of inference', which are supposed to justify
inferences, as in the works of Frege
and Russell, have no sense, and would be superfluous.
‘If p follows from q, I can make an inference
from q to p, deduce p from q.’
here is a propositional game
in the game context we are not dealing with an inference –
rather – a rule of play
and a game is not ‘justified’ – it is rule governed
in the logical / critical context – an inference is a
relational proposal –
the inference is not ‘gathered from’ the two propositions –
the inference proposal – is separate to – and external to
the propositions it relates –
it must be proposed – if is to be
there is no ‘justification’ for a proposal – for a
proposition –
a proposition is open – open to question – open to doubt –
and is uncertain
a so called ‘law of inference’ – is nothing more than a
relational proposal – wrapped up in pretentious rhetoric
and as with any proposal – an inference – is open to
question – open to doubt – and – is uncertain
5.133. All deductions are made a priori.
deductions are propositional games
5.134. One elementary proposition cannot be deduced from
another.
and the reason is – there are no elementary propositions
a proposition is a proposal – open to question – open to
doubt – and uncertain –
a proposition is not beyond interpretation – not beyond
reformulation
deduction is a rule governed propositional game
any genuine proposition can be a token in a deductive game
5.135. There is no possible way of making an inference from
the existence of one situation to the existence of another, entirely different
situation
inference – is a relational proposal –
in the propositional activity of relating proposals – we are
relating different proposals
if there is no possible way of making an inference from one situation
– one proposal – to another – there are no – there can be no – relational
proposals –
and if there are no relational proposals – there is no
propositional activity
this argument defies propositional reality – and is absurd
5.136. There is no causal nexus to justify such an
inference.
the only ‘nexus’ is propositional –
inference is a relational proposal
any explanation – of a proposed relation between
propositions – be it causal or otherwise – is propositional – is open to
question – open to doubt – and uncertain
logically speaking there is no ‘justification’ – if by
‘justification’ you mean a logical end to question doubt and uncertainty
‘justification’ – is best seen as a pragmatic decision – to
proceed – in the face of uncertainty
5.1361. We cannot infer the events of the future from
those of the present.
Superstition is nothing but belief in the causal nexus.
human beings do infer events of the future from those
of the present
an inference is a proposal – a proposal is open to question
– open to doubt – and uncertain
5.1362. The freedom of the will consists in the
impossibility of knowing actions that still lie in the future. We could know
them only if causality were an inner necessity like that of logical
inference. – The connection between knowledge and what is known is that of
logical necessity.
(‘A knows that p is the case’, has no sense if
p is a tautology.)
our freedom rest in – is a consequence of – propositional
uncertainty
proposals concerning the past – proposals concerning the
present – and proposal concerning the future – are open to question – open to
doubt – and uncertain
causality is a proposal –
logical inference is a propositional relation – a
propositional action – relating propositions –
the relating proposition and the propositions related – are
external to one another
there is no inner dimension to propositions – there is no
propositional necessity –
propositions are open to question – open to doubt – and
uncertain
our knowledge – is what we propose – and what we know – is
propositional – open to question – open to doubt – and uncertain
the connection between knowledge and what is known – is the
proposal
in ‘A knows that p’ –
if p is constructed or analysed as a tautology (p
v-p) – then the A knows that p is a proposition of truth functional analysis
that is to say A knows that p is a game
proposition
and that in the truth functional analysis game – the
tautology has function
5.1363. If the truth of a proposition does not follow
from the fact that it is self-evident
to us, then its self-evidence in no way justifies our belief
in its truth.
the truth – the affirmation of a proposition – is a proposal
in relation to the proposition
a proposition does not – cannot affirm – or deny – itself
a proposition has no ‘self’ – no internality –
a proposition is a proposal of signs –
any proposed relation between signs – is a separate proposal
– external to the signs
this idea of the self-evident proposition – is at best a
game proposal
self-evidence as a propositional game
in the realm of logic – it makes no sense
in terms of prejudice and rhetoric – self evidence has a
long and inglorious history
a proposition is open – not closed – open to question
– to doubt – to response – to interpretation
self-evidence – is evidence only – of a closed mind –
or the desire to put an end to uncertainty – which amounts
to the end of propositional reality
it’s the ‘logical’ death wish –
so the above statement –‘
‘If the truth of a proposition does not follow from the fact
that it is self-evident to us, then its self-evidence in no way justifies our
belief in its truth’ –
ironically – is on the right track
the truth of proposition does not follow from the
fact that it is self-evident to us –
and so this claim of self-evidence – this pretence of
self-evidence – has nothing to do with the question of the proposition’s truth
– has nothing to do with whether the proposition is affirmed or denied
‘justification’ – at best is a pragmatic decision – to simply
proceed – in the face of uncertainty
at worst it is the ignorant assumption of certainty
5.14. If one proposition follows from another, then the
latter says more than the
former, and the former less than the latter.
‘If one proposition follows from another …’ – what you have
is a propositional game –
and you can propose whatever rules you like to this game –
the object of the game – is its play –
game playing is not the activity of propositional logic –
propositional logic is the activity of question – of doubt –
and of dealing with uncertainty
from a logical point of view what you actually have with
this ‘follow on’ game – is simply a
proposition put in relation to the
initial proposition –
there is no magical ‘following on’ of propositions one to
the other
propositions are put or
they are not put –
the putting of a proposition in relation to another
proposition – is a propositional act
– an action made independent of the subject proposition
and whether one proposition says more or less than the other
– is a matter open to question – open to doubt – and is uncertain
5.141. If p follows from q and q from p,
then they are one and the same proposition.
you can propose this game – that is the ‘follows
from’ game
a propositional game is a play with propositions –
a propositional game is a ruled governed play –
that is to say the game as played – is not open to
question – open to doubt – or uncertain
you don’t question the game – you play it – or you don’t
however if we are talking about logical analysis – a
critical assessment of propositions – as
distinct from propositional game playing –
then p and q – if they are genuine proposals
– genuine propositions – they are different and distinct
and therefore they are not one in the same
furthermore – p and q – as genuine propositions – are open to question – open to doubt – and
uncertain –
as indeed is any proposed relation between them
5.142. A tautology follows from all propositions: it says
nothing
a tautology is a game proposition – the tautology is a game
the rule of the game is that the truth value of the
tautological proposition – i.e. ‘p ˅ ~p’
– in a truth functional analysis – is always ‘true’
the rule is the game – the game is the rule
and yes – you can
play the tautology game with the ‘follows’ from game
the key thing to understand is that a game is played –
a game does not propose
5.143. Contradiction is that common factor of propositions
which no proposition has
in common with another. Tautology is the common factor of
all propositions that have
nothing in common with one another.
Contradiction, one might say, vanishes outside all
propositions: tautology vanishes
inside them.
Contradiction is the outer limit of propositions: tautology
is the unsubstantial point at
the centre.
the contradiction as with the tautology is a propositional game
construction
the contradiction as with the tautology is a game in the
truth functional analysis game –
it is not a proposal
a propositional game is a rule governed construction
a proposition in the logical sense – is not rule governed –
it is a proposal – that is open – open to question –
open to doubt – and uncertain
in our propositional life – there are two modes of
propositional practice – the game mode and the logical mode
we play games with propositions – and – we put
propositions to question – to doubt – and we explore their uncertainty
we play and we question
5.15. If Tr is the number of truth grounds of a
proposition 'r', and if Trs is the number
of truth grounds of a proposition ‘s’ that are at the
same time truth-grounds of 'r', then
we call the ratio Trs: Tr the degree of probability
that the proposition 'r' gives to the
proposition 's'.
this is an outline of a truth-functional game
from a logical point of view – the truth grounds of a
proposition – are those proposals put – as the reasons for affirmation – of the
proposition
these proposals as with the subject proposals – are open to
question – open to doubt – and uncertain
in the ‘Trs game’ –
if Trs is the number of truth grounds of a
proposition ‘s’ that are the same truth grounds of ‘r’ – then ‘s’
and ‘r’ share the same truth grounds –
what you have here is a rule and its play
probability is a propositional game –
you can play the probability game with the Trs game
5.151. In a schema like the one above in 5.101, let Tr
be the number of 'T's' in the
proposition r, and let Trs be the number of 'T's'
in the proposition s that stand in
columns in which the proposition r has 'T's'.
Then the proposition r gives to the
proposition s the probability Trs : Tr.
what we have here is a propositional game and its rule –
if the number of ‘T’s’
in the proposition s that stand in columns in which the proposition r
has T’s –
then s and r share the same number of ‘T’s’
in the relevant columns –
this is a sign game
5.1511. There is no special object peculiar to probability
propositions.
probability is a rule governed propositional game
it has no logical significance
5.152. When propositions have no truth arguments in common
with one another, we
call them independent of one another.
Two elementary propositions give one another the probability
1/2.
If p follows from q,
then the proposition 'q' gives to the
proposition 'p' the probability
1. The certainty of logical inference is a limiting case of
probability.
(Application of this to tautology and contradiction.)
in logical terms – one proposition is independent of another
– regardless of whether it has truth grounds in common with the other –
the truth grounds of propositions are separate proposals –
separate to the propositions in question
that two (elementary) propositions give one another the
probability ½ is a game construction – as is the ‘follow-on’ game
games within games
the so called ‘certainty’ of logical inference – is a
fraud
in propositional logic an inference is a proposal –
open to question – open to doubt – and uncertain
if ‘inference’ is put as a game rule – then yes that rule
determines a limiting play in the probability game
the tautology and the contradiction are game propositions –
and in the truth functional analysis game – they function as limiting cases –
or the limits of play
5.153. In itself, a proposition is neither probable nor
improbable. Either an event
occurs or it does not: there is no middle way.
a proposition is a proposal – open to question – open to
doubt – and uncertain
probability is a game – a rule governed propositional
construction
any event – in the absence of proposal – in the absence of
description – is an unknown
the event as proposed – as described – is open to question –
open to doubt – and uncertain
‘either an event occurs or it does not’ – is to say – ‘p ˅ ~p’
a neat little propositional game – the tautology –
however as Wittgenstein has been at pains to point out –
‘it says nothing’ – that is – nothing is proposed
5.154. Suppose that an urn contains black and white balls in
equal numbers (and none
of any other kind). I draw one ball after another, putting
them back in the urn. By this
experiment I can establish that the number of black balls
drawn and the number of
white balls drawn approximate to one another as the draw
continues.
So this is not a mathematical truth.
Now, if I say, 'The probability of my drawing a white ball
is equal to the probability of
my drawing a black one', this means that all the
circumstances that I know of
(including the laws of nature assumed as hypotheses) give no
more probability to the
occurrence of one event than to the other. That is to say,
they give each the probability
1/2 as can easily be gathered from the above definitions.
What I confirm by the experiment is that the occurrence of
the two events is
independent of the circumstances of which I have no more
detailed knowledge.
the rule of equal black and white – already establishes the
‘approximation’
that there is an equal probability of drawing a white as a
black – is the rule of this probability game
how the game plays out – what actually happens – is
another matter –
all we can really say before any draw – is that that the result is uncertain
and that is the case – regardless of what I know of the
circumstances surrounding the two events
what will happen is uncertain –
probability is a game – the ground of which is – uncertainty
in propositional analysis we explore uncertainty – in
probability games we play with uncertainty
5.155. The minimum unit for a probability proposition is
this: The circumstances – of
which I have no further knowledge – give such and such a
degree of probability to the
occurrence of a particular event.
a proposal – a proposition – is what I know –
any such proposal is open to question – open to doubt – and
uncertain
my knowledge is uncertain
from a logical point of view – ‘the circumstances of which I
have no further knowledge’ – is what is not proposed – has not been proposed
what is not proposed – has not been proposed – is not
propositionally relevant – is not propositionally active –
what is not proposed – is not there –
what we deal with in our propositional life is – what is –
and what is – is what is proposed
as to the probability game – yes it is a play with
the unknown –
grounded in uncertainty
5.156. It is in this way that probability is a
generalization.
It involves a general description of the propositional form.
We use probability only in default of certainty – if our
knowledge of a fact is not
indeed complete, but we do know something about its
form.
(A proposition may well be an incomplete picture of a
certain situation, but it is
always a complete picture of something.)
A probability proposition is a sort of excerpt from other
propositions.
probability is a game – the generalization is the game
the relevant propositional form / structure here – is the
game – rule governed propositional action
there is no – ‘in default of certainty’ –
any propositional form / structure is open to
question – open to doubt – and is uncertain
you can use probability game if you are interested in
playing games –
as soon as you propose a ‘probability proposition’ – you
propose the probability game
5.2. The structures of propositions stand in internal
relations to one another.
the structures of propositions do not stand in internal relations to one another
any proposed relation between structural proposals –
is a separate and external
proposal to the proposals of
structure
5.21. In order to give prominence to these internal
relations we can adopt the
following mode of expression: we can represent a proposition
as a result of an
operation that produces it out of other propositions (which
are the bases of the
operation).
‘we can represent a proposition as a result of an operation
that produces it out of other propositions (which are the bases of the
operation)’ –
is a game rule –
a propositional game rule –
you can construct a game with any rule – any notion – even
one as fanciful as ‘internal relations’ –
and you can play the game in terms of that rule
5.22. An operation is the expression of a relation between
the structures of its results and of its bases
an operation – however analysed – is a proposal – a
propositional action – open to question – open to doubt – and uncertain
in a propositional game context – it is a rule-governed
action
5.23. The operation is what has to be done to the one
proposition in order to make the
other out of it.
propositions do not
‘come out’ of propositions –
propositions are proposed
in relation to propositions
in a game context you can have the rule that propositions
come out of one another –
but this is a game play –
not a logical action
5.231. And that will, of course, depend on their formal
properties, on the internal
similarity of their forms.
the formal properties / structures – and internal
similarities of their forms / structures – will be an analysis of the
game propositions – of the game tokens –
and will most likely result in the formulation of game rules
in propositional logic on the other hand – proposed
relations between propositions – are open to question – open to doubt and
uncertain
5.232. The internal relation by which a series is ordered is
the equivalent to the
operation that produces one term from another.
here again – game theory – game rule
propositional logic on the other hand is the critical
investigation of proposals – and proposed relations – between proposals –
propositions are external to each other – open to question –
open to doubt – and uncertain
5.233. Operations cannot make their appearance before the
point at which one
proposition is generated out of another in a logically
meaningful manner; i.e. the point
at which the logical construction of propositions begins.
this is really just
a statement of game theory or game protocol
and you play the game with this understanding
if on the other hand we are talking propositional logic
here – the critical evaluation of
propositions –
‘operations’ – are not game rules – they are proposals –
propositions put – open to question – open to doubt and uncertain
one proposition is not generated from another –
a proposition is proposed in response to another
proposition
and the point at which the logical construction of
propositions begins – is the proposal –
and the proposal is –
open to question – open to doubt – and uncertain
5.234. Truth functions of elementary propositions are
results of operations with
elementary propositions as their bases.
(These operations I call truth-operations.)
the above is the meta-rule of the truth functional analysis
game
a proposition of any kind – is open to question – open to
doubt – and uncertain
if by ‘elementary’ propositions is meant – propositions that
are not open to question – not open to doubt – and not – uncertain –
then there are no elementary propositions
what goes for an elementary proposition in the
truth-functional analysis game – is a proposition that is designated as
not analysable
the elementary proposition is then a game rule
a rule without which the game – that game – cannot be played
in the truth functional analysis game – truth functions of
elementary propositions are results of operations with those propositions
designated as elementary propositions –
that propositions are designated as elementary is essential
to the truth function game
without this designation – there is no truth functional game
5.2341. The sense of a truth-function of p is a
function of the sense of p.
Negation, logical addition, logical multiplication, etc.
etc. are operations.
(Negation reverses the sense of a proposition)
in the truth functional analysis game – the ‘sense’ –
of a truth function is irrelevant – the
sense of p is irrelevant
the truth functional analysis game is played in accordance
with its rules –
it is a rule governed manipulation of symbols
p is a token in the game
negation – addition – multiplication – are rule governed
operations – or moves in the game
there is no ‘sense’ in such a game – but its play – so whatever function negation
has in such a game – it is not the reversal of sense
in propositional analysis and evaluation – as distinct from
propositional game playing –
to negate p is to dissent from p
in any propositional action of dissent – one’s ‘sense’ – or
one’s understanding of the subject proposition
– is open to question – open to doubt – and is uncertain
5.24. An operation manifests itself in a variable; it shows
how we can get from one
form of proposition to another.
