Tractatus 3

3. A logical picture of facts is a thought

a picture is a proposal – a representational proposal

a picture of facts – will be a proposal representing facts

as to logical –

the picture / proposal – will be logical –

if it is held open to question – open to doubt – and regarded as uncertain

now do we call this ‘logical picture of facts’ – this proposal that represents facts – a ‘thought’?

this strikes me as a definition from Wittgenstein –

as it were a starting point from which he will argue

there is nothing against this – it is a proposal –

and a proposal – open to question – open to doubt – and uncertain

just why he regards a picture of facts – a thought – and what exactly this amounts to –

he is yet to explained

3.01. The totality of true thoughts is a picture of the world.

any representative proposal / any propositional picture – can be described as a picture of the world

a proposal is true – if assented to

logically speaking – a thought – is a proposal –

a proposal open to question – open to doubt – and uncertain

a ‘totality’ – is definitive –

propositional action is on-going – is indefinite

3.02. A thought contains the possibility of the situation of which it is the thought.

What is thinkable is possible too.

a proposal can be described as a ‘thought’

a proposal can be described a ‘situation’

here we have a proposal described as a ‘thought’ – and further described as a ‘situation’ –

this proposal / thought – is – the proposal / situation –

a thought does not contain the possibility of which it is a thought –

‘containing the possibility of which it is a thought’ – is metaphysical mumbo-jumbo

a proposal is an actuality –

what is thinkable – is what is proposed –

any proposal – any proposition –

is open to question – open to doubt – is uncertain

3.03. Thought can never be of anything illogical, since, if it were, we should have to

think illogically.

a proposal – a thought – that is not held open to question – not held open to doubt –

and regarded as certain – is illogical

uncritical thinking is illogical

we can – we do – think and act – illogically

3.031. It used to be said that God could create anything except what would be contrary to the laws of logic. – The truth is that we could not say what an 'illogical' world would look like.

our proposals – our propositions – are the world

an ‘illogical’ world is the world of uncritical and pretentious propositions

we all know what that looks like

3.032. It is impossible to represent in language anything that 'contradicts logic' as it is

in geometry to represent by its co-ordinates a figure that contradicts the laws of space,

or to give the co-ordinates of a point that does not exist.

language as proposal – contradicts logic – if it is uncritical and pretentious

the laws of space – as with any set of proposals are open to question – open to doubt – and uncertain

a point that does not exist – is a proposal that is not proposed –

to pretend such a proposal – is to corrupt propositional logic –

3.0321.Though a state of affairs that would contravene the laws of physics can be

represented by us spatially, one that would contravene the laws of geometry cannot.

geometry is a rule governed propositional game

3.04. If a thought were correct a priori, it would be a thought whose possibility

ensured its truth.

so called a priori truth – in so far as it is not open to question – not open to doubt – and is regarded as certain – is illogical

such a proposal – is a corruption of the proposal – of propositional logic

such a proposal is better termed a prejudice

3.05. A priori knowledge that a thought was true would be possible only if its truth

were recognizable from the thought itself (without anything to compare it with).

a proposition itself – is neither true nor false

the truth or falsity of any claim to knowledge – of any proposal – of any thought –

is a matter of assent or dissent –

and proposals of assent and proposals of dissent – are open to question – open to doubt – and uncertain

whether or not there is anything to compare a proposal to – to compare a thought to – is logically irrelevant –

what is logically relevant – is that a proposal is recognized as being open to question –

open to doubt – and uncertain

if by ‘a priori knowledge’ – is meant – proposals / propositions – not open to question – not open to doubt – and certain –

so called ‘a priori knowledge’ is illogical

the better term here is ‘a priori prejudice’

3.1. In a proposition a thought finds an expression that can be perceived by the

senses.

a proposal made public – i.e. spoken or written – can be perceived by the senses –

a proposal – not made public –  a proposal / thought not expressed – will not be perceived by the senses

3.11. We use the perceptible sign of the proposition (spoken or written, etc.) as a

projection of a possible situation.

