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'.

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'.

in Wittgenstein’s propositional game the rule is that you can’t say ‘there are 100 objects'  or 'there are  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'

                                                                                                                             

‘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

© greg . t. charlton. 2018.