It gives expression to the difference between forms.
(And what the bases of an operation and its result have in
common is just the bases
themselves)
there is no ‘manifestation here’ – we are dealing here with
– games and game rules – not mystical apparitions
an operation in a
game is a rule –
and a rule that
determines the action – the moves – from
one propositional structure – to another
and that action –
those moves – are the game-play
the difference
between forms – that is ‘propositional structures’ – in propositional games –
is rule-governed
what the bases of the operation and its result have in
common – is the game rules
5.241. An operation is not the mark of a form, but only the
difference between forms.
a play (a rule-governed operation) is a play with forms –
with propositional structures
play is rule governed – forms (structures) are rule governed
5.242. The operation that produces 'q' from 'p'
also produces 'r' from 'q' and so on.
There is only one way of expressing this: 'p', 'q',
'r', etc. have to be variables that give
expression in a general way to certain formal relations.
yes – that is the rule – if that is the game
5.25. The occurrence of an operation does not characterize
the sense of a proposition.
Indeed, no statement is made by an operation, but only by
its result, and this depends
on the bases of the operation.
(Operations and functions must not be confused with each
other.)
an operation in a propositional game – is a rule governed
action
in a propositional game an operation determines the function
of the proposition
in a propositional game an operation is a rule governed
action – not a statement
in a rule governed operation – the result of the operation –
the result of the play –
will be determined by the rules of the game
the bases of the operation – are rule governed
operations are rule governed actions with propositions
functions are rule governed actions of propositions
5.251. A function cannot be its own argument, whereas an
operation can take one of
its own results as its basis.
the standard view of
the function is that for any given first term – there is exactly one second
term i.e. if Rxy and Rxz imply y = z then R is a
function
the constituents of
the first term are the argument(s) of the function – and the second the value
of the function
a game-operation is
a rule governed open ended play
whereas a
game-function is a rule governed definitive play
5.252. It is only in this way that the step from one term of
a series of forms to another
is possible (from one type to another in the hierarchies of
Russell and Whitehead).
(Russell and Whitehead did not admit the possibility of such
steps, but repeatedly
availed themselves of it.)
any so called ‘step’ – in any game – is rule governed –
Wittgenstein’s ‘logic’ is based on his theory of internal
relations –
there are no internal relations – there is only the fantasy
of internal relations –
a fantasy played out in propositional games
Wittgenstein does not see ‘logic’ as the play of rule
governed games
the logical types theory of Russell and Whitehead – is an
hierarchical theory –
again a theory of internal relations
formal logic is propositional game playing – and
propositional game playing is rule governed
Russell and Whitehead did not see the theory of types in
this way
5.2521. An operation is applied repeatedly to its own
results, I speak of successive
applications of it. ('O'O'O'a' is the result of three
successive applications of the
operation 'O'x to 'a'.)
In a similar sense I speak of successive applications of more than one operation to a
number of propositions.
this is then a rule in a propositional game
5.2522. Accordingly I use the sign '[a,x, O'x] for
the general term of the series of
forms a, O'a, O'O'a.... . This bracketed expression
is a variable: the first term of the
bracketed series is the beginning of the series of forms,
the second is the form of a
term arbitrarily selected from the series, and the third is
the form of the term that
immediately follows x in the series.
here again – rules for the game
5.2523. The concept of successive applications of an
operation is equivalent to the
concept 'and so on'.
ok
5.253. One operation can counteract the effect of another.
Operations can cancel one another.
here is game-play rule
5.254. An operation can vanish (e.g. negation in '~~p': ~~p
= p).
the vanishing game – why not?
5.3. All propositions are results of truth operations on
elementary propositions.
A truth-operation is the way in which a truth-function is
produced out of elementary
propositions.
It is of the essence of truth-propositions that, just as
elementary propositions yield a
truth-function of themselves, so too in the same way
truth-functions yield a further
truth-function. When a truth-function is applied to truth
functions of elementary
propositions, it always generates another truth function of
elementary propositions,
another proposition. When a truth operation is applied to
the results of truth
operations on elementary propositions, there is always a single
operation on
elementary propositions that has the same result.
Every proposition is the result of truth-operations on
elementary propositions.
all propositions are not the results of truth
operations on elementary propositions
a proposition is a proposal – a proposal open to question –
open to doubt – and uncertain
in the truth functional game – the result of an operation on
a so called ‘elementary proposition’ – is a truth function – is another
‘proposition’ – another game token
the truth operation is a game play – a game play on elementary
propositions –
the result of which is a truth function –
the application of a truth functions – to truth functions of
elementary propositions – generates another truth function of elementary
propositions –
that is the truth function game
and when a truth operation – a rule governed action or play
– is applied to the results of truth operations on elementary propositions –
yes – there is always a single operation that has the same
result –
that’s the game
a proposition is a proposal – open to question – open to
doubt – and uncertain
when we deal with the proposition as a logical entity – we
explore its uncertainty
truth operations on elementary propositions – are game plays
a game as played is not open to question – open to doubt –
is not uncertain
5.31. The schemata in 4.31. have a meaning even when 'p',
'q', 'r', etc. are not
elementary propositions.
And it is easy to see that the propositional sign in 4.442
expresses a single truth-
function of elementary propositions even when 'p' and
'q' are truth-functions of
elementary propositions.
the schemata in 4.31 – when ‘p’ ‘q’ and
‘r’ are not elementary propositions – is a game –
a sign game – a different sign game to the elementary
proposition game
and yes – the propositional game sign in 4.442 expresses a single truth-function of
elementary propositions even when 'p' and 'q' are truth-functions
of elementary propositions
we can say the game sign in 4.442 is not game specific
5.32. All truth functions are results of successive
applications to elementary
propositions of a finite number of truth-operations.
that is the truth-function game
5.4. At this point it becomes manifest that there are no
'logical objects' or 'logical
constants' (in Frege's and Russell's sense).
an ‘object’ – however described – is a proposal –
open to question – open to doubt – uncertain
5.41. The reason is that the results of truth-operations on
truth functions are always
identical whenever they are one and the same truth-function
of elementary
propositions.
the reason that the results of truth operations on truth
functions are always identical whenever they are one and the same truth
functions of elementary propositions – is that that the truth operations on the
truth functions of elementary propositions are rule governed game plays
5.42. It is self-evident that v, É,
etc. are not relations in the sense in which right and
left are relations.
The interdefinability of Frege's and Russell's 'primitive
signs' of logic is enough to
show that they are not primitive signs, still less signs for
relations.
And it is obvious that the 'É'
defined by means of '~' and 'v' is identical with the one
that figures '~' in the definition of 'v'; and that the
second 'v' is identical with the first
one; and so on.
v and É are propositional game
signs that relate game propositions in truth functional games
left
and right are relata in a spatial or geometric game
in logic there is no ‘primitive’ –
logically speaking any sign is open to question – open to
doubt – is uncertain
however in logical games – like those developed by
Frege – Russell and Wittgenstein
for these games to be –
there must be a foundation of rules
different games – different foundations – different signs –
different ‘primitives’
it makes no sense to say that the rules of draughts are
inadequate because they are not the rules of chess – or visa versa
‘And it is obvious
that the 'É' defined by means of '~' and
'v' is identical with the one
that figures '~' in the definition of 'v'; and that the
second 'v' is identical with the first
one; and so on.’
here we have truth-functional identity rules
5.43. Even at first sight it seems scarcely credible that
there should follow from one
fact p infinitely many others, namely ~~p,
~~~~p, etc. And it is no less remarkable
that the infinite number of propositions of logic
(mathematics) follow from half a
dozen 'primitive propositions'.
But in fact all the propositions of logic say the same
thing, to wit nothing.
if we are talking logical reality – ‘it is scarcely credible
that there should follow from one fact p infinitely many others’
it is not just scarcely credible – it is plain nonsense
to take such a view is to surrender logic – to surrender
propositional reality – to fantasy
propositions – proposals – are put – and put in relation to
each other –
there is no magical ‘follow from’ – or ‘follow on’
however if we are talking games – and playing
fanciful games – then – yes you can set up a propositional game according to
whatever rules you like –
and the point of such games?
I would suggest in all truth – simply the pleasure of
playing them
the reason that ‘all the propositions of logic say the same
thing, to wit nothing’ –
is because a game – is not a logical proposal –
with a game – you play – and play according to
the rules of the game –
the game is a function of itself – of its rules – nothing is
proposed
in a proposition you propose a reality – and put the
proposal to question – to doubt –
you explore its uncertainty
proposing and playing are the two modes of
propositional activity
we do both – and we should not get them confused
5.44. Truth functions are not material functions.
For example, an affirmation can be produced by double
negation: in such a case does
it follow that in some sense negation is contained in
affirmation? Does '~~p' negate –
p, or does it affirm p – or both?
The proposition '~~p' is not about negation, as if
negation were an object: on the other
hand, the possibility of negation is already written into
affirmation.
And if there were an object called '~', it would follow that
'~~p' said something
different from what 'p' said, just because the one
proposition would then be about '~'
and the other not.
'~~p' – is a sign-game in the game of
truth-functional analysis
the rule of the game is that if ‘~p’ is negated – the
result is ‘p’ –
‘~~p' can stand for ‘p’ – can be played
as ‘p’
negation in the truth-function game – just is the sign ‘~’
–
what we have here is a rule governed sign-game
in propositional analysis – as distinct from game
construction and playing –
a proposition – a proposal – can be affirmed – can be denied
– or –judgment can be withheld
denial is not ‘written into affirmation’ –
denial is the propositional action of rejection – the decision not to proceed with the
proposal
affirmation – is the propositional action of acceptance –
the decision to proceed with the proposal –
and any decision of affirmation or denial – is open to
question – open to doubt – and uncertain
the idea that one ‘is written into’ the other – is stupid –
and proposes a contradictory state of affairs – which
results in – nothing
affirmation and denial – are different – distinct – separate
– and indeed opposite propositional
responses to the subject proposition
5.441. The vanishing of the apparent logical constants also
occurs in the case of
'~ ($x) . ~fx' which says the same as '(x
) . fx', and in the case of '($x) . fx . x = a',
which says the same as 'fa'.
this ‘vanishing’ of the ‘apparent logical constants’ – is no
mystery –
if you understand that what is going on here is a game –
where the rules of the game are just that formulations of
the play can be substituted
in propositional logic – as distinct from game construction
and playing – the only ‘constants’ are the constants of propositional practice
and use –
‘constants’ – are nothing more than contingent propositional
regularities
and these ‘constants’ – as with any aspect of propositional
behaviour – are open to question – open to doubt – and uncertain
5.442. If we are given a proposition, then with it we are
also given the results of all
truth-operations that have it as their base.
well yes – that is the theory of the game – the game of
truth-functional analysis
5.45. If there are primitive logical signs, then any logic
that fails to show clearly how
they are placed relatively to one another and to justify
their existence will be incorrect. The construction of logic out of its
primitive signs must be made clear.
there are no ‘primitive’ signs in logic – any sign is open
to question – open to doubt – and uncertain
Wittgenstein mistakes logic for game playing – and he
confuses the two –
any game – any well constructed game – will require signs –
that is rule governed signs
how the signs are placed – is rule governed
if the game signs – are not made clear – the ‘game’ will be
unplayable – there will be no game
as to the justification of the signs –
the game is the ‘justification’ for their existence
5.451. If logic has primitive ideas they must be independent
of each other. If a
primitive idea has been introduced, it must have been
introduced in all the
combinations in which it ever occurs. It cannot, therefore,
be introduced first for one
combination and later re-introduced for another. For example,
once negation has been
introduced, we must understand it in propositions of the
form ‘~p’ and in propositions
like '~(pvq)',
‘($x).
~fx', etc. We must not introduce it first for the one class of cases
and then for the other, since it would be then left in doubt
whether its meaning were
the same in both cases, and no reason would have been given
for combining the signs
in the same way in both cases.
(In short Frege's remarks about introducing signs by means
of definitions (in The
Fundamental Laws of Arithmetic) also apply mutatis
mutandis, to the introduction of
primitive signs.)
‘If logic has primitive ideas they must be independent of
each other’
in a sign game what goes for a primitive sign will be a sign
that functions as the basis of a game –
in a complex sign game – the relation of different signs to
each other – is rule governed
if a sign is not independent of other signs – it is not a
genuine sign –
a sign that is not independent of other signs – is a
confusion –
a sign game cannot be played with confused signs –
confused signs indicated confused rules
a sign game cannot be played with confused rules –
sign games are rule governed –
and the function of signs is rule governed
‘If a primitive idea has been introduced, it must have been
introduced in all the
combinations in which it ever occurs’
in a game – a sign game – you can introduce whatever
concepts you like – and give them whatever status you like –
and if they are rule governed then you have a game
as to negation – in standard symbolic logic games –
the rule for the sign is that it has the same
significance whenever and wherever it is introduced –
that’s the rule
Frege’s remarks about introducing signs by means of
definitions – is in the ball park –
once you understand that what you are dealing with is
propositional games –
it is a short hop from definitions to rules
5.452. The introduction of any new device into symbolic
logic is necessarily a
momentous event. In logic a new devise should not be
introduced in brackets or in a
footnote with what one might call a completely innocent air.
(Thus in Russell and Whitehead's Principia Mathematica
there occur definitions and
primitive propositions expressed in words. Why this sudden
appearance of words? It
would require justification, but none is given, or would be
given, since the procedure
is in fact illicit.)
But if the introduction of a new device has proved necessary
at a certain point, we
must immediately ask ourselves, 'At what point is the
employment of this device now
unavoidable?' and its place in logic must be made
clear.
the introduction of a new devise – that is to say – a new
rule – or a new move – into the (symbolic logic) game – will be disruptive
when this is proposed – what you get – what you will have is
a different game – a new game
how it is introduced – what form the introduction takes – is
basically irrelevant
and yes – how necessary is this new device – this new rule –
this new play –
why the new game?
presumably someone has a reason for this move to a new game
if the new game is well constructed – that is rule governed
– then it will be as legitimate as any other game
5.453. All numbers in logic stand in need of justification.
Or rather, it must become evident that there are no numbers
in logic.
There are no pre-eminent numbers.
a number is a sign – in a sign-game – a calculation game
what you include in your game – be it ‘logic’ – so called –
or whatever –
depends on how you construct your game – what rules you
introduce
i.e. – in the truth functional analysis game – there are no
numbers
games do not require justification – you play a game
– you don’t justify it.
that ‘there are no pre-eminent numbers – will be a rule for a
numbers game
5.454. In logic there is no co-ordinate status, there can be
no classification.
In logic there can be no distinction between the general and
the specific.
the above are proposed rules for a `logic game’ –
5.4541. The solutions to the problems of logic must be
simple, since they set the
standard of simplicity.
Men have always had a presentiment that there must be a
realm in which the answers
to questions are symmetrically combined – a priori – to form
a self contained system.
A realm subject to the law: Simplex sigillum veri.
the ‘problems of logic’ here – are game problems – problems
of the design or architecture of a class of sign-games –
and here we are likely talking about the construction of
games within games –
simplicity is in the eye of the beholder
nevertheless the beauty of a well constructed game –
regardless of how complex the game is – is characterized by clear-cut rules and
straightforward play –
the self contained system is the game
‘simplex sigillum veri’ – simplicity is the sign of truth –
games as rule governed exercises – are straightforward – are
simple
in a game however –
there is no question of truth – the game is neither true nor false – it
is rule governed –
you follow the rules – you play the game – if you don’t
follow the rules – you don’t play the game – simple
5.46. If we introduced logical signs properly, then we
should also have introduced at
the same time the sense of all combinations of them; i.e.
not only 'p v p' but '~(p v -q)'
as well etc. etc. We should also have introduced at the same
time the effect of all
possible combinations of brackets. And thus it would have
been made clear that the
real general primitive signs are not 'p v q', ' ($x) .
fx' etc. but the most general form of their combinations.
the ‘sense’ of a rule-governed sign game – is – the
rules of the game
if you understand the rules of the logical game – you
understand – or can understand –
all combinations of signs in the game
and the effect of all combinations of brackets – is rule
governed –
understanding this is knowing the game – knowing its rules
as to ‘the most general form of their combinations’ –
the form of their combinations – is the structure of their
combinations
and in general we can say here –
that any form / structure of sign combinations – in any
propositional game – is rule governed
and that is to say – the ‘general form’ of any game – is
that it is rule-governed
5.461. Though it seems unimportant, it is in fact
significant that the pseudo-relations
of logic, such as v and É need brackets – unlike real
relations.