The method of projection is to think of the sense of the proposition.

the perceptible sign of the proposition – is the proposition –

a proposal is an actual situation – not a possible situation

the ‘method of projection’ – is proposal

the sense of the proposition – is open to question – open to doubt – and is uncertain

3.12. I call the sign with which we express a thought a propositional sign. – And a

proposition is a propositional sign in its projective relation to the world.

the propositional sign is the proposal – is the proposition

the world is propositional

a proposition’s ‘projective relation to the world’ – is its proposed relation to other propositions

3.13. A proposition includes all that the projection includes, but not what is projected.

Therefore, though what is projected is not itself included, its possibility is.

A proposition therefore, does not actually contain its sense, but does contain the

possibility of expressing it.

('The content of the proposition' means the contents of a proposition that has sense).

A proposition contains the form, but not the content, of its sense.

the proposition is what is proposed

there is no ‘projection’ – just what is proposed –-

a proposal – a proposition is actual – not possible

what is ‘possible’ – is pre-propositional

the  sense of a proposition – logically speaking – is a separate proposal – to the subject proposition – a proposal put in relation to the subject proposition –

the content of a proposition – is what is proposed –

and what is proposed is open to question – open to doubt – and uncertain

the form of a proposition – is a proposed structure of the proposition –

a proposal – open to question – open to doubt – and uncertain

3.14. What constitutes a propositional sign is that in it its elements (the words) stand

in a determinate relation to one another.

A propositional sign is a fact.

what constitutes a propositional sign – is open to question – open to doubt and uncertain

this elemental / determinist characterization is one view –

and to adopt this view – may have some pragmatic value – some pragmatic use – in a particular context

however it is not the only view possible

i.e. – one may think of – and use – the proposition as it where as a whole – without any elemental analysis –

and this I would suggest is how propositions by and large are regarded in common everyday usage

in a word game – where the idea is to construct propositions – out of a limited number of words – the relation of the words may well be regarded as indeterminate – even after a proposition is constructed –

and when we are stuck for a word – and try different words to finish a sentence – do we regard the exercise of ‘constructing a proposition’ – to be determinate?

isn’t it rather that the resulting proposition is an outcome of indeterminacy? –

and where the proposition’s ‘construction’ if you want to call it that  – is seen to be – uncertain?

any so called ‘determinate’ view of the proposition – of language – will only get a start in a defined propositional context

and even there – questions can always be raised – doubts can emerge – uncertainties can be explored

a propositional sign can be described as a fact – can be regarded as a fact

3.141. A proposition is not a blend of words. – (Just as a theme in music is not a blend

of notes).

a proposition could be described – as a blend of words – just as a theme in music could be described as a blend of notes

the proposition – the nature of the proposition – is open –

open to question – open to doubt – and open to interpretation .

3.142. Only facts can express a sense, a set of names cannot.

facts are proposals –

sense is a proposal – open to question – open to doubt – and uncertain

names are proposals –

names can and do express sense –

the sense of a name – is open to question – open to doubt – and uncertain

3.143. Although a propositional sign is a fact, this is obstructed by the usual form of

expression in writing or print.

For in a printed proposition, for example, no essential difference is apparent between

a propositional sign and a word.

(That is what made for Frege to call a proposition a composite name).

a fact is a proposal –

any form of expression is a proposal –

there is no essential difference between a propositional sign and a word

the propositional sign is a proposal – a word is a proposal –

a proposal is open to question – open to doubt – and uncertain

3.1431. The essence of a propositional sign is very clearly seen if we imagine one

composed of spatial objects (such as tables, chairs, and books) instead of written signs

Then the spatial arrangement of these things will express the sense of a proposition

imagining spatial objects – is proposing objects – and proposing a relation between them

a relation – described as – proposed as – ‘spatial’

whether written or not we are dealing with proposals – propositions –

the sense of any proposal / proposition – is open to question – open to doubt – and uncertain

3.1432. Instead of, ‘The complex sign "aRb" says a stands in relation to b in the relation

R', we ought to put, 'That "a" stands to "b" in a certain relation says that aRb'.

we have the proposal "aRb" –

this proposal – as with any proposal – is open to interpretation –

the propositional analysis – ‘a stands in relation to b in the relation R' – is one interpretative proposal of "aRb"

'That "a" stands to "b" in a certain relation says that aRb' – is another

the difference between – ‘a stands in relation to b’ and ‘That a stands to b in a certain relation’ – if anything – comes down to a difference of emphasis or a difference of presentation

the difference is rhetorical – not logical

3.144. Situations can be described but not given names.

(Names are like points; propositions like arrows – they have sense.)

