Tractatus 5

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

© greg . t. charlton. 2018.