Indeed the use of brackets with these apparently primitive
signs is itself an indication
that they are not the real primitive signs. And surely no
one is going to believe that
brackets have an independent meaning.
v and É – are game function signs
in e.g. –‘~(p v ~q)' –
the brackets signify the range
and scope of the first negation sign – it’s range is the game sign ‘p
v ~q’
so brackets determine logical
range of sign application
and in the above example –
brackets – by the bye – indicate that the second negation is subject to the
first
brackets distinguish games within
games
5.4611. Signs for logical operations are punctuation marks.
a logical operation is a rule governed propositional action
a sign for a rule governed propositional action – signifies
the rule governed game action
I think you could say any sign – is a punctuation mark – if
you want to look at it like that way
5.47. It is clear that whatever we can say in advance about
the form of all
propositions, we must be able to say all at once.
An elementary proposition really contains all logical
operations in itself. For 'fa' says
the same thing as
'($x) . fx . x = a'.
Wherever there is compositeness, argument and function are
present, and where these
are present, we already have all the logical constants.
One could say the sole logical constant was what all
propositions, by their very nature,
had in common with one another.
But that is the general propositional form.
what we can say in advance about the form – that is the
structure – of all game propositions – is that their form / structure is rule-governed
and – it is not too hard to say “rule-governed” – all at
once – as in the one vocal act
(though ‘all at once’ does sound more like magic than logic
– perhaps just a hint of mysticism here?)
an elementary proposition does not contain all
logical operations in itself –
an elementary
proposition is a token in a propositional game
it is the game that
contains the ‘logical operations’ – the game rules
there will be
different games – different ‘logical operations’ / rules
that 'fa' says the same thing as '($x) . fx . x = a' – is
the game
‘Wherever there is compositeness, argument and function are
present, and where these are present, we already have all the logical
constants’
well we have the logical constants that are in use
as to the general propositional form –
the proposition is a proposal – open to question –
open to doubt – and uncertain
in the game context the proposition is a rule-governed
token
5.471. The general propositional form is the essence of a
proposition.
‘the general proposition form’ – ‘the essence of the
proposition’ – (if you still want to use the term ‘essence’) – is the
proposal –
and the proposal is open to question – open to doubt – and
is uncertain
5.4711. To give the essence of a proposition means to give
the essence of all
description, and thus the essence of the world.
this ‘essence’ – of all description – is the proposal
the ‘essence’ of the world – is unknown – is the unknown
we make known with description – with proposal –
proposal – open to question – open to doubt – and uncertain
5.472. The description of the most general propositional
form is the description of the
one and only general primitive sign in logic.
‘The description of the most general propositional form is
the description of the
one and only general primitive sign in logic.’ – is quite
unnecessary rhetoric
a proposition is a proposal – open to question – open
to doubt – and uncertain –
call that ‘the most general propositional form’ – if you
like
there are no ‘primitive’ propositions – if by a ‘primitive proposition’ is meant –
a proposition that is not open to question – not open to
doubt – and not held to be uncertain
such a ‘proposition’ is not a ‘primitive’ – it is a
prejudice
in logic games – what goes for primitive propositions – just
are the propositions / signs –
on which the game is based –
and these propositions / signs – are rule governed
5.473. Logic must look after itself.
If a sign is possible, then it must also be capable of
signifying. Whatever is possible is
also permitted. (The reason why 'Socrates is identical'
means nothing is that there is
no property called 'identical'. The proposition is nonsensical
because we have failed to
make an arbitrary determination, and not because the symbol,
itself, would be
illegitimate.)
In a certain sense we cannot make mistakes in logic.
logic must look after itself?
‘logic’ as in symbolic logic – and all that that involves –
is a propositional game –
a propositional game is a rule governed propositional
exercise
and yes – rule governed propositional exercises –
take care of themselves
if a sign doesn’t signify – it’s not a sign
it is not a question of what is ‘permitted’ – it is rather a
question of what is proposed
‘Socrates is identical’ – is a proposal – and as a proposal
– is open to question – open to doubt – and is uncertain –
yes – you can argue that it is nonsensical – as Wittgenstein
does
however whether a proposal makes sense or not – is open to
question – open to doubt – and uncertain –
and one way to understand this – is to consider
propositional context –
i.e. – in a poetic context – that is as a line in a poem –
‘Socrates is identical’ –
may well be quite significant
‘we cannot make mistakes in logic?
if by logic you mean rule governed propositional games –
there are no mistakes –
if you follow the rules you play the game – if you don’t
follow the rules – you don’t play the game –
in the critical analysis that is propositional logic – there
are no mistakes –
propositions are proposals – open to question – open to
doubt – and uncertain
what we deal with in propositional logic is not ‘mistakes’ –
but uncertainty
5.4731. Self-evidence, which Russell talked about so much,
can become dispensable
in logic, only because language itself prevents every
logical mistake – What makes
logic a priori is the impossibility of illogical
thought.
if by a self-evident proposition is meant a proposition that
is beyond question – beyond doubt – and certain
there are no self-evident propositions
a so called self-evident proposition – is a prejudice – a
philosophical prejudice –whether it is perpetrated by Bertrand Russell – or the
guy on the next bar stool
in propositional games – there are no logical mistakes –
propositional games are rule governed
if you don’t play according to the rules there is no game
in propositional logic – there are no mistakes –
a proposition is a proposal – open to question – open to
doubt – and uncertain
if by ‘a priori’ you mean rule governed –
logical games – such as the truth functional analysis game –
are rule governed
the impossibility of illogical thought?
a proposition that is not held open to question – not held
open to doubt – and regarded as certain – is not held logically – it is held
illogically –
illogical thought is not impossible
we deal with prejudice of one form or another – at every
turn
5.4732. We cannot give a sign the wrong sense.
in a non-game context – a sign is a proposal – its sense is open to question – open to doubt
– and uncertain
in propositional games – the significance or function of a
sign is rule governed
5.47321. Ockham's maxim is of course, not an arbitrary rule,
nor one that is justified
by it's success in practice; its point is that unnecessary
units in a sign-language mean
nothing.
Signs that serve one purpose are logically equivalent, and
signs that serve none are
logically meaningless.
in a properly constructed game – there will only be signs
that have a function
we only need one sign to perform one function –
where more than one sign performs the one function – you
have unnecessary signs –
and the prospect of confusion
a ‘sign’ that has no function – is not a sign – of anything
a sign will only be proposed – if it is believed that it has
function
5.4733. Frege says that legitimately constructed
propositions must have a sense. And I
say that any possible proposition is legitimately
constructed, and, if it has no sense,
that can only be because we have failed to give meaning to
some of its constituents.
(Even if we think that we have done so.)
Thus the reason why 'Socrates is identical' says nothing is
that we have not given any
adjectival meaning to the word 'identical'. For when
it appears as a sign for identity, it
symbolizes in an entirely different way – the signifying
relation is a different one –
therefore the symbols also are entirely different in the two
cases: the two symbols
have only the sign in common, and that is an accident.
‘a legitimately constructed proposition must have sense?’
there is no ‘legitimate’ construction – there are different
constructions – different ways of proposing –
and any proposed construction – is open to question – open
to doubt – and uncertain
and as to sense –
the sense of a proposal – of a proposition – is open to
question – open to doubt – and uncertain
if a proposition ‘has no sense’ – then presumably that is
because no one has been able to make sense of it
now this of course could change –
however – if it doesn’t – then it will be dropped from
consideration as a proposition –
it will not be of any use to anyone
‘Socrates is identical’ –
the proposal is open to question – open to doubt – and
uncertain
and any decision on the meaning – or meaninglessness – of
the proposal – and any decision on the meaning of the sign – or the meaning of
the symbol –
is open to question – open to doubt – and uncertain
5.474. The number of fundamental operations that are
necessary depends solely on our
notation.
the number of operations necessary will be determined by the
rules of the game in question –
which is to say – how the game is constructed
notation is the game – represented
5.475. All that is required is that we should construct a
system of signs with a
particular number of dimensions – with a particular
mathematical multiplicity.
yes – if that is the game you want to construct – that you
want to play
5.476. It is clear that this is not a question of a number
of primitive ideas that have to
be signified, but rather the expression of a rule.
exactly
5.5. Every truth-function is a result of successive
applications to elementary
propositions of the operation
'(-----T)( x,
....)'.
This operation negates all propositions in the right-hand
pair of brackets, and I call it
the negation of those propositions.
here are rules for the truth-function game
5.501. When a bracketed expression has propositions as its
terms – and the order of
the terms inside the brackets is indifferent – then I
indicate it by the sign of the form
-
‘(x)’, ‘x’ is a variable whose values are terms of
the bracketed expression and the bar over the variable indicates that it is
representative of all its values in the brackets.
-
(E.g. if x has the three values P, Q, R,
then (x) = (P, Q, R).)
What the values of the variable are is something that is
stipulated.
The stipulation is a description of the propositions that
have the variable as their
representative.
How the description of the terms of the bracketed expression
is produced is not
essential.
We can distinguish three kinds of description: 1.
direct enumeration, in which case we
can simply substitute for the variable the constants that
are its values; 2. giving a
function fx whose values for all values of x
are the propositions to be described; 3.
giving a formal law that governs the construction of the
propositions, in which case
the bracketed expression has as its members all the terms of
a series of forms.
-
‘(x)’ and ‘x’ – are signs that function as rules
and the values of the variables
are stipulated – rule governed
in terms of the game – the play
–
how the description of the terms of the bracketed expression
is produced is incidental
the three kinds of description listed above – are three
different ways of describing the game
any one of these descriptions can function as a rule
-
5.502. So instead of '(-----T)(x,....)',
I write ‘N(x)’.
-
‘N(x)’ is the negation of all the values of
the propositional variable x.
here we have a rule of syntax and of play
5.503. It is obvious that we can easily express how propositions
may be constructed
with this operation, and how they may not be constructed
with it; so it must be
possible to find an exact expression for this.
the game as a rule governed propositional action – if well
constructed – is exact
if its not exact – there is no game
5.51. If x has
only one value, then N(x) = ~p (not p); if it has two values,
then
N(x) = ~p . ~q (neither p nor q).
a game rule
5.511. How can logic – all embracing logic, which mirrors
the world – use such
peculiar crotchets and contrivances? Only because they are
all connected with one
another in an infinitely fine network, the great mirror.
this ‘logic’ here – is propositional game construction
it mirrors nothing
5.512. '~p' is true if 'p' is false.
Therefore, in the proposition '~p', when it is true, 'p' is a
false proposition. How then can the stroke '~' make
it agree with reality?
But in '~p' it is not '~' that negates; it is
rather what is common to all the signs of this
notation that negate p.
That is to say the common rule that governs the construction
of '~p' ,'~~~p', '~p v ~p',
'~p .~p', etc. etc. (ad infin.). And this
common factor mirrors negation.
what we have here is the game sign '~' – and the rules of its use – which means its
combinations
the construction of '~p' ,'~~~p', '~p v
~p', '~p .~p', etc. etc. (ad infin.) – is a game
there is no ‘agreement with reality’ here –
it is just a game – its rules and its play –
the game – and the game played is real – that is the best
you can say –
furthermore the key point is that any propositional activity
is real –
what we do – does not ‘agree with reality’ – it is reality
this notion of ‘agreement with reality’ – is false – and
pretentious
it proposes a relationship that does not exist
it is to suggest that
our propositional activity – is – or can be – something separate from
and different to – reality
our propositional activity is our reality
propositions relate to propositions
any proposal of agreement – is open to question – open to
doubt – is uncertain
in propositional games – agreement is rule-governed
5.513. We might say that what is common to all symbols that
affirm both ‘p and q’ is
the proposition 'p . q'; and that what is
common to all symbols that affirm either p or q
is the proposition 'p v q'.
And similarly we can say that two propositions are opposed
to one another if they
have nothing in common with one another, and that every
proposition has only one
negative, since there is only one proposition that lies
completely outside it.
Thus in Russell's notation too it is manifest that 'q: p
v ~p' says the same thing as 'q',
that 'p v ~p' says nothing.
here we have from Wittgenstein propositional – truth
functional – game rules –
and analysis of these rules
5.514. Once a notation has been established, there will be
in it a rule governing the
construction of all propositions that negate p, and a
rule governing the construction of
all propositions that affirm p or q; and so
on. These rules are equivalent to the
symbols; and in them their sense is mirrored.
this is a clear statement that what is being proposed here
is a sign game
5.515. It must be manifest in our symbols that it can only
be propositions that can be
combined with one another by 'v', ' .', etc.
And this is indeed the case, since the symbol in 'p'
and 'q' itself presupposes 'v' '~', etc.
If the sign 'p' in 'p v q' does not
stand for a complex sign, then it cannot have sense by
itself; but in that case the signs 'p v q', 'p
. p' etc., which have the same sense as p,
must also lack sense. But if 'p v p' has no sense,
then 'p v q' cannot have sense either.
propositions are proposals – open to question – open to
doubt – and uncertain
in the game proposed here – the ‘propositions’ referred to
by Wittgenstein – are not open to question – open to doubt – or regarded as
uncertain
these game ‘propositions’ – are in fact tokens –
tokens of play
and their play is rule-governed within a complex of rules
5.5151. Must the sign of a negative proposition be
constructed with that of the
positive proposition? Why should it not be possible to
express a negative proposition
by means of a negative fact? (E.g. suppose that 'a' does
not stand in a certain relation
to 'b'; then this might be used to say that aRb
was not the case.)
But really in this case the negative proposition is
constructed by an indirect use of the
positive.
The positive proposition necessarily presupposes the
existence of the negative
proposition and visa versa.
in sign games – what Wittgenstein refers to a ‘propositions’
– are tokens of play
sign-games are not concerned with ‘facts’ –
sign-games are concerned with the rule-governed manipulation
of signs
where aRb – is not the case – aRb – is not a
valid play within the rules of the game
‘this negative proposition is constructed by an indirect use
of the positive’ –
the construction of the negative proposition – of the sign
for it in the formal logic game – involves a use of the positive proposition
‘The positive proposition necessarily presupposes the
existence of the negative
proposition and visa versa.’
you can make a rule about the relation and construction of
positive and negative propositions / tokens
however there is no presupposition in games – there are only rules
5.52. If x has as its values all
the values of a function fx for all values of x, then
-
N(x)
= ~ ($x) . fx.
yes – a rule of the game – a rule of play
5.521. I dissociate the concept all from
truth-functions.
Frege and Russell introduced generality in association with
logical product or sum.
This made it difficult to understand the propositions ‘($x) .fx' and '(x).fx', in which both
ideas are embedded.
does the concept ‘all’ – have a place in the truth function
game?
it is a question of game design
so to with Frege and Russell’s generality and logical
product –
with different games – different rules
5.522. What is peculiar to the generality-sign is first,
that it indicates a logical
prototype, and secondly, that it gives prominence to
constants.
the generality sign in the logical game – functions firstly
as a categorization of the variable – and secondly as a directive for its play
I don’t see that it gives prominence to the constants
5.523. The generality-sign occurs as an argument.
there is no argument in the logical game
the game is characterized – not be argument – but by
rule
5.524. If objects are given, then at the same time we are
given all objects.
If elementary propositions are given, then at the same time
all elementary propositions
are given.
ok – you can propose this game –
5.525. It is incorrect to render the proposition '($x) . fx' in the words, 'fx is possible', as
Russell does.
The certainty, possibility, or impossibility of a situation
is not expressed by a
proposition, but by an expression's being a tautology, a
proposition with sense, or a
contradiction.
The precedent to which we are constantly inclined to appeal
must reside in the symbol
itself.
' ($x) . fx' – as a sign-game – or – as a game within a game – is
rule determined
'fx is possible' – is a valid rule-determination of ‘($x) . fx'
the tautology and the contradiction – express nothing
the symbol itself – if it is to have any game-function – is
rule determined
the ground of any such determination – is logically
irrelevant
a game – is proposed – it’s rules are proposed
– that is where the matter begins and ends
you either play the game – and play according to its rules –
or you don’t play it –
simple as that
5.526. We can describe the world completely by means of
fully generalized
propositions, i.e., without first correlating any name with
a particular object.