a propositional situation can be given a name – propositional situations are named

take for example the propositional situations of the weather patterns – el nino and la nina

names are proposals – and proposals can be variously interpreted and described

the sense of any proposal – of any proposition – is open to question

3.2. In a proposition a thought can be expressed in such a way that elements of the

propositional sign correspond to the objects of thought.

a thought is a proposal – is a proposition

a proposition can be given an elemental analysis –

and it can be proposed that the elements of one proposition – of one propositional sign correspond to the elements in another

these propositions – the relational proposition – and the subject propositions – are open to question – open to doubt – and are uncertain

3.201. I call such elements 'simple signs', and such a proposition 'completely

analysed'.

you can call your elements ‘simple signs’ – and you can call such a proposal – ‘completely analysed’ – if it suits your purposes

logically speaking though – no proposition is completely analysed

a proposition is open – open to question – open to doubt – open to analysis – and uncertain

a so called ‘completely analysed’ proposition – is a logically dead proposition

you can – for whatever reason – decide to stop the logical actions of question and doubt –

at best this is a pragmatic decision – the point of which is to proceed – to get on with it

at worst it is an ignorant and pretentious decision – that is a turning away from critical analysis – a turning away from logic

any propositional decision is open to question – to doubt – and is uncertain

3.202. The simple signs employed in propositions are called names.

a proposal can be analysed – can be described in terms of simple signs – and you can call these simple signs names

and this analytical proposal of simple signs as names – is logically speaking – open to question – open to doubt – and is uncertain

3.203. A name means an object. The object is its meaning. ('A' is the same sign as 'A'.)

a name proposal – is an identifying proposal –

the proposal that ‘a name means an object’ – is to propose a relation between a name proposal – and an object proposal

it is to say that the name proposal identifies the object proposal –

the relational proposal – the name proposal – and the object proposal – are open to question – open to doubt – and uncertain

‘the object is its meaning’ –

is to propose that the object proposal – is identified by the name proposal –

this may or may not be the case – but it is the proposal

“A’ is the same sign as ‘A” – is to posit ‘A’ as ‘A’ – which is pointless

repetition does not elucidate anything –

to suggest that it does – is just pretentious rhetoric

3.21. The configuration of objects in a situation corresponds to the configuration of

simple signs in the propositional sign.

the configuration of objects is a proposal – a propositional construction – and is the propositional situation

that there is a correspondence between this proposal – and the proposal of a configuration of simple signs – is a proposal – a relational proposal

these proposals are open to question – open to doubt – and uncertain

3.22. In a proposition a name is the representative of an object.

a name in a proposition is a proposal –

an object is a proposal

that a name proposal represents an object proposal – is a proposal –

a proposal open to question – open to doubt and uncertain

3.221. Objects can only be named. Signs are their representatives. I can only speak

about them: I cannot put them into words. Propositions can only say how things are,

not what they are.

we propose in relation to proposals –

object proposals – can be named – and they can be described –

it can be proposed that propositions / signs represent object proposals –

speaking about object proposals – is – proposing in relation to them – is – putting them into words

‘things’ are proposals –

I can propose how things / propositions are – and I can propose – what they are

and any proposal put – is open to question – open to doubt – and is uncertain

3.23. The requirement that simple signs be possible is the requirement that sense be

determinate.

sense – the sense of a proposition – from a logical point of view – is open to question – open to doubt – and uncertain

logically speaking – sense is indeterminate

simple signs – as with any other propositional construct – are open to question – open to doubt and uncertain

3.24. A proposition about a complex stands in an internal relation to a proposition

about a constituent of the complex.

A complex can be given by its description, which will be right or wrong. A

proposition that mentions a complex will not be non-sensical if the complex does not

exist, but simply false.

When a propositional element signifies a complex, this can be seen from an

indeterminateness in the propositions in which it occurs. In such cases we know that

the proposition leaves something undetermined. (In fact the notation for generality

contains a prototype.)

The contraction of a symbol for a complex into a simple symbol can be expressed in a

definition.

a proposition about a complex – and a proposition about a constituent of the complex – are two different and separate propositions –

to say that one is internal to the other – that one is ‘in’ the other – is to confuse them

a relation between propositions is a proposal – separate to the two propositions in question –

the relation is an external proposal

a propositional description – is not right or wrong – it is open to question – open to doubt – and is uncertain –

you can proceed with a description – or not – in either case your decision is logically uncertain –

and any reasons you have for proceeding or not – are open to question

a proposition – a proposal concerning a non-existent propositional complex – is a ridiculous notion

a proposition exists if it is proposed

if it is not proposed – it’s not there – it doesn’t exist

an element – is an element of a complex – by definition

and an element signifying a complex – will leave unsaid – what is left of the complex

and yes proposing a symbol for a complex is really a matter of definition

even so – such a definition is open to question

3.25. A proposition has one and only one complete analysis.

the idea that a proposal – a proposition has one and only one complete analysis – is illogical – and pretentious

regardless of any proposed analysis – a proposition is logically speaking – open –

open  to question – open to doubt – and uncertain –

3.251. What a proposition expresses it expresses in a determinate manner, which can

be set out clearly: a proposition is articulate.

what is proposed is open to question –

any determination of what is proposed – is a proposal –

a proposal – open to question – open to doubt and uncertain

a clear presentation – is open to question

a proposition is articulate

3.26. A name cannot be dissected any further by means of a definition: it is a primitive sign.

a name is a sign – is a proposal

a proposal / name – is open to question – open to doubt – and uncertain –

a definition – is a proposal – open to question – open to doubt – and uncertain

if by ‘primitive sign’ is meant a proposal – that is not open to question – open to doubt – and certain

there is no primitive sign

3.261. Every sign that has a definition signifies via the signs that serve to define it;

and the definitions point the way.

Two signs cannot signify in the same manner if one is primitive and the other is

defined by means of primitive signs. Names cannot be anatomized by means of

definitions.

(Nor can any sign that has a meaning independently and on its own.)

if a sign – (a proposal) – is defined – in terms of other proposals (signs) – it is transformed by the signs (proposals) that define it

what way a proposed definitions points – is open to question

a sign that is not propositionally transformed – will be different to one that is

what one sign signifies relative to another is open to question –

there are no ‘primitive’ signs

any sign is open to question – open to doubt – and uncertain

a name is a proposal – open to question – open to doubt – and uncertain

a definition is a proposal – open to question – open to doubt – and uncertain

a name can be defined –

a defining proposal can be put to a name –

i.e. – this name means this in this context

signs are given meaning –  that is to say meaning is proposed

no sign has a meaning ‘independently and on its own’

any proposed meaning of any sign is open to question – open to doubt – and is uncertain

3.262. What signs fail to express, their application shows. What signs slur over, their

application says clearly.

what a sign expresses is open to question – open to doubt and uncertain

the application of a sign is open to question – open to doubt and uncertain

3.263. The meanings of primitive signs can be explained by means of elucidations.

Elucidations are propositions that contain primitive signs. So they can only be

understood if the meanings of those signs are already known.

so called ‘primitive signs’ are proposals – open to question – open to doubt – and uncertain

any elucidation of a proposal / sign – is propositional

an elucidating proposition refers to the proposal / sign – to be elucidated

the meaning of the sign – before and after any propositional elucidation – is open to question – open to doubt and uncertain

what is known – is what is proposed –

what is proposed – is open to question – open to doubt and uncertain

3.3. Only propositions have sense; only in the nexus of a proposition does a name

have meaning.

there is nothing other than proposal

sense is a proposal – a name is a proposal – meaning is a proposal

a name can have meaning as a stand alone proposition –

or ‘in the nexus of a proposition’ –

that is a sign in a proposal

any proposal – is open to question – open to doubt – and is uncertain

3.31. I call any part of the proposition that characterizes its sense an expression (a

symbol).

(A proposition is itself an expression.)

Everything essential to their sense that propositions can have in common with one

another is an expression.

An expression is the mark of form and content.

any characterization of sense – is a proposal –

a proposal – put in relation to the proposition in question

‘a proposition in itself’ – is a proposal –

any proposal of sense – is open to question

there is nothing ‘essential’ any proposal of sense

what propositions have in common with one another is that they are open to question – open to doubt – and uncertain

an expression is a proposal – if it is a mark of form (structure) and content – it is proposed as a mark of form (structure) and content

and as such – open to question – open to doubt – and uncertain

3.311. An expression presupposes the forms of all the propositions in which it can

occur. It is the common characteristic mark of a class of propositions.

an expression – a proposal – occurs where it does occur – where it is proposed

an expression – a proposal – does not presuppose where it can occur

an expression / proposal – is not the common characteristic mark of a class of propositions –

unless it is proposed as such

3.312. It is therefore presented by means of the general form of the propositions that

it characterizes.