Then, in order to arrive at the customary mode of
expression, we simply need to add,
after an expression like, 'There is one and only one x such
that...', the words, 'and that
x is a'.
there is no ‘complete’ description of anything –
any description is open – open to question – open to
doubt – is uncertain –
and as such – incomplete
'There is one and only one x such that...’ – 'and
that x is a' –
is a rule governed propositional game
5.5261. A fully generalized proposition, like every other
proposition, is composite.
(This is shown by the fact that in '($x, f) . fx'
we have to mention f and
'x' separately.
They both, independently, stand in signifying relations to
the world, just as is the case
in ungeneralized propositions.)
It is a mark of a composite symbol that it has something in
common with other
symbols.
this is a theory and rules for the structure of a proposed
symbolic logic game –
it is about how to understand the signs – their relations
and their use
game propositions do not stand in signifying relations to
the world –
their relation is to each other – in terms of the rules of
the game
game propositions – are not proposals – they are rule governed
tokens of play
5.5262. The truth or falsity of every proposition does make some alteration in the
general construction of the world. And the range that the
totality of elementary
propositions leaves open for its construction is exactly the
same as that which is
delimited by entirely general propositions.
(If an elementary proposition is true, that means, at any
rate, one more true elementary
proposition.)
the world is what is proposed
and there will be proposals of the ‘general construction of
the world’
a proposition is true – when assented to – false when
dissented from –
what propositions you assent to – and what propositions you
dissent from – will determine how you propose the world –
any such proposal and all it involves – is open to question
– open to doubt – and uncertain
any propositional action of assent or dissent – is open to
question –
the ‘world’ is uncertain – we live and operate in and with
this uncertainty
one way of obtaining relief from this propositional reality
– is to play – to play games –
one such game favoured by logicist philosophers is the
elementary proposition game
you can play this elementary proposition game – with
whatever rules are proposed
i.e. – as above – that ‘the range that the totality of
elementary propositions leaves open for its construction is exactly the same as
that which is delimited by entirely general propositions’
playing the elementary proposition game – may well be
therapeutic – it may well have
applications –
but it is a game – it is a play –
it is not the logical activity of question – of doubt – and
of dealing with propositional uncertainty
Wittgenstein and Russell – and many others – confuse the two
5.53. Identity of object I express by identity of sign, and
not by using a sign of
identity. Difference of objects I express by difference of
signs.
not using the identity sign – is fair enough
identity of objects – is the identity of propositions – is
the repetition of propositions –
the identity of signs – the repetition of signs
difference of objects is – is different propositions –
different signs
5.5301. It is self evident that identity is not a relation
between objects. This becomes
clear if one considers, for example, the proposition '(x):
fx.É
.x = a'. What this
proposition says is simply that only a satisfies
the function f, and not that only things
that have a certain relation to a satisfy the
function f.
Of course it might then be said that only a did have
a relation to a; but in order to
express that, we should need the identity sign itself.
if ‘identity’ were a relation – it would be a relation
between different propositions
in ‘a = a’ – we have the one proposition duplicated – there
is no relation –
'(x): fx.É .x =
a' – is a game proposition –
what it says – is that the function f is a substitute
for a
‘a = a’ – does not express a relation – as the
propositions here – are not different
and ‘a = a’ is not a propositional game – as there is
no substitution
‘a = a’ – is a dummy proposition
at best you could say ‘a = a’ – is the proposal of ‘a’
– in a badly constructed form
5.5302. Russell's definition of '=' is inadequate, because according to it we
cannot say
that two objects have all their properties in common. (Even
if this proposition is never
correct, it still has sense.)
as to the ‘=’ sign – it is a game sign –
and it signifies and defines a substitution game
two propositions that have all their properties in common?
well first up – the properties of a proposition – are open
to question – open to doubt – and uncertain
if it is decided
that two propositions have all their
properties in common – then you have one proposition – repeated
with two propositions with the same sign – at best what you have is two different
propositions – that are not properly differentiated in the sign
language
and until they are properly differentiated – as ‘two’
propositions – as two signs – they are useless
5.5303. Roughly speaking, to say of two things that they are
identical is nonsense, and
to say of one thing that it is identical with itself is to
say nothing at all.
roughly speaking – yes
5.531. Thus I do not write 'f(a,b).a = b', but 'f(a,a)'
(or 'f (b,b)')); and not 'f(a,b). ~a = b', but 'f(a,b)'.
ok – so here we have a reworking of identity propositions
that eliminates the identity sign
'f(a,b).a = b' is a sign substitution game –
and 'f(a,a)' (or 'f (b,b)')) and 'f(a,b)'
– transforms 'f(a,b).a = b' into a different game
just as 'f(a,b)' is a different play to 'f(a,b). ~a = b'
different signage – different rules – different games
and the action of going e.g. from 'f(a,b). ~a = b' –
to 'f(a,b)' is the action of
producing a game from a game
5.532. And analogously I do not write '($x,y).
f(x,y).x = y', but '($x).f(x,x)';
and not
'($x,y).f(x,y).
~x = y', but '($x.y).f(x,y)'.
(So Russell's '($x,y).
fxy' becomes '($x,y). f((x,y).v . ($x).f(x,x)'.)
and once again – the elimination of the identity sign
and the reworking of Russell’s ($x,y).
fxy'
different rules – different games
5.5321. Thus, for example, instead of '(x): fx. É x = a' we write
'($x).fx
É.fa:~($x,y).fx.fy'.
And the proposition, 'Only one x satisfies f(
)', will read ‘($x).fx: ~($x,y).fx.fy’
yes we can eliminate the ‘=’ sign by reinterpreting the game
– by proposing an alternative and different signage – and thus a different set
of rules – a different game
it is producing a game from a game
5.533. The identity sign, therefore, is not an essential
constituent of conceptual
notation.
no sign is essential – to any notation
a sign has function in a propositional game if it is rule
governed
outside of a rule governed game context – a sign is a
proposal – open to question – open to doubt – and uncertain
5.534. And now we see that in a correct conceptual notation
pseudo-propositions like
'a = a', 'a = b. b = c. É a = c', '(x). x = x', '($x).x
= a', etc. cannot even be written
down.
the issue is not
whether we are dealing with ‘pseudo-propositions’ – but whether or not we have
genuine propositional games
there is no game – no substitution with 'a
= a'
as to – 'a = b. b = c. É a = c' –
I would read this as saying –
if a can be substituted for b – and b can be substituted for
c – then a can be substituted for c –
a simple game of substitution
and I don’t see a problem with the ‘($x).x
= a' game – as x and a are different signs –
it’s a substitution game
5.535. This also disposes of all the problems that were
connected with such pseudo-
propositions.
All the problems that Russell's 'axiom of infinity' brings with
it can be solved at this
point.
What the axiom of infinity is intended to say would express
itself in language through
the existence of infinitely many names with different
meanings.
the axiom of infinity – is not a pseudo-proposition – it is
a proposal – open to question – open to doubt – and uncertain
Russell’s proposal of the axiom of infinity was really a
‘fix-up’ for his theory of types –and as Russell himself acknowledged – it had
no apparent basis in logic
as a proposal for ‘the existence of infinitely many names of
different meanings’ –
we can ask – in what propositional context does such a
proposal function?
another way of looking at it is –
how is a game with infinitely many names of different
meanings constructed – how is such a game played?
and would not such a game require an infinite number of
rules?
with any proposal – it is a question of propositional
context and utility –
it is argued that the axiom of infinity – is required as a
rule for the construction of set-theoretical games –
games such as the definition of the real numbers as infinite
sequences of rational numbers
in this context – the axiom of infinity – is a game rule
5.5351.
There are certain cases in which one is tempted to use expressions of the form
'a = a' or 'p É p' and the like. In fact this happens when
one wants to talk about
prototypes, e.g. about proposition, thing, etc. Thus in
Russell's Principles of
Mathematics 'p is a proposition' which is
nonsense – was given the symbolic meaning
'p É p' and placed as an
hypothesis in front of certain propositions in order to exclude
from their argument-places everything but propositions.
(It is nonsense to place the hypothesis 'p É p' in front of a proposition, in order to
ensure that its arguments shall have the right form, if only
because with a non-
proposition as argument the hypothesis becomes not false but
nonsensical, and
because arguments of the wrong kind make the proposition
itself nonsensical, so that
it preserves itself from wrong arguments just as well, or as
badly, as the hypothesis
without sense that was appended for that purpose.)
‘a = a’ and ‘p É p’ have no value –
as proposals – they
are unnecessary distortions
as game proposals – they don’t register
‘p is a proposition’ is ok – as a definition – but
how necessary is it?
if you understand that in propositional activity what we
deal with – all that we deal with is proposals – is propositions – there is
simply no reason ‘to exclude from their argument-places everything but
propositions’
placing 'p É p' in front of a proposition – ensures
– nothing
there is no ‘non-proposition as argument’ –
all argument is propositional
and any argument is open to question – open to doubt – and
uncertain
5.5352. In the same way people have wanted to express,
'There are no things', by
writing '~($x).x
= x'. But even if this were a proposition, would it not be equally true
if in fact 'there were things', but they were not identical
with themselves?
‘there are no things’ – is a proposal – and as with any
proposal – is open to question – open to doubt – and uncertain
'~($x).x
= x' – has the form of a substitution game – but there is no substitution
‘a thing identical with itself’?
identity – is a substitution game – a thing – is not
a substitute for itself
one thing may be a substitute for another thing – in a
substitution game
‘self-identity’ – or the idea that a thing – a proposal – is
identical – with itself – is a confused and stupid notion
5.54. In the general propositional form propositions occur
in other propositions only
as bases of truth-operations.
the ‘general propositional form’ – is the proposal
propositions do not occur in other propositions –
propositions are proposed in relation to other propositions
and a proposition put in relation to the subject proposal
may well be an argument for the truth or falsity of the subject proposition
any proposition put – in any propositional action – is open
to question – open to doubt – and is uncertain
this is the domain of critical propositional logic
if on the other hand we are talking about propositional games
– and game playing
Wittgenstein is here putting the rule – that in the truth function game – propositions occur in
other propositions as the bases of truth-operations –
that’s the rule and that is the game he is proposing
5.541. At first sight it looks as if it were also possible
for one proposition to occur in
another in a different way.
Particularly with certain forms of proposition in
psychology, such as 'A believes p is
the case' and 'A has the thought p', etc.
For if these are considered superficially, it looks as if
the proposition p stood in some
kind of relation to an object A.
(And in modern theory of knowledge (Russell, Moore, etc.)
these propositions have
actually been construed in this way.)
'A believes p is the case' – or 'A has
the thought p' – is ‘A
proposes p’
logically speaking – it is irrelevant who proposes ‘p’ –
and so the correct analysis is – ‘p’
5.542. It is clear, however that ‘A believes that p’, ‘A has the thought p’, and ‘A has the
thought p’, and ‘A says p’ are of the form ‘"p"
says p’: and this does not involve a
correlation of a fact with an object, but rather a
correlation of facts by means of the
correlation of their objects.
in – ‘"p"
says p’ –
"p" – is
logically irrelevant –
the correct analysis is ‘p’
5.5421. This shows too that there is no such thing as the
soul – the subject, etc. as it is
conceived in the superficial psychology of the present day.
Indeed a composite soul could no longer be a soul.
what it shows is that the ‘subject’ – as in the A in
–‘A believes that p’ is logically irrelevant when it comes
to a logical assessment of the proposition –‘p’
the subject here – has put the proposition
it is the proposition put – that is open to question
– open to doubt – and is uncertain
however this is not to say that the existence of the soul
cannot be proposed
‘the soul’ – is a proposal
– and like any other proposal – open to question – open to doubt and
uncertain
‘a composite soul could no longer be a soul’ – another proposal –
open to question –
open to doubt – and uncertain
5.5422. The correct explanation of the proposition, 'A makes
the judgement p', must
show that it is impossible for a judgement to be a piece of
nonsense.
(Russell's theory does not satisfy this requirement.)
a judgment is a proposal –
any proposal is open to question – open to doubt – and
uncertain –
just as is any claim of ‘nonsense’
5.5423. To perceive a complex means to perceive that its
constituents are related to
one another in such a way.
This no doubt also explains why there are two possible ways
of seeing the figure
as a cube; and all similar phenomena. For we really see two
different facts.
(If I look in the first place at the corners marked a and
only glance at the b's, then the
a's appear to be in front, and via versa).
our perceptions logically speaking – are proposals
to perceive a complex is to propose a complex
how the parts are related is another proposal
a proposal – any proposal is open to question – open to
doubt – is uncertain
it is propositional uncertainty that is the
basis of – ‘possible ways of seeing’
5.55. We now have to answer a priori the question about all
possible forms of
elementary propositions.
Elementary propositions consists of names. Since, however,
we are unable to give the
number of names with different meanings, we are also unable
to give the composition
of elementary propositions
if by ‘an a priori answer’ is meant – a proposal that is
beyond question – beyond doubt – and
certain – there are no ‘a priori answers’
a so called ‘a priori answer’ – is a prejudice – not
a proposal
in any case ‘elementary propositions’ – if they amount to anything – are game
propositions – tokens – in a rule governed propositional game
elementary propositions – are tokens in rule governed
propositional games
Wittgenstein however does not see elementary propositions as
game propositions
he defines them as propositions consisting of names –
and he argues that we are unable to give the number of names
with different meanings
and therefore we are unable to give the composition of elementary
propositions
he wants the elementary proposition to function as the
ground of propositional knowledge – as our basic connection with the world
if Wittgenstein can’t say what the elementary proposition is
– and that is just what he does say –
then his theory doesn’t work
– it’s a waste of time
if his elementary proposition is meant as a mystical entity
–
it is still of no use
and really the mystical argument is really just the fall
back position for analytical or philosophical failure –
it is when the philosophical issue goes right back into the
too hard basket –
and instead of admitting defeat – you pretend the victory –
trying to make a mystery out of it – is no answer
it is pretence – plain and simple
5.551. Our fundamental principle is that whenever a question
can be decided by logic
at all it must be possible to decide it without more ado.
(And if we get into a position where we have to look at the
world for an answer to
such a problem, that shows that we are on a completely wrong
track.)
here we are talking about rule-governed propositional games
and the reason we can answer any question in a logic game
‘without much ado’ –
is just that it is rule-governed –
if there is any question that cannot be answered in such a
game – then the ‘game’ – is poorly constructed – and is not a ‘game’ as such
looking to the world for an answer – is to mistake
game-playing for the critical activity of question – of doubt – and the
exploration of uncertainty
propositional games – such as Wittgenstein’s ‘logic’ – have
nothing to do with how the world is – except to say that such games are played
‘in the world’ –
and that is no more than to say – they are played
5.552. The ‘experience’ that we need in order to understand
logic is not that something
or other is the state of things, but that something is:
that, however is not an
experience.
Logic is prior to every experience – that something is
so.
It is prior to the question 'How?', not prior to the
question 'What?'
our experience is propositional – our reasoning is
propositional
that something is – is a proposal – open to
question – open to doubt and uncertain
logic is the propositional activity of question – of doubt –
of dealing with propositional uncertainty
what is ‘prior’ to the proposal – to the proposition – is
the unknown
‘that something is so’ –
is a proposal
what is prior to the question ‘how?’ – and what is prior to
the question ‘what? – is a proposal
if by ‘logic’ is meant – certain rule governed sign games –
the only ‘experience’ relevant – is that of following the
rules of the game – and thus – the experience of the play
5.5521. And if this were not so, how could we apply logic?
We might put it in this
way: if there would be a logic even if there were no world,
how then could there be a
logic given that there is a world?
logic is rule governed propositional action –
logic is the game
whenever we play games – rule governed actions – in any
context – we apply logic
game playing – without a world to play it in –
seriously?
game playing – in the world – that is in propositional
contexts –
is a propositional behaviour that human beings – (and I
think other sentient animals) –
do.
5.553. Russell said there were simple relations between
different numbers of things
(individuals). But between what numbers? And how is this
supposed to be decided? –
By experience?
(There is no pre-eminent number.)