In fact, in this form the expression will be constant and everything else variable.

‘It is therefore presented by means of the general form of the propositions that

it characterizes.’ –

the form of a proposition – is its proposed propositional structure –

as to ‘general form’ –

a proposition is a proposal – and any proposal of a ‘general structure’ – a structure common to all propositions – is open to question – open to doubt – and uncertain

an expression / proposal – put as a characterization of other propositions – is a proposal – open to question – open to doubt – and uncertain

‘In fact, in this form the expression will be constant and everything else variable.’

a proposed characterization – will be ‘constant’ – so long as the proposal is adhered to

as to ‘everything else is variable’ –

presumably that means that the class of propositions – that this proposal of characterization is put in relation to – is variable

what is being proposed here – is a propositional game

3.313. Thus an expression is presented by means of a variable whose values are the

propositions that contain the expression.

(in the limiting case the variable becomes a constant, the expression becomes a

proposition.)

I call such a variable a 'propositional variable'.

it is not that an expression becomes a proposition – when a variable becomes a constant

the expression is a proposition – to begin with – however it is played

what you have here – is two different – propositional games

game one – the expression / proposal / proposition – as a variable

game two – the expression / proposal / proposition – as a constant

3.314. An expression has meaning only in a proposition. All variables can be

constructed as propositional variables.

(Even variable names)

an expression is a proposal – is a proposition –

we can simply drop this notion of ‘expression’ – it is a logical redundancy

a variable is a propositional game –

variable names – is a variable game

3.315. If we turn a constituent of a proposition into a variable, there is a class of

propositions all of which are values of the resulting variable proposition. In general,

this class too will be dependent on the meaning that our arbitrary conventions have

given to parts of the original proposition. But if all the signs in it that have arbitrarily

determined meanings are turned into variables, we shall still get a class of this kind.

This one, however, is not dependent on any convention, but solely on the nature of the

proposition. It corresponds to a logical form – a logical prototype.

there are two modes of propositional activity –

the critical or logical mode – and the game mode

in the critical mode – propositions are put to question – put to doubt – and their uncertainty – explored –

in the game mode – propositions and propositional structures are rule governed

if you play the game – you play in accordance with the rules proposed –

if you don’t play in accordance with the rules – you don’t play the game

a propositional game – as played is not open to question – open to doubt – or uncertain

the game is not questioned – it is played

Wittgenstein begins by saying –

‘If we turn a constituent of a proposition into a variable, there is a class of propositions all of which are values of the resulting variable proposition.’

here he is proposing a propositional game – the variable game

the first move in this game is to turn a ‘constituent’ of a proposition – into a variable –

Wittgenstein is using the definition of the variable commonly used in formal logic –

the ‘variable’ – as ‘the unspecified member of a class or set’

(in propositional logic the letters p – q – and r – are conventionally used as propositional variables – in predicate logic – the letters x – y – an z – are used as variables)

and a rule of Wittgenstein’s ‘variable game’ – is that there is a class of propositions all of which are values of the resulting variable proposition

‘In general, this class too will be dependent on the meaning that our arbitrary conventions have given to parts of the original proposition.’

‘our arbitrary conventions’ – whatever they may be – will be operating rules of this variable game

‘But if all the signs in it that have arbitrarily determined meanings are turned into variables, we shall still get a class of this kind’ –

this is to say that if all the signs in the game are turned into variables – we still have this variable game

‘This one, however, is not dependent on any convention, but solely on the nature of the proposition. It corresponds to a logical form – a logical prototype.’

‘a logical form’ – is  a proposed propositional  structure –

there are no ‘logical prototypes’ – there are different logical forms – that is different propositional / game structures – and there are different propositional games –

in practise propositional games – if they are generally accepted propositional practises – are conventions –

rule governed conventions

3.316. What values a propositional variable may take is something that is stipulated.

The stipulation of values is the variable.

a propositional game – is a rule governed propositional action

‘What values a propositional variable may take is something that is stipulated.’

the values – are the rules adopted for the game

‘the stipulation of values is the variable’ – is the variable game

3.317. To stipulate values for a propositional variable is to give the propositions

whose common characteristic the variable is.