‘individuals’ are proposals – and relations
between them – are proposed
‘numbers’ are proposals – signs in a rule governed
propositional game – the calculation game –
‘relations between numbers’ – are the rules of the
calculation game
‘experience’ is
proposal
there are no pre-eminent numbers – unless a ‘pre-eminent
number game’ – is proposed
5.554. It would be completely arbitrary to give any specific
form.
a proposal is put –
the form of the proposal – that is – its structure – is a
proposal put after the fact –
after the fact of the proposition being put
and a proposal of form / structure – as with the subject proposition – is open
to question – open to doubt – and is uncertain
in a propositional game – on the other hand – the form /
structure of the proposition – is rule determined
and the rules of the game – determine the game – prior to
the action of the game
5.5541. It is supposed to be possible to answer a priori the
question whether I can get
into a position in which I need the sign for a 27-termed
relation in order to signify
something.
if a 27-termed relation is proposed – a sign can be proposed
for it
whether or not such a proposal is put – is not an a
priori question –
it is an a posteriori question – a contingent matter
5.5542. But is it really legitimate to ask such a question?
Can we set up a form of a
sign without knowing whether anything can correspond to it?
Does it make sense to ask what there must be in order that
something can be the case?
is it really legitimate to ask such a question?
any question is legitimate
can we set up a form of a sign without knowing whether
anything corresponds to it?
if the proposal is put – what corresponds to it – is what is
proposed –
and what is proposed – is open to question – open to doubt –
and uncertain
does it make sense to ask what there must be in order that
something can be the case?
yes – i.e. – I would reckon that physicians on a daily basis
would approach the problem of cancer by asking the question what must be the
case if the disease is / can be present
5.555. Clearly we have some concept of elementary
propositions quite apart from their
logical forms.
But when there is a system by which we can create symbols,
the system is what is
important for logic and not the individual symbols.
And anyway, is it really possible that in logic I should
have to deal with forms that I
can invent? What I have to deal with is that which makes it
possible for me to invent
them.
logical form is a proposed structure of a proposition
the best we can say of the elementary proposition – is that
it is a game proposition – a game token – whatever its structure
the system is the game – the propositional game
and the game is a rule governed propositional action
what defines a game – is its rules
any form – that is any proposed propositional structure – is
a propositional ‘invention’
we can propose answers to the question what makes it
possible to ‘invent’ proposals of logical structure
what makes it possible to ‘invent’ – that is to propose
– is a matter – open to question – open to doubt – and uncertain
we can propose answers to this question
5.556. There cannot be a hierarchy of forms of elementary
propositions. We can
foresee only what we ourselves can construct.
well this amounts to a game rule – for Wittgenstein’s game –
and yes – what we ‘see’ – is what we propose
5.5561. Empirical reality is limited by the totality of
objects. The limit also makes
itself manifest in the totality of elementary propositions.
Hierarchies are and must be independent of reality.
reality – however it is described – i.e. as ‘empirical’ – is
open – open to question – open to doubt – and uncertain
reality is not limited – it is uncertain
elementary propositions – are game propositions – are game
tokens
game making – or game production – is an on-going human /
propositional activity
how many elementary propositions there are – is really an
irrelevant question
our reality is propositional – what is proposed – is what is
real
if ‘hierarchies are and must be independent of reality’ –
then they are by definition not real – end of story –
there is nothing to talk about here
the idea of anything ‘independent of reality’ – is just
plain stupid
5.5562. If we know on purely logical grounds that there must
be elementary
propositions, then everyone who understands propositions in
their unanalysed form
must know it.
the fact is we play propositional games – with game
propositions – with game tokens
Wittgenstein wants to call these game tokens – ‘elementary
propositions’ –
he can’t define his ‘elementary proposition’ – but
nevertheless insists on their existence
whatever his idea of the elementary propositions amounts to
– what it comes down to is a philosophical prejudice
now we can avoid all this confusion – or is it mysticism? –
by simply recognizing that if a
proposition is rule governed – if that is how we are using and defining it –
then it is a game proposition – a token in a game
5.557. The application of logic describes what
elementary propositions there are.
What belongs to its application, logic cannot anticipate.
It is clear that logic must not clash with its application.
But logic has to be in contact with its application.
Therefore logic and its application must not overlap.
Wittgenstein’s ‘elementary propositions’ – are rule governed
game propositions – tokens – in a ‘logical game’
the game determines what ‘elementary propositions’ there are
this game – this logical game – will be the same game –
wherever and however it is applied – only the propositional context – the
setting – changes
where and how a logical game is applied – is a contingent
matter
you play the game – wherever you play – in whatever
propositional context –
there can be no clash between the game and the context of
play
the application of a logical game – is just the playing of
it
context is setting
5.5571. If I cannot say a priori what elementary
propositions there are, then the
attempt to do so must lead to obvious nonsense.
‘elementary propositions’ – if they mean anything at all –
are game propositions – game tokens
‘what elementary propositions there are’ –
is determined by the game as constructed
5.6. The limits of my language mean the limits of my
world.
my language is open to question – open to doubt – uncertain
my world – the world – is propositional – open to question –
open to doubt – and uncertain
5.61. Logic pervades the world; the limits of the world are
also its limits.
So we cannot say in logic, 'The world has this in it, and
this, but not that.'
For that would appear to presuppose that we were excluding
certain possibilities, and
this cannot be the case, since it would require that logic
should go beyond the limits of
the world; for only in that way could it view those limits
from the other side as well.
We cannot think what we cannot think; so we cannot say
what we cannot say either.
our world is propositional
our world is open – open to question – open to doubt
– and uncertain
there are two modes of propositional activity –
we construct and play rule governed propositional games –
some of which have been termed ‘logical’
and we critically evaluate the propositions that we propose
and that are proposed to us
we put them to question – to doubt – and we explore their
uncertainty
‘So we cannot say in logic, 'The world has this in it, and
this, but not that’.’ –
in a ‘logical’ sign-game – we are playing with signs
–
if we put that 'The world has this in it, and this, but not
that’ – we put a proposal –
a proposal open to question – open to doubt – and uncertain
nothing is excluded – in question – doubt – and uncertainty
we propose – what we propose –
what is not proposed – is not proposed
5.62. This remark provides the key to the problem, how much
truth there is in
solipsism.
For what the solipsist means is quite correct; only it
cannot be said, but makes itself
manifest.
The world is my world; this is manifest in the fact that the
limits of language (of that
language which alone I understand) means the limits of my
world.
what the solipsist says – can be said – proposed – as
Wittgenstein well knows
his idea here of solipsism as a manifestation – is mystical
rubbish
language – is proposal – open to question – open to doubt –
and uncertain
the limits of my world – are open to question – open to
doubt – and uncertain
our propositional world – is the reality of external
relations
solipsism runs on the false notion of internal relations
I put propositions – and – propositions are put to
me –
that’s the end of solipsism
solipsism – like any other crack-pot theory – is open to
question – open to doubt – and is uncertain
5.621. The world and life are one.
everything is alive?
a proposal open to question – open to doubt – and uncertain
5.63. I am my world. (The microcosm)
the human world is a world of proposal
and yes there is a sense in which – I am what I propose –
and what I propose –
is open to question – open to doubt – and uncertain
5.631. There is no such thing as the subject that thinks or
entertains ideas.
If I were to write a book called The World as I found it, I should have to include a
report of my body, and should have to say which parts are
subordinate to my will, and
which were not, etc., this being a method of isolating the
subject, or rather of showing
that in an important sense there is no subject; for it alone
could not be mentioned in
that book. –
‘that there is a subject that thinks and entertains ideas’ –
is a proposal –
a proposal – open to question – open to doubt – and
uncertain
if I were to write a book – ‘the world as I found it’ –
the book would contain whatever I propose –
and what I propose is open to question – open to doubt – and
uncertain
5.632. The subject does not belong to the world; rather it
is the limit of the world.
‘‘the subject’ and its relation to the world’ – if you want
to put the matter in these terms –
is open to question
our world is propositional –
it is open to question – open to doubt – and uncertain
as is any proposed limit
5.633 Where in the
world is the metaphysical subject to be found?
You will say that this is exactly like the case of the eye
and the visual field. But really
you do not see the
eye.
And nothing in the visual field allows you to infer that it
is seen by an eye.
‘Where in the world is the metaphysical subject to be
found?’ –
wherever it is proposed that it is found
and wherever it is proposed that it is found – is open to
question – open to doubt – and uncertain
‘You will say that this is exactly like the case of the eye
and the visual field. But really
you do not see the
eye.’
the eye is what does the seeing – it is not what is seen –
‘And nothing in the visual field allows you to infer that is
seen by an eye.’
again – the eye is what does the seeing – it is not what is
seen –
however in a mirror the eye is in the visual field –
and if you close your eyes – your eyes – in the visual field
– disappear –
you don’t loose your eyes – just your vision of them
you don’t loose your sight – just what you were looking at
you still see – have a visual field – but its contents have
changed –
with closed eyes – your visual field will most likely be
black
this experiment with the mirror image – is one way in
which we commonly infer that the visual field is a function of the eye –
though any such inference / proposal – is open to question –
open to doubt – and uncertain.
5.6331. For the form of the visual field is surely not like
this
the form / structure of the visual field – is open to
question – open to doubt
the form / structure of the visual field – is uncertain
5.6344. This is connected with the fact that no part of our
experience is at the same
time a priori.
Whatever we see could be other than it is.
Whatever we could describe at all could be other than is.
There is no a priori
order of things
our reality is propositional – open to question – open to
doubt and uncertain
if this propositional reality is described as ‘our
experience’ – the ‘our experience’ – is open to question – open to doubt – and
uncertain
whatever we propose – is open to question
any description we propose – is open to question
any proposed ‘order of things’ – is open to question – open
to doubt – and uncertain
outside of description – outside of proposal – the world is
unknown
if ‘an a priori order of things’ – (whatever that is
supposed to mean) – is proposed –
it is just another proposal –
open to question – open to doubt – and uncertain
5.64. Here it can be seen that solipsism, when its
implications are followed out
strictly, coincides with pure realism. The self of solipsism
shrinks to a point without
extension, and there remains the reality co-ordinated with
it.
the reality that coordinates with a point of no
extension – will be a reality that is a point of no extension
if solipsism coincides with pure realism – then pure
realism on this view – is a point of no extension
what has ‘shrunk’ is not only the ‘self’ – but the ‘world’
–.
shrunk – to nothing
a great result – congratulations
5.641. Thus there really is a sense in which philosophy can
talk about the self in a
non-psychological way.
What brings the self into philosophy is the fact that ‘the
world is my world’.
The philosophical self is not the human being, not the human
body, or the human
soul, with which psychology deals, but rather the
metaphysical subject, the limit of the
world – not part of it
the notion of ‘self’ – where and when it is proposed – is
open to question – open to doubt – and
uncertain
what brings the ‘self into philosophy’ – or for that matter
– into any propositional context – is that it is proposed -
make of that what you will – but keep an open mind
Tractatus 6
- - -
6. The general form of a truth function is [p, x, N(x)]
This is the general form of a proposition.
truth functional analysis is a propositional game
- -
-
with [p, x, N(x)] – what you have is a general rule for the
truth-function game
in propositional logic – as
distinct from propositional game playing –
the proposition is a proposal
– open to question – open to doubt – and uncertain
the form of a proposition is a proposed structure of
the proposition –
any such proposal is open to question – open to doubt – and
uncertain
as to a ‘general form’ – in the
sense of general structure – a structure common to all proposals
any such proposal –
is open to question – open to doubt – and is uncertain
6.001. What this says is just that every proposition is a
result of the successive
applications to elementary propositions of the
operation -
N(x)]
every proposition is a proposal
–
a proposition – a proposal
– is not a result of successive applications to elementary propositions
-
the successive application to
elementary propositions of the operation N(x)]
is a propositional game
-
N(x) – is the game
playing a truth-function game is not propositional
analysis
propositional analysis is the
logical activity of question – of doubt – and the exploration of propositional
uncertainty
6.002. If we are given the general form according to which
propositions are
constructed, then with it we are also given the general form
according to which one
proposition can be generated out of another by means of an
operation.
yes – this is how the game is constructed and played
-
6.01. Therefore the general form of an operation Ω‘(h) is
- -
- - - -
[x, N(x)’(h) (= (hxN(x)))
This is the most general form of transition from one
proposition to another.
what you have here is a game rule for the transition
of one game proposition to another –
it is a rule of play
6.02. And this is how we arrive at numbers. I give
the following definitions
x =
Ω°’ x Def.,
Ω’Ω ͮ
’x = Ω ͮ + ¹’ x Def.
So in accordance with these rules, which deal with signs, we
write the series
x, Ω’x,
Ω’ Ω’x, Ω’ Ω’ Ω’ x, ...,
in the following way
Ω’°'x,
Ω’°+¹'x, Ω’°+¹+¹'x, Ω’°+¹+¹+¹'x, .....
Therefore, instead of '[x, x,Ω'x]',
I write [Ω°’x,
'Ω ͮ ’x, Ω ͮ + ¹]'.
And I give the following definitions
0+1 = 1 Def.,
0+1+1 = 2 Def.,
0+1+1+1 = 3 Def.,
(and so on).
what we have here is game rules – transformation rules –
rules for transforming from one game to another
6.021. A number is the exponent of an operation.
an exponent of an operation? – yes – but this characterization
is rather woolly – rather imprecise
a number is a sign in a calculation game
‘calculation’ – is the game – is the operation
6.022. The concept of number is simply what is common to all
numbers, the general
form of a number.
The concept of the number is the variable number.
And the concept of numerical equality is the general form of
all particular cases of
numerical equality.
what is common to all numbers is that they are signs in a
calculation game
this notion of ‘general form’ – sounds impressive – but it
goes nowhere – and amounts to nothing
outside of a calculation game – there is no number
saying that the concept of number is the variable number –
is to say the concept of number – is the number
and in that case – the ‘concept of number ‘ is rendered –
superfluous – and irrelevant –
numerical equality – is a sign game – a substitution game
6.03. The general form of the integer is [0, x, x + 1].
[0, x, x + 1] – is a rule – a definition
6.031. The theory of classes is completely superfluous in
mathematics.
This is connected with the fact that the generality required
in mathematics is not
accidental generality.
the theory of classes functions as a game theory
and what is ‘general’ in mathematics – is the game –
the game – is rule
governed
6.1. The propositions of logic are tautologies.
the propositions of logic are rule governed – game
propositions
the tautology is a game proposition
6.11. Therefore the propositions of logic say nothing. (They
are the analytic
propositions.)
games – do not propose – games are played
6.111. All theories that make a proposition of logic appear
to have content are false.
One might think, for example, that the words 'true' and
'false' signified two properties
among other properties, and then it would seem to be a
remarkable fact that every
proposition possessed one of these properties. On this
theory it seems to be anything
but obvious, just as, for instance, 'All roses are either
yellow or red', would not sound
obvious even if it were true. Indeed, the logical
proposition acquires all characteristics
of a proposition of natural science and this is the sure
sign that it has been constructed
wrongly.
content is proposed –
games – logical games – sign-games – do not propose – they are
rule governed propositional actions
logical games – are played.
6.112. The correct explanation of the propositions of logic
must assign to them a
unique status among propositions.
the logical game – is
just another propositional game –
and as a game – it has no special status – among
propositional games
6.113. It is the peculiar mark of logical propositions that
one can recognize that they
are true from the symbol alone, and this fact contains in
itself the whole philosophy of
logic. And so too it is a very important fact that the truth
or falsity of non-logical
propositions cannot be recognized from propositions alone.
a ‘symbol alone’ without – interpretation – without context
– is simply a ‘mark’ –unknown
if however – a rule is introduced that symbols of a
particular game or set of games are true –
those who play these games in terms of that rule – will
recognise the symbols as true
according to Wittgenstein all logical propositions are
tautologies – and tautologies say nothing
the tautology is empty – its ‘truth’ amounts to nothing –
it is a game – a truth function game – where regardless of
the truth values assigned to the propositions – T or F – the result of the play
is T
logical propositions – are games – propositional games
such games can be fun to play – as any game can be – but to
suggest that they have any significance beyond the pleasure of play – is
entirely misconceived
it is plain rubbish
what Wittgenstein here calls ‘non-logical propositions’ –
are non-game propositions –
propositions that are not rule governed
‘non-logical propositions’ – are proposals –
a proposal is open to question – open to doubt – and
uncertain
a proposal – a non-game proposition – is true – if assented
to – false – if dissented from –
assent and dissent are propositional actions – open to
question – open to doubt – and uncertain
6.12. The fact that the propositions of logic are
tautologies shows the formal – logical –
properties of language and the world.
The fact that a tautology is yielded by this particular
way of connecting its
constituents characterizes the logic of its constituents.