The stipulation is the description of those propositions.

The stipulation will therefore be concerned only with symbols, not with their

meaning.

And the only thing essential to the stipulation is that it is merely a description of

symbols and states nothing about what is signified.

How the description of the proposition is produced is not essential

to stipulate values for a propositional variable –  is to give the rule for the variable game

the rule of a propositional game – determines the propositions to be played

the stipulation is the rule of the game –

the rule of the game does not ‘describe’ the game propositions – it determines the game propositions – and the possibilities of their play

the rule of the game determines the play of the symbols –

their ‘meaning’ – in the game – is not relevant

the rule of the game defines the symbols and  determines the play of the symbols –

a game does not signify – a game is played

if the proposition is a game proposition – that is to say – rule governed –

‘description’ of it – is effectively irrelevant to the game –

what is essential to the game – is that the proposition – the play of the proposition – is rule governed

if it is not rule governed – it is not a game proposition

3.318. Like Frege and Russell I construe a proposition as a function of the expressions

contained in it.

the proposition is not a function of the expressions contained in it –

a proposition is a proposal –

we can regard the proposition critically – as open to question – open to doubt – and uncertain

or we can regard the proposition as rule governed – as a token in a propositional game

a functional analysis of the proposition – transform the proposition into a game

that is – a rule-governed propositional play

like Frege and Russell – Wittgenstein is a game designer and a game player

you can design whatever propositional game you like – and play it to your heart’s content

on the other hand – ‘logic’ – properly understood – is the critical activity – of question – of doubt – and the exploration of uncertainty

3.32. A sign is what can be perceived of a symbol.

a sign is / can be – what is perceived of a symbol – if it is so proposed

3.321. So the one and the same sign (written or spoken, etc.) can be common to two

different symbols – in which case they will signify in different ways.

two different symbols will signify differently –

and this will be the case whether or not the one and the same sign is said to be common to two different symbols –

if the sign is – prime facie –‘common’ to different symbols – it will – in different symbols – have a different significance –

it will – as it were – be transformed by the symbol

it will in different symbols – signify differently –

effectively – despite appearances – it will be a different sign – from one symbol to another

the symbol – relative to the sign is best understood as the propositional context of the sign –

we have the one sign functioning in different propositional contexts

in different contexts signs will have different signification

and once this is understood – in formal language – a difference in notation should be indicated – should be signed

3.322. Our use of the same sign to signify two different objects can never indicate a

common characteristic of the two, if we use it with two different modes of

signification. For the sign, of course is arbitrary. So we could choose two different

signs instead, and then what would be left in common on the signifying side?

the use of the one sign / proposal – to signify different object / proposals – doesn’t work –

it is either logical laziness – or  the two object / proposals – are not different –

the mode of signification is how the sign is expressed – and how the sign is expressed – just is the sign expressed

different modes – different signs

and in formal propositional language – in formal logical games – we should use different sign / proposals to indicate different object / proposals

what would be left in common on the signifying side?

signs – open to question – open to doubt – and uncertain

3.323. In every day language it very frequently happens that the same word has

different modes of signification – and so belongs to different symbols – or that two

words that have different modes of signification are employed in propositions in what

is superficially the same way.

Thus the word 'is' figures as the copula, as a sign for identity, and as an expression for

existence; 'exist' figures as an intransitive verb like 'go', and 'identical' as an adjective;

we speak of something, but also of something's happening.

(In the proposition, 'Green is green' – where the first word is the proper name of a

person and the last an adjective – these words do not merely have different meanings:

they are different symbols).

where the same word has different modes of signification – we understand the difference if we understand the different propositional contexts / symbols in which the word is being used –

different symbols are different propositional contexts –

and where two words that have different modes of signification are employed in propositions in what is superficially the same way –

you either understand the different propositional contexts of use – or you find different words

outside of a rule-governed / game propositional context – propositional use is never clear-cut or uncontroversial –

all non-game propositional use is open to question – open to doubt – and uncertain

we live and in and deal with propositional uncertainty

‘(In the proposition, 'Green is green' – where the first word is the proper name of a

person and the last an adjective – these words do not merely have different meanings:

they are different symbols).’