If propositions are to yield a tautology when they are
connected in a certain way, they
must have certain structural properties. So their yielding a
tautology when combined
in this way shows that they posses these structural
properties.
the tautology is a propositional game – it is not
a proposal
in saying that tautologies show the formal – logical
properties of language and the world
Wittgenstein puts that the tautology is a proposal –
and in so doing – gets the tautology wrong – and –
gets the proposition wrong –
he confuses the two
the tautology game is a rule-governed propositional
construction
a proposition – is a proposal – open to question –
open to doubt – and uncertain
any proposal regarding the relation between language and the
world – is open to question – open to doubt – and is uncertain
‘The fact that a tautology is yielded by this particular
way of connecting its
constituents characterizes the logic of its constituents.’
‘the logic of it’s constituents’ – is rule determined
‘If propositions are to yield a tautology when they are
connected in a certain way, they
must have certain structural properties. So their yielding a
tautology when combined
in this way shows that they posses these structural
properties.’
if propositions yield a tautology – you are playing a
propositional game –
the structural properties of game propositions are
rule-governed
combining propositions in this way is game construction
6.1201. For example, the fact that the propositions 'p'
and '~p' in the combination
'~(p. -p)' yield a tautology shows
that they contradict one another. The fact that the
propositions 'p É q', 'p' and 'q', combined
with one another in the form
'(p É q) .(p): É (q)',
yield a tautology shows that q follows from p and p É q.
The fact that '(x). fx: É : fa' is a tautology shows
that fa follows from (x).fx. Etc. etc.
playing the tautology game
6.1202. It is clear that one could achieve the same purpose
by using contradictions
instead of tautologies.
yes – same game – same rules – different coloured tokens
6.1203. In order to recognize an expression as a tautology,
in cases where no
generality-sign occurs in it, one can employ the following
intuitive method: instead of
'p', 'q', 'r', etc. I write 'TpF',
'TqF', 'TrF', etc. Truth combinations I express by means of
brackets, e.g.
and I use lines to express the correlation of the truth or
falsity of the whole proposition
with the truth combinations of its truth-arguments, in the
following way
So this sign, for instance, would represent the proposition p
É
q. Now, by way of
example, I wish to examine the proposition ~(p.
~p)
(the law of contradiction) in order
to determine whether it is a tautology. In our notation the
form ‘~x’ is written as
and the form ‘x.h’ as
hence the proposition ~(p. ~p) reads as follows
If we here substitute ‘p’ for ‘q’ and examine
how the outermost T and F are connected with the innermost ones,
the result will be that the truth of the whole proposition is
correlated with all the truth values of its argument,
and its falsity with none of the
truth combinations.
what we have here in the above bracket presentation is an
explanation of the tautology game in illustration
6.121. The propositions of logic demonstrate the logical
properties of propositions by
combining them so as to form propositions that say nothing.
This method could be called a zero method. In a logical
proposition, propositions are
brought into equilibrium with one another, and the state of
the equilibrium then
indicates what the logical constitution of these
propositions must be.
propositions that say nothing – are game propositions
the game says nothing because the game proposes nothing –
the game is not a proposal
this ‘zero method’ – is nothing more than game construction
6.122. It follows from this that we can actually do without
logical propositions; for in
a suitable notation we can in fact recognize the formal
properties of propositions by
mere inspection of the propositions themselves.
yes – we can do without logical propositions – we can do
without propositional games –
but the reality is that we construct and play games
we can do without them – but we are not going to
a so called ‘suitable notation’ – will just be a game
notation – and recognised as such
the ‘formal properties’ of (game) propositions are rule
determined
you will only recognise a rule – if you recognise – a game
‘mere inspection of the propositions themselves’ – tells you
nothing –
the point is – you need to know if you are playing a game –
or not
rules – are the key –--
if you are not operating in a rule governed (game) context –
a proposition – of whatever form – is a proposal –
a proposal – open to question – open to doubt – and
uncertain
6.1221. If, for example, two propositions 'p' and 'q' in the combination 'p É q' yield a
tautology, then it is clear that q follows from p.
For example, we see from the two propositions themselves
that ‘q’ follows from
‘p É q. p’, but it is also
possible to show it in this way: we combine them to form
‘p É q. p:É :q’, and then show that this is a
tautology.
we are not ‘doing without’ logical / game
propositions here –
here we have a play of the tautology game
6.1222. This throws some light on the question why logical
propositions cannot be
confirmed by experience any more than they can be refuted by
it. Not only must a
proposition of logic be irrefutable by any possible
experience, but it must be
unconfirmable by any possible experience.
a game – is neither true nor false
you play games – you don’t confirm or refute them
6.1223. Now it becomes clear why people have often felt as
if it were for us to
‘postulate’ the ‘truths of logic’. The reason is that
we can postulate them in so far as we
can postulate an adequate notation.
the so called ‘truths of logic’ – are sign-games –
there are no truths of logic
you don’t affirm or deny a game –
you play it – or you don’t play it
‘adequate notation’ – is game language
6.1224. It also becomes clear now why logic was called the
theory of forms and of
inference.
‘logic’ – is a sign-game – a symbolic game – a rule-governed
propositional activity
the game is a propositional use –
there are two uses of the proposition – the critical use –
and the game use
inference in a game – is rule governed
inference in a critical context – is a proposal – open to
question – open to doubt – and uncertain
6.123. Clearly the laws of logic cannot in their turn be
subject to the laws of logic.
you set up rules for a game – and you play the game –
according to the rules –
it is as simple as that
6.1231. The mark of a logical proposition is not
general validity.
To be general means no more than to be accidentally valid
for things. An
ungeneralised proposition can be tautological just as well
as a generalized one.
the mark of a ‘logical proposition’ – is that it is rule
governed –
the mark of the ‘logical proposition’ – is the game
‘validity’ – is a game concept – a rule-governed concept
as to ‘accidental validity’ –
in a game – all actions are rule governed
the tautological game can be played with ungeneralised
propositions as well as generalized
6.1232. The general validity of logic might be called
essential, in contrast with the
accidental general validity of such propositions as 'All men
are mortal'. Propositions
like Russell's 'axiom of reducibility' are not logical
propositions, and this explains our
feeling that, even if they were true, their truth could only
be the result of a fortunate
accident.
‘the general validity of logic’ –
‘logic’ – is a class of rule governed propositional
sign-games
‘All men are mortal’ –
is a proposal –
open to question – open to doubt – and uncertain
as to Russell’s axiom of reducibility – it has the form of a
rule –
it was introduced by Russell in an attempt to deal with
contradictions he discovered in his analysis of set theory
it is a rule in Russell’s set theory game
6.1233. It is possible to imagine a world in which the axiom
of reducibility is not
valid. It is clear, however, that logic has nothing to do
with the question whether our
world really is like that or not.
the axiom of reducibility is a game rule Russell
devised to deal with contradictions he found in his analysis of set theory
and Wittgenstein is right it has nothing to do with the
question of how the world is –
games – and game-rules – are not proposals –
they are not open to question – open to doubt – or uncertain
rules determine games – and games are played
6.124. The propositions of logic describe the scaffolding of
the world, or rather they
represent it. They have no 'subject-matter'. They presuppose
that names have meaning
and elementary propositions have sense; and that is their
connection with the world. It
is clear that something about the world must be indicated by
the fact that certain
combinations of symbols – whose essence involves the
possession of a determinate
character – are tautologies. This contains the decisive
point. We have said that some
things are arbitrary in the symbols that we use and that
some things are not. In logic it
is only the latter that express: but that means that logic
is not a field in which we
express what we wish with the help of signs, but rather one
in which the nature of the
absolutely necessary signs speaks for itself. If we know the
logical syntax of any sign-
language, then we have already been given all the
propositions of logic.
the propositions of logic are game propositions
the ‘scaffolding of the world’ – is a metaphysical proposal
in saying that the propositions of logic describe the
scaffolding of the world – or that they represent it –
Wittgenstein is taking the logic game – and presenting it as
a descriptive proposal
the logic game describes nothing – nothing but itself
pretending that it has descriptive significance is to
completely confuse the two modes of propositional activity
it is to confuse the critical mode and the game playing mode
and perhaps it is to suggest that one is the other – that
the logic game – describes the world?
in any case this ‘argument’ – destructive and hopeless as it
is – is indeed the central argument of the Tractatus
any proposal regarding the ‘scaffolding of the world’ – is
not a rule-governed propositional game – it is a proposal – a proposal open to
question – open to doubt – and uncertain
the propositions of logic – have no bearing – on any
metaphysical question –
unless they are misapplied
and in philosophy there is a rich and deep history of this
misapplication –
and Wittgenstein’s misapplication here – is one of the most
influential
these presuppositions that names have meaning and that
elementary propositions have sense – are entirely irrelevant to the logic game
the logic game is a rule governed sign game – it has nothing
to do with names – meaning – or sense
names – meaning – sense – are irrelevant to the game
construction – its rules – and its play –
here – logic or game theory – has been hijacked by
philosophers – to give a foundation to their philosophical theories
this is the decisive point
this has happened because they don’t understand the nature
of the proposition
if they understood that the proposition is a proposal – open
to question – open to doubt – and uncertain – they would have no reason to
pretend that logical games provide a foundation to their descriptive theories
‘We have said that some things are arbitrary in the symbols
that we use and that some things are not.’
in a properly constructed propositional game the symbols are
rule governed
what is ‘indicated’ by tautologies – is rule governed
propositional behaviour
signs do not speak for themselves –
signs in propositional games express the rules of the game –
express the play of the game
6.125 It is possible – indeed possible even according to the
old conception of logic – to
give in advance a description of all ‘true’ logical
propositions.
all language games are rule governed constructions
6.1251. Hence there can never be surprises in logic.
there are no surprises in rule governed – propositional
games
6.126. One can calculate whether a proposition belongs to
logic, by calculating the
logical properties of the symbol.
And this is what we do when we ‘prove’ a logical
proposition. For, without bothering
about sense or meaning, we construct the logical proposition
out of others by using
only rules that deal with signs.
The proof of logical propositions consists in the following
process: we produce them
out of other logical propositions by successively applying
certain operations that
always generate further tautologies out of the initial ones.
(And in fact only
tautologies follow from a tautology.)
Of course this way of showing that the propositions of logic
are tautologies is not at
all essential to logic, if only because the propositions
from which the proof starts must
show without any proof that they are tautologies.
there is no mystery as to whether a proposition belongs to
‘logic’ as Wittgenstein is using the word –
a proposition ‘belongs to logic’ if it is a game proposition
–
that is rule governed
proof is a game – a propositional game
using only rules that deal with signs is a definition
of the game
‘successively applying certain operations that generate
further tautologies’ – is the application of a rule – i.e. only tautologies
follow from a tautology
the tautology is a propositional game – and here
Wittgenstein employs the tautology as the ground of the proof game
games within games
6.1261. In logic process and result are equivalent. (Hence
the absence of surprise).
in logic – process and result – are rule governed
6.1262. Proof in logic is merely a mechanical expedient to
facilitate the recognition of
tautologies in complicated cases.
proof is a rule governed propositional game – with or
without the incorporation of the tautology game
6.1263. Indeed, it would be altogether too remarkable if a
proposition that had sense
could be proved logically from others, and so too
could be a logical proposition. It is
clear from the start that a logical proof of a proposition
that has sense and a proof in
logic must be two entirely different things.
the proof game is a rule-governed propositional action
as regards propositions that ‘have sense’ – such
propositions are not game propositions –
proof – the proof-game – is irrelevant to propositions ‘that
have sense’ –
and if the proof game is placed in this propositional
context – it is misplaced
‘propositions that have sense’ – are proposals – open
to question – open to doubt – and uncertain
6.1264. A proposition that has sense states something, which
is shown by its proof to
be so. In logic every proposition is the form of a proof.
Every proposition of logic is a modus ponens represented in
signs. (And one cannot
express modus ponens by means of a proposition.)
‘a proposition that has sense’ – is a proposal – open to
question – open to doubt – and uncertain
whether a proposition is ‘to be so’ – depends on whether it
is put – on whether it is proposed – the matter is entirely contingent
the existence of a proposal – has nothing to do with
proof
‘proof’ is a propositional game – a rule governed
propositional action
Wittgenstein’s ‘logic’ – is a game – a propositional game –
and a proof game
modus ponens – is a rule – a game rule – the rule of
affirming the antecedent – ‘if p then q . p – therefore q
it is a formulation of the proof game
6.1265. It is always possible to construe logic in such a
way that every proposition is
its own proof.
a game is determined by its rules
a rule that every proposition is its own proof – is just
another rule
6.127. All propositions of logic are of equal status: it is
not the case that some of them
are essentially primitive propositions and others
essentially derived propositions.
Every tautology shows itself that it is a tautology
all ‘propositions of logic – are game propositions – are
rule governed
the tautology is a propositional game
6.1271. It is clear that the number of the 'primitive
propositions of logic' is arbitrary,
since one could derive logic from a single primitive
proposition, e.g. by simply
constructing the logical product of Frege's primitive
propositions. (Frege would
perhaps say then we should then no longer have an
immediately self-evident primitive
proposition. But it is remarkable that a thinker as rigorous
as Frege appealed to the
degree of self evidence as the criterion of a logical
proposition.)
a ‘primitive’ is some basis on which to begin
Wittgenstein is right here – the starting point is arbitrary
and he puts that you construct the game by constructing the
logical product of the primitive proposition
what you have here is a theory of game construction
no proposition is ‘self-evident’ – any proposition – any
proposal – is open to question – open to doubt – and is uncertain –
this notion of the
‘self-evident’ in propositional logic is pretentious
in game theory – game propositions – are not open to
question – not open to doubt – or not
uncertain –
game-propositions – are tokens of play –
calling them ‘self-evident’ – is still pretentious – and
misleading – but in the end
no real harm is done
6.13. Logic is not a body of doctrine, but a mirror image of
the world.
Logic is transcendental.
logic is a game – a language-game – or a series of
language-games –
a language-game is a rule-governed propositional action
a language-game is not a mirror image of anything – a
language-game is a play with signs and symbols
logic is not transcendental – logic – ‘logical games’ – are
contingent – human creations
6.2. Mathematics is logical method.
The propositions of mathematics are equations, and therefore
pseudo-propositions.
mathematics is a language-game – a game of signs and symbols
equations are rule-governed sign-games – substitution games
the propositions of mathematics are rule governed
propositions
a game is not a proposal – is not a proposition –
a game (as played) is not open to question – not open to
doubt – and not – uncertain
a game is a play – not a proposal
6.21. A proposition of mathematics does not express a
thought.
a proposition of mathematics – is a sign-game
a proposition that expresses a thought is a proposal
– open to question – open to doubt – and uncertain
a game – is not a proposal –
a game – a language-game – is a play – a play with
signs and symbols
6.211. Indeed in real life a mathematical proposition is
never what we want. Rather
we make use of mathematical propositions only in
inferences from propositions that
do not belong to mathematics to others that likewise do not
belong to mathematics.
(In philosophy the question, 'What do we actually use this
word or this proposition
for?' repeatedly leads to valuable insights.)
mathematical games can be played in any propositional
context
6.22. The logic of the world, which is shown in tautologies
by propositions of logic, is
shown in equations by mathematics.
logical games – mathematical games –
the tautology game – the equation game – are different
games
the logic of the world – is the logic of the proposal – of
the proposition
the proposal – the proposition – is open to question – open
to doubt – and uncertain
propositional reality is uncertain –
the world is uncertain
6.23. If two expressions are combined by means of the sign
of equality, that means
that they can be substituted for one another. But it must be
manifest in the two
expressions themselves whether this is the case or not.
When two expressions can be substituted for one another,
that characterizes their
logical form.
it is the equality sign that determines that the two
expressions can be substituted
there is no substitution without the equality sign
so to say that the substitution must be manifest in the two
signs themselves – in the absence of the equality sign – is meaningless
when two expressions are substituted for one another
– they are tokens in a substitution game
when two expressions can be substituted for each other –
this characterizes the structure of the game
6.231. It is a property of affirmation that it can be
construed as double negation.
It is a property of '1+1+1+1' that it can be construed as
'(1+1) + (1+1)'.
that an affirmation can be constructed as a double negation
– is a play – in the
‘affirmation game’
that '1+1+1+1' can be constructed as '(1+1) + (1+1)' – is a
numbers game
6.232. Frege says that the two expressions have the same
meaning but different
senses.