these words in standard usage – have different meanings and can be analysed in terms of different symbols

a symbol represents a propositional context – different symbols – different propositional contexts

3.324. In this way the most fundamental confusions are easily produced (the whole of

philosophy is full of them).

if you understand that a proposition – outside of a rule governed / game context – is open to question – open to doubt and uncertain – there is no room for confusion –

what we face and what we deal with is uncertainty

3.325. In order to avoid such errors we must make use of a sign-language that

excludes them by not using the same sign for different symbols and by not using in a

superficially similar way signs that have different modes of signification: that is to say

a sign-language that is governed by logical grammar – by logical syntax.

(The conceptual notation of Frege and Russell is such a language, though it is true, it

fails to exclude all mistakes.)

the use of a sign-language that excludes the use of the same sign for different symbols – makes obvious sense –

a sign-language that doesn’t do this – is a failure

a sign-language governed by ‘logical syntax’ – is rule-governed – a rule governed language – a game language

‘logical syntax’ – here – is a game language – and its accompanied set of rules

strictly speaking there are no mistakes in a game – or in a game language

if the rules are inadequate or faulty – there is no game to begin with

also – one game may be more comprehensive – more wide-ranging than another –

and if so – this will be determined by the rules –

and here we will be dealing with different games

the conceptual notation of Frege and Russell – is a different game – to that proposed by Wittgenstein

3.326. In order to recognize a symbol with its sign we must observe how it is used

with a sense.

the use of a symbol with its sign – in a formal language is rule governed

which is to say – has nothing to do with questions of sense

3.327. A sign does not determine a logical form unless it is taken together with its

logico-syntactical employment.

a sign is a representative of logical form – of a proposed logical structure

its logico-syntactical employment is the rule governed application of structure – in a propositional game

3.328. If a sign is useless, it is meaningless. That is the point of Occam's maxim.

(If everything behaves as if a sign had meaning, then it does have meaning.)

if a sign has no use – no rule governed application – no game application – yes – it is useless –

this has nothing to do with Occam or his razor

3.33. In logical syntax the meaning of a sign should never play a role. It must be

possible to establish a logical syntax without mentioning the meaning of a sign: only

the description of expressions may be presupposed.

in logical syntax – signs are rule governed

in rule governed propositional games – meaning is not in the picture

the point of a rule governed propositional game – is its play

the establishment of logical syntax is the establishment of a game language –

what it presupposes is – the rules of the game

propositional rules are the instruments of propositional play –

if you want to play – you set up the  rules

3.331. From this observation we turn to Russell's 'theory of types'. It can be seen that

Russell must be wrong, because he had to mention the meaning of signs when

establishing the rules for them.

Russell confused propositional logic – with propositional game playing

3.332. No proposition can make a statement about itself, because a propositional sign

cannot be contained in itself.

propositions are proposals – but propositions do no not propose –

propositions are proposed by human beings

a proposition about a proposition – is a separate proposition –

a separate proposal –

the theory of types is a proposal of propositional relation – a proposal of propositional structure –

as with any proposal – it is open to question – open to doubt – and is uncertain –

and as with any proposal – its value is a question of its utility –

and utility is a matter – open to question

3.333 The reason why a function cannot be its own argument is that the sign for a function already contains the prototype of its argument, and it cannot contain itself.

For let us suppose that the function F(fx) could be its own argument: in that case there would be a proposition ‘F(F(fx))’, in which the outer function F and the inner function F must have different meanings, since the inner one has the form f(fx) and the outer has the form y(f(fx)). Only the letter ‘F’ is common to the two functions, but the letter by itself signifies nothing.

This immediately becomes clear if instead of ‘F(Fu)’ we write ‘($f): F(fu). fu = Fu’.

That disposes of Russell’s paradox.

a function is a propositional game –

the rule of the game is that for any given first term – there is exactly one second term

the constituent(s) of the first term are called the argument(s) of the function – and of the second term the value of the function

the function game – can be analysed into the components – ‘argument’ and ‘value’ –

seen this way the ‘argument’ is a component of the function – not the function itself –

and the sign for the function is not a component of itself

it makes no sense to speak of a proposition – or a propositional game – or for that matter – anything else – containing itself

a propositional game – is a rule governed propositional