But the essential point about an equation is that it is not
necessary in order to show
that the two expressions connected by the sign of equality
have the same meaning,
since this can be seen from the two expressions themselves.
meaning and sense are irrelevant when it comes to sign games
an equation is a sign game – a substitution game
the ‘=’ sign signifies that one sign can be substituted for
the other
it is the ‘=’ sign – not the ‘two expressions themselves’ –
that signifies – substitution
substitution is a play of tokens
6.2321. And the possibility of proving the propositions of
mathematics means simply
that their correctness can be perceived without its being
necessary that what they
express should itself be compared with the facts in order to
determine its correctness.
proving the propositions of mathematics – is playing the
proof-game –
‘facts’ – are irrelevant to the proof game
6.2322. It is impossible to assert the identity of
meaning of two expressions. For in
order to be able to assert anything about their meaning, I
must know their meaning,
and I cannot know their meaning without knowing whether what
they mean is the
same or different.
identity is a substitution game
the question of meaning is a critical issue –
the meaning of an expression – is open to question – open to doubt – and
uncertain
6.2323. An equation merely marks the point of view from
which I consider the two
expressions: it marks their equivalence in meaning.
the substitution game – avoids the whole question of – the
propositional issue of – meaning –
the equation – the substitution game – as it were –‘jumps’ – the question of
meaning altogether – and declares equivalence –
it is a rule governed declaration
the game is rule governed – it is a separate propositional
mode to logical assessment –
logical assessment is the critical the mode of question – of
doubt – and of dealing with uncertainty
6.233. The question whether intuition is needed for the
solution of mathematical
problems must be given the answer that in this case language
itself provides the
necessary intuition.
the solution of mathematical problems is in the art of the
game
which games apply to this problem – and which rules apply?
and indeed it may well involve the construction of new games
and new rules
a well versed mathematician will have at his or her
fingertips – games already developed and played –
are we to say a new discovery is a result of intuition or
the result of being deeply engaged in the mathematical experience?
could it come down to a lucky guess?
who knows?
6.2331. The process of calculating serves to bring
about the intuition.
Calculation is not an experiment.
calculation is a rule governed operational game
6.234. Mathematics is a method of logic.
mathematics is a sign-game
logic is a sign-game –
mathematics and logic are different games
6.2341. It is the essential characteristic of mathematical
method that it employs
equations. For it is because of this method that every
proposition of mathematics must
go without saying.
the equations game – is mathematics – is the mathematics
game
every ‘proposition’ of mathematics – is rule governed
nothing goes without saying –
no game goes without playing
6.24. The method by which mathematics arrives at its
equations is the method of
substitution.
For equations express the substitutability of two
expressions and, starting from a
number of equations, we advance to new equations by
substituting different
expressions in accordance with the equations.
that is the game
6.241. Thus the proof of the proposition 2 x 2 = 4 runs as
follows:
(Ω²) ͧ ’x
= ͮ
ͯ ͧ x Def.,
Ω² ˟ ² = (Ω²)²’ x = (Ω²)¹+¹'x
= Ω²’ Ω²’x =
Ω¹+¹ Ω¹+¹x = (Ω’Ω)’ (Ω’Ω)’ x
= (Ω’Ω)’ (Ω’Ω)’ x = Ω¹+¹ Ω¹+¹+¹+¹’x = Ω⁴x.
if you understand the substitution game – and it has been
constructed correctly –
the proof is unnecessary and irrelevant
proof is really just a parallel game
6.3. The exploration of logic means the exploration of everything
that is subject to
law. And outside logic everything is accidental.
logic is a rule governed language game
‘outside’ of propositional game-playing is the critical
evaluation of proposals –
critical evaluation is not rule-governed –
critical evaluation is the putting of propositions –
proposals – to question – to doubt
critical evaluation – is the exploration of propositional
uncertainty
6.31. The so-called law of induction cannot possibly be a
law of logic, since it is
obviously a proposition with sense. – Nor therefore, can it
be a priori.
the so called law of induction – is a proposal – open to
question – open to doubt –
and uncertain
6.32. The law of causality is not a law but the form of a
law.
the law of causality – is a proposal –
a proposal – open to question – open to doubt – uncertain
6.321. 'Law of causality' – that is a general name. And just
as in mechanics, for
example, there are 'minimum-principles', such as the law of
least action, so too in
physics there are causal laws, laws of the causal form.
‘laws of the causal form’ – are causal proposals in
different propositional contexts
6.3211. Indeed people even surmised that there must be a
'law of least action', before
they knew exactly how it went. (There as always, what is
certain a priori proves to be
something purely logical.)
a ‘law of least action’ is proposal – open to
question – open to doubt – and uncertain
we don’t know exactly how any proposal will function – until
we put it to use –
until we put it to question – to doubt – and we explore its
uncertainty
‘purely logical’ propositions – are rule governed propositions – in propositional
games
if by a priori propositions is meant – propositions that are
certain – there are no a priori propositions –
a proposition – is a proposal – open to question – open to
doubt – and uncertain
a proposition not held open to question – not held open to
doubt – and regarded as certain
is a proposition held as a prejudice
6.33. We do not have a priori belief in a law of
conservation, but rather a priori
knowledge of the possibility of a logical form.
what we have is a proposal – the proposal of a law of
conservation –
a proposal – open to question – open to doubt – and as with
any proposal – uncertain
‘the possibility of a logical form’ – is not knowledge –
it is not actually anything
Wittgenstein once again abandons logic and embraces
mysticism
logical form is a proposal of propositional structure
there is no logical form – that is a proposal of
propositional structure – unless there is a proposal –
our knowledge is actual proposal – cash on the
barrelhead
not some other-world possibility
6.34. All such propositions including the principle of
sufficient reason, the laws of
continuity in nature and of least effort in nature, etc.
etc. – all these are a priori insights
about the forms in which the propositions of science can be
cast.
all propositions including the proposal of sufficient reason
– the proposals of continuity in nature and of least effort in nature etc. etc.
– are proposals – open to question – open to doubt – and uncertain
the ‘forms’ in which the propositions of science can be cast
– are proposals – proposals of propositional structure –
proposals – open to question – open to doubt – and uncertain
6.341. Newtonian mechanics, for example, imposes a unified
form on the descriptions
of the world. Let us imagine a white surface with irregular
black spots on it. We then
say whatever kind of picture these make, I can always
approximate as closely as I
wish to the description of it by covering the surface with a
sufficiently fine square
mesh, and then saying of every square whether it is black or
white. In this way shall I
have imposed a unified form on the description of the
surface. The form is optional,
since I could have achieved the same result by using a net
with a triangular or
hexagonal mesh. Possibly the use of a triangular mesh would
have made the
description simpler: that is to say, it might be that we
could describe the surface more
accurately with a course triangular mesh than with a fine
square mesh (or conversely)
and so on. The different nets correspond to different
systems for describing the world.
Mechanics determines one form of description of the world by
saying that all
propositions used in the description of the world must be
obtained in a given way
from a set of propositions – the axioms of mechanics. It
thus supplies the bricks for
building the edifice of science, and it says, 'Any building
that you want to erect,
whatever it may be, must somehow be constructed with these
bricks, and with these
alone.'
(Just as with the number-system we must be able to write
down any number we wish,
so with the system of mechanics we must be able to write
down any proposition of
physics that we wish.)
‘The different nets correspond to different systems for
describing the world.’
different systems for describing the world – different proposals
for describing the world
‘Mechanics determines one form of description of the world
by saying that all
propositions used in the description of the world must be
obtained in a given way
from a set of propositions – the axioms of mechanics.’
yes – Newtonian mechanics is one descriptive proposal
the axioms of mechanics – are proposals –
proposals – open to question – open to doubt – and from a logical point of view – uncertain
'Any building that
you want to erect, whatever it may be, must somehow be constructed with these
bricks, and with these alone.'
Newtonian mechanics
is a comprehensive proposal –
and if you are going with the proposal that is Newtonian
mechanics – then any building you construct will be described in its terms
however logically speaking Newtonian mechanics is a proposal
open to question – open to doubt – and uncertain
and it is this uncertainty – which accounts for the
development of alternative descriptions
‘(Just as with the number-system we must be able to write
down any number we wish,
so with the system of mechanics we must be able to write
down any proposition of
physics that we wish.)’
any number we wish – must be a number of the proposed number
system –
if you somehow or another – have in mind a number not
compatible with the number system –
you need to find or develop a number system that
accommodates it –
or forget about it
yes – if Newtonian mechanics is to function as a
comprehensive account of the physical world – it must accommodate any proposed
proposition of physics
where a proposed proposition of physics does not fit with
the Newtonian system –
or where an alternative system is proposed –
the adequacy of Newtonian mechanics – is brought into
question
any proposed description – whether enjoying acceptance – or
not – is open to question – open to doubt – and is uncertain
6.342. And now we can see the relative position of logic and
mechanics. (The net may
also consist of more than one kind of mesh: e.g. we could
use both triangles and
hexagons.) The possibility of describing a picture like the
one mentioned above with
the net of a given form tells us nothing about the picture.
(For that is true of all such
pictures). But what does characterize the picture is that it
can be described completely
by a particular net with a particular size of mesh.
Similarly the possibility of describing the world by means
of Newtonian mechanics
tells us nothing about the world: but what does tell us
something about it is the precise
way in which it is possible to describe it by these means.
We are also told something
about the world by the fact that it can be described more
simply with one system of
mechanics than with another.
‘(The net may also consist of more than one kind of mesh:
e.g. we could use both triangles and hexagons.)’
this is just to say that the proposal – ‘the world’ – is
open to question – open to doubt and is uncertain
and therefore different proposals are valid
‘The possibility of describing a picture like the one
mentioned above with the net of a given form tells us nothing about the
picture.’ –
‘the picture’ – is the
description proposed
in the absence of description – in the absence of proposal –
‘the picture’ – is an unknown
‘But what does characterize the picture is that it can be
described completely by a particular net with a particular size of mesh.’
what characterizes the picture – is the description proposed
and any such description – any such proposal – is open to
question – open to doubt – and uncertain
and thus – logically speaking – incomplete
‘Similarly the possibility of describing the world by means
of Newtonian mechanics
tells us nothing about the world: but what does tell us
something about it is the precise
way in which it is possible to describe it by these means.’
the world as proposed – as described – is the world
and yes – of course the Newtonian description tells us that
the world can be described in the precise terms – of the Newtonian description
‘We are also told something about the world by the fact that
it can be described more simply with one system of mechanics than with another.’
different descriptions ‘tell us’ that we can describe differently
– that we can put – different proposals
and simplicity is in the eye of the beholder
6.343. Mechanics is an attempt to construct according to a
single plan all the true
propositions that we need for the description of the world.
yes – a complex proposal – or set of proposals –
open to question – open to doubt – and uncertain
6.3431. The laws of physics, with all their logical
apparatus, still speak, however
indirectly, about the objects of the world.
the objects of the world are proposals
the ‘laws’ of physics are proposals in relation to these
object / proposals
and any such proposal – is direct
6.3432. We ought not to forget that any description of the
world by means of
mechanics will be of the completely general kind. For
example, it will never mention
particular point-masses; it will only talk about any
point masses whatsoever.
‘any point-mass’ covers ‘particular point masses’
6.35. Although the spots in our picture are geometrical
figures, nevertheless
geometry can obviously say nothing at all about their actual
form and position. The
network, however, is purely geometrical; all its properties
can be give a priori.
Laws like the principle of sufficient reason, etc. are about
the net and not about what
the net describes.
geometry is a rule governed propositional game –
a game – whether ‘geometrical’ or not is not a proposal –
a game says nothing
propositions of form / structure – and propositions of
position – are proposals –
proposals open to question – open to doubt – and uncertain
geometry is a propositional game – its properties are not a
priori – they are rule governed
any description of the net – or any so called law like the
principle of sufficient reason – is a proposal – open to question – open to
doubt – and uncertain
and what the net describes – is a different proposal
– to a proposed description of the net
6.36. If there were a law of causality, it might be put in
the following way: There are
laws of nature.
But of course this cannot be said; it makes itself manifest.
well of course it can be said – because it is
said – because it is proposed – and proposed here
– by Wittgenstein
‘laws of nature’ – are
proposals –
proposals – open to question – open to doubt – and uncertain
6.361. One might say using Hertz's terminology, that only
connections that are subject
to law are thinkable.
so called ‘laws’ – are well established propositions –
‘well established’ – because they are generally accepted and
used
as to what is ‘thinkable’ –
the short answer is that what is thinkable is what is
proposed
a thought is a proposal –
it can remain private – or it can be made public
6.3611. We cannot compare a process with 'the passage of
time' – there is no such
thing – but only with another process (such as the working
of a chronometer).
Hence we can describe the lapse of time only by relying on
some other process.
Something exactly analogous applies to space: e.g. when
people say that neither of
two events (which exclude one another) can occur because
their is nothing to cause
the one to occur rather than the other, it is really a
matter of being unable to describe
one of the two events unless there is some sort of
asymmetry to be found. And if such
an asymmetry is to be found, we can regard it as the cause
of the occurrence of the
one and the non-occurrence of the other.
to compare a process with the passage of time – yes you need
a definition of the passage of time – and a chronometer functions as such a
definition
likewise with the lapse of time – it is a calculation
in either case you construct a game – a rule governed
propositional game
‘something analogous applies to space’ –
the idea is that ‘neither of two events (which exclude one
another) can occur because their is nothing to cause the one to occur
rather than the other’ –
here we are unable to describe one of the two events – ‘unless
there is some sort of asymmetry to be found’ –
that is to say – unless a rule is put that there is ‘some
sort of asymmetry’ –
and then you have a
rule – a game – an asymmetry game
so yes – there is ‘something’ of an analogy – here – you end up with two games – two
different propositional games
6.36111. Kant's problem about the right hand and the left
hand, which cannot be made
to coincide, exists even in two dimensions. Indeed, it
exists in one-dimensional space
- - - - o------x - - x------o - - - -
a b
in which the two congruent figures, a and b,
cannot be made to coincide unless they
are moved out of this space. The right hand and the left
hand are in fact completely
congruent. It is quite irrelevant that they cannot be made
to coincide.
A right hand glove could be put on the left hand, if it
could be turned around in four
dimensional space.
‘left and right’ here
is a propositional game –
a rule governed propositional game
the left token and the right token in this game are
congruent –
they are distinguished by their positions relative to a
nominated centre point
one side of the centre point is termed ‘left’ – the other
‘right’ –
‘a’ and ‘b’ – would do just as well
that they cannot be made to coincide is the game-rule
if a ‘right token’ was played to coincide with the ‘left token’ – or visa
versa –
you have a different game
6.362. What can be described can happen too: and what the
law of causality is meant
to exclude cannot even be described.
what can be described / proposed – may or may not happen
presumably what the law of causality excludes – is un-caused
events
uncaused events – will not be described by a law of
causality
the notion of the uncaused event – causa sui – is a proposal
– one that has a long history in philosophy – and one that is central to the
philosophical system of Spinoza
a proposal – that as with the causal proposal – is open to
question – open to doubt – and uncertain
6.363. The procedure for induction consists in accepting as
true the simplest law that
can be reconciled with our experiences.
what is to count as the ‘simplest law’ – the simplest
proposal – that can be reconciled with our experiences?
any proposed ‘simplest law’ – will be open to question –
open to doubt – and uncertain
and any affirmation of a proposal here – will likewise be
open to question –
so where does this
leave ‘induction’?
6.3631. The procedure, however, has no logical justification
but only a psychological
one.
It is clear that there are no grounds for believing that the
simplest eventuality will in
fact be realized.
a proposal – described as ‘logical’ – or described as
‘psychological’ – is open to question – open to doubt – and uncertain
logically speaking – there is no ‘justification’ for any proposal
– if by justification is meant the end of questioning – the end of doubt – and
an end to uncertainty
if we proceed with a proposal – and we proceed logically –
we proceed with uncertainty – in
uncertainty
‘there are no grounds for believing that the simplest eventuality will in fact be realized’ –
any so called grounds for any proposal – are open to
question – open to doubt – and uncertain
6.36311. It is an hypothesis that the sun will rise
tomorrow; and this means that we do
not know that it will rise.
our knowledge is what we propose – whatever we propose
and what we propose – is open to question – open to doubt –
and uncertain
6.37. There is no compulsion making one thing happen because
another has happened.
the only necessity that exists is logical necessity.
any proposal regarding the relation between events is open
to question – open to doubt – and uncertain
if by logical necessity is meant – a proposition that is
true by definition – i.e. – ‘no unmarried man is married’ – then all logical
necessity amounts to is a language game –
and here we are
talking about a language game that goes nowhere –
if by logical necessity is meant that the proposal is true –
because it could not be otherwise – i.e. it is certain –
then there is no logical necessity
a proposal – a proposition – is open to question – open to
doubt – and is uncertain
6.371. The whole modern conception of the world is founded
on the illusion that the
so-called laws of nature are the explanations of natural
phenomena.
the ‘so-called laws of nature’ – are proposed as
explanations of proposed natural phenomena –
and they function as explanations of proposed natural
phenomena
however from a logical point of view – these proposals – as
with any proposal of any kind – are open to question – open to doubt – and
uncertain
there is nothing illusory here
a proposal is open to question – open to doubt – and uncertain
6.372. Thus people today stop at the laws of nature,
treating them as something
inviolable, just as God and Fate were treated in past ages.
And in fact both are right and wrong: though the view of the
ancients is clearer in so
far as they have a clear terminus, while the modern system
tries to make it look as if
everything were explained.
the idea that the laws of nature are inviolable – is
illogical
any proposed explanation of proposed natural events – is
open to question – open to doubt and uncertain
6.373. The world is independent of my will.
‘my will’ – is a proposal –
a proposal – open to question – open to doubt – and
uncertain
likewise any proposed relation between ‘my will’ and the
‘the world’ – whatever that is supposed to mean – is open to question – open to
doubt – and uncertain
6.374. Even if all we wish for were to happen, still this
would only be a favour
granted by fate, so to speak: for there is no logical
connection between the will and the
world, which would guarantee it, and the supposed physical
connection is surely not
something that we could will.
proposed connections of any kind – are proposed relations – between
propositions
any proposed relation between propositions – is open to question – open to doubt – and uncertain
6.375. Just as the only necessity that exists is logical necessity, so too the only impossibility
that exists is logical impossibility.
logical necessity – as in the proposition – ‘no unmarried
man is married’ – is a language game
likewise – logical impossibility – as in ‘it is raining and
it is not raining’ – is a language game
language games – signifying nothing
if by logical necessity is meant – the proposal is true –
because it could not be otherwise – i.e. it is certain –
then there is no logical certainty –
a proposal is open to question – open to doubt – and uncertain
–
if by logical impossibility is meant the proposal is false –
because it could not be otherwise – i.e. it is certainly false
there is no logical impossibility –
a proposal is open to question – open to doubt – and is
uncertain
these notions of ‘logical necessity’ and ‘logical impossibility’
– are really just pretentious covers for
ignorance and prejudice
at the root of this –
is fear of uncertainty
6.3751. For example, the simultaneous presence of two
colours at the same place in
the visual field is impossible, in fact logically
impossible, since it is ruled out by the
logical structure of colour.
Let us think how this contradiction appears in physics: more
or less as follows – a
particle cannot have two velocities at the same time; that
is to say, it cannot be in two
places at the same time; that is to say particles that are
in different places at the same
time cannot be identical.
(It is clear that the logical product of two elementary
propositions can neither be a
tautology nor a contradiction. The statement that a point in
the visual field has two
different colours at the same time is a contradiction.)
the presence of two colours at the same place in the visual
field –
will depend on how the ‘one colour’ is described –
i.e. – the one colour could be described as a combination of
different colours – and in that case – there is no ‘one’ colour in the visual
field –
but different colours in the same place
there is no logical impossibility – there is only
propositional / logical uncertainty
and how the proposal of colour and the proposal of the
visual field are interpreted provides a good example of propositional
uncertainty – and therefore of propositional options
and again – the structure of colour – is a matter – open to
question
a particle cannot have two velocities at the same time?
isn’t this a question of reference points and theories of
measurement?
with different reference points – and different theories of
measurement – it may well be proposed that one particle has different
velocities
as to different places at the same time?
with different set of spacial co-ordinates there will be
different positions at the same time
as to identity – the question is – can one proposed set of
co-ordinates – be substituted for the other?
that will depend on the theory or theories being tested at
the time
the propositions of physics are not game propositions – they
are proposals –
open to question – open to doubt – and uncertain
6.4. All propositions are of equal value.
all propositions are proposals – open to question – open to
doubt – and uncertain
6.41. The sense of the world must lie outside the world. In
the world everything is as
it is, and everything happens as it does happen: in it no value exists – and if it did
exist, it would have no value.
If there is any value that does have value, it must lie
outside the whole sphere of what
happens and is the case. For all that happens and is the
case is accidental.
What makes it non-accidental cannot lie within the world, since if it did it would not be accidental.
It must lie outside the world.
our world is propositional
sense is proposed –
what happens – is what is proposed
value is a proposal
proposals of value are open to question – open to doubt –
and uncertain
our world is
uncertain
‘outside’ of our proposals
– is the unknown
we propose to make
known
6.42. So too it is impossible for there to be propositions
of ethics.
Propositions can express nothing that is higher.
well there are propositions of ethics – to suggest
otherwise – is just plain ridiculous
propositions of ethics are an empirical fact –
and propositions of ethics are central to our propositional
lives
and as with any proposal – any proposition – the
propositions of ethics are – open to question – open to doubt and – and
uncertain
‘propositions of ethics can express nothing that is higher’
–
our reality is propositional –
there is no ‘non-propositional reality’ – unless by that is
meant – the unknown
if by ‘higher’ – is meant – something like a
non-propositional realm of morality –
there is no such realm –
this idea of ‘higher’ – is more in the realm of poetic
imagery – i.e. Dante’s Divine Comedy –
it has no logical significance –
it is just plain rubbish
6.421. It is clear that ethics cannot be put into words.
Ethics is transcendental.
(Ethics and aesthetics are one in the same.)
the plain fact is that ethics is put into words
if by ‘transcendental’ – is meant that a non-propositional
reality – there is no such reality
and the idea that ethics – a propositional activity –
transcends propositional activity – is absurd
as to the relation of ethics to aesthetics – that is a
matter – open to question – open to doubt – and uncertain
6.422. When an ethical law of the form, 'Thou shalt....', is
laid down, one's first
thought is, 'And what if I do not do it?' It is clear,
however that ethics has nothing to
do with punishment and reward in the usual sense of the
terms. So our question about
the consequences of an action must be unimportant – At least
those consequences
should not be events. There must indeed be some kind of
ethical reward and ethical
punishment, but they must reside in the action itself.
(And it is also clear that reward must be something pleasant
and the punishment
something unpleasant)
‘when an ethical law
…is laid down’ – by whom?
logically speaking –
there are no ethical laws – and there are no ethical authorities –
though there is
ethical prejudice – and ethical pretension
from a logical point
of view – the only ‘authority’ is authorship –
authorship of a
proposal –
you may decide – as
Wittgenstein has – that the consequences of an action are not ethically
relevant
however the question
of the ethical relevance of the consequences of an action – is not
unimportant
and why must
there be some kind of ethical reward and ethical punishment?
our ethical
proposals – like any other – are our responses to the question of how to
understand the world and how to live in the world
and these proposals
– like any other – are open to question – open to doubt – and uncertain
we operate with
uncertain proposals – in an uncertain world
6.423. It is impossible to speak of the will in so far as it
is the subject of ethical
attributes.
And the will as a phenomenon is of interest only to
psychology.
well – it’s not ‘impossible’ to propose that the will is the
subject of ‘ethical attributes’ –
it is just another proposal
any proposition – be it described as ‘psychological’ or not
– is open to question – open to doubt – and uncertain
6.43. If the good or bad exercise of the will does alter the
world, it can alter only the
limits of the world, not the facts – not what can be
expressed by means of language.
In short the effect must be that it becomes an altogether
different world. It must, so
to speak, wax and wane as a whole.
The world of a happy man is a different one from that of a
unhappy man.
how the world is – and how we affect it – is open to
question – open to doubt – and is uncertain
perhaps it is best to speak of different propositional
worlds –
different propositional realities – the focus of which is
the unknown
the world of one man is different to that of another –
the propositional life of one man is different to that of
another
6.431. So too at death the world does not alter, but comes
to an end.
what happens at death – is open to question – open to doubt
– and uncertain
logically speaking it is no different to what happens in
life
6.4311. Death is not an event in life: we do not live to
experience death.
If we take eternity to mean not infinite temporal duration
but timelessness, then
eternal life belongs to those who live in the present.
Our life has no end in just the way in which our visual
field has no limits.
death is an event in life –
outside of life – in the absence of life – it would make no
sense to speak of death
I would say we have no experience after death –
and therefore there is no way of knowing if we have an
experience of death or not
however whether we have experience after death – or not – is
really a matter open to question – open to doubt – and uncertain
there are people who have been declared medically dead and
have ‘come back to life’ to report an experience of death –
i.e. – some have reported an experience of nothingness –
others have reported a bright light – outer body experiences – bliss – peace – beatific visions – etc. –
etc. –
whether these reports – and any others – count as reports of
death – or indeed of experience –
is open to question – open to doubt – and uncertain
perhaps death – like so many physical / biological changes
in the body – is not experienced – but just happens?
all this begs the question – what is death? –
and Wittgenstein has nothing to say here
living in the present – is not timelessness –
the past – the present – the future – are categories
of time –
to live in the present – is to question – is to doubt – and
is to explore propositional uncertainty
that we cannot see an end to our own lives – does not
mean there is no end
experience tells us that human beings die –
whether death is the end of life or not – is open to
question – open to doubt – and is uncertain
6.4312. Not only is there no guarantee of the temporal
immortality of the human soul,
that is to say of its eternal survival after death; but, in
any case, this assumption
completely fails to accomplish the purpose for which it has
always been intended. Or
is some riddle solved by my surviving for ever? Is not
eternal life itself as much of a
riddle as our present life? The solution of the riddle of
life in space and time lies
outside space and time.
(It is certainly not the solution of any problems of natural
science that is required.)
and is not ‘outside of space and time’ – ‘as much of a
riddle’ as ‘eternal life’ and ‘our present life’?
a riddle is a game – and yes – you can regard ‘our present
life’ – as a riddle – as a game –
this however is not to deal with any of the critical matters
we face in life –
and is therefore quite a superficial view of life
any so called ‘solution’ to the ‘problems’ of life – is a
proposal – or proposals – open to question – open to doubt – and uncertain
we live in and with and through propositional uncertainty
6.432. How things are in the world is a matter of
complete indifference for what is higher. God does not reveal himself in
the world.
‘God’ is a proposal –
open to question – open to doubt – and uncertain
6.4321. The facts all contribute to the setting of the
problem, not its solution.
‘facts’ – are proposals – open to question – open to doubt –
and uncertain –
as are ‘problems’ and ‘solutions’
6.44. It is not how things are in the world that is
mystical, but that it exists.
once you step into mysticism – you turn your back on
propositional reality – (or at least try to) – and pretend – a superiority – a
‘higher’ understanding
it is really just a retreat into ignorance and prejudice –
and one that is bound to come unstuck – if you have a brain
6.45. To view the world sub specie aeterni is to view it as
a whole – a limited whole.
Feeling the world as a limited whole – it is this that is
mystical.
the world – our world – is what is proposed –
we can only ‘view’ what we propose – and what is put to us –
and yes – that is limited
our feelings – are proposals
what we feel is what we propose – and that is propositional
– not mystical
6.5. When the answer cannot be put into words, neither can
the question be put into
words.
The riddle does not exist.
If a question can be framed at all, it is also possible to
answer it.
it is not a matter of question and answer –
a proposal – a proposition is put – and put to question –
put to doubt – its uncertainty –
explored
and any propositional responses to the initial proposal –
are put to question – put to doubt – their uncertainty explored –
a riddle can exist – it’s a propositional game – a rule-governed propositional
game
in a critical
propositional process – there is no riddle – just proposal – question – doubt –
uncertainty
a proposal – a
proposition – can be put to question
and any response – any
so called ‘answer’ – is open to question – open to doubt – and is uncertain
6.51. Scepticism is not irrefutable, but obviously
nonsensical, when it tries to raise
doubts where no questions can be asked.
For doubt can only exist where a question exists, and an
answer only where something
can be said..
scepticism – as with any other proposal – is open to
question – open to doubt – and is uncertain
what is ‘nonsensical’ is that there are proposals
that are not open to question – not open to doubt – and are certain
where no question is asked – is where no proposition has
been put
when ‘something is said’ – that is – when a proposal is put
– it can be doubted – questions can be raised – and its uncertainty explored
6.52. We feel that even when all possible scientific
questions have been answered, the
problems of life remain completely untouched. Of course
there are no questions left,
and this itself is the answer.
any and all scientific propositions – are open to question –
open to doubt – and uncertain
our lives are propositional – we deal with proposals –
propositions – and we put them to question – put them to doubt – and we proceed
– with and in uncertainty
there are no questions if there are no proposals –
and any ‘answer’ – is open to question
6.521. The solution of the problem of life is seen in the
vanishing of the problem.
(Is not this the reason why those who have found after a
long period of doubt that the
sense of life became clear to them have then been unable to
say what constituted that
sense?)
life is not a problem
life – human experience – is a propositional exploration –
our logical tools are question and doubt – and with question
and doubt – we explore propositional uncertainty
with a bit of luck – what ‘vanishes’ – is ignorance
prejudice and stupidity – in short –
mysticism
‘(Is not this the reason why those who have found after a
long period of doubt that the
sense of life became clear to them have then been unable to
say what constituted that
sense?)’
the reason they have nothing to say – is because they have
stopped proposing – stopped
questioning – stopped doubting – and have fallen into the
delusion of certainty –
they have become dead-heads
6.522. There are indeed, things that cannot be put into
words. They make themselves
manifest. They are what is mystical.
‘There are indeed things that cannot be put into words.’ –
like what?
if it can’t be proposed – it’s not there
‘They make themselves manifest’
what is ‘manifest’ – is what human beings propose
‘They are what is mystical.’ –
‘they’ are what is not there –
the point is Wittgenstein cannot avoid referring to what he
says can’t be referred to
his ‘mysticism’ – is a self-refuting argument –
and his ‘logic’ ends up – in a contradictory mess –
his mysticism – is his failure – and it’s a deep failure
6.53.The correct method in philosophy would really be the
following: to say nothing
except what can be said, i.e. the propositions of natural
science – i.e. something that
has nothing to do with philosophy – and then, whenever
someone else wanted to say
something metaphysical, to demonstrate to him that he had
failed to give a meaning to
certain signs in his propositions. Although it would not be
satisfying to the other
person – he would not have the feeling that we were teaching
him philosophy – this
method would be the only strictly correct one.
‘to say nothing except what can be said’ – says nothing –
and tells us nothing
the propositions of natural science – and metaphysical
propositions – are proposals
and as with any proposal – they are open to question – open
to doubt – and uncertain
logically speaking – philosophy is no different from any
other propositional activity
and any method adopted – in any propositional endeavour – is
open to question – open to doubt – and is uncertain
6.54. My propositions serve as elucidations in the following
way: anyone who
understands me eventually recognizes them as nonsensical,
when he has used them –
as steps – to climb up beyond them. (He must, so to speak,
throw away the ladder after
he has climbed up it.)
He must transcend these propositions, and then he will see
the world aright.
Wittgenstein’s propositions are open to question – open to
doubt – and uncertain
anyone who understands them – can put them to question – put
them doubt – and explore their uncertainty
as to throwing away the ladder after it has been climbed –
of course you can stop questioning – you can put an end to
doubt – and you can close your mind to propositional uncertainty –
or at least you can try to do this – but if you have an
ounce of intelligence – your attempt
to withdraw to ignorance – will fail
if we are to live intelligently in this world –
we have to question – we have to doubt – we have to explore
uncertainty
ignorance and prejudice and pretension – are not sustainable
options
we don’t ‘transcend’ propositional reality – we can’t – our
reality is propositional
there is no actual transcendence – the idea is delusional
if seeing the world ‘aright’ – means seeing the world
without question – without doubt – and as a certainty –
then you will not see the world –
for you will be blinded by ignorance – prejudice and
pretension
Tractatus 7
7. What we cannot speak about we must pass over in silence.
what we cannot propose – in thought – word – or deed –
is not proposed
© greg . t. charlton. 2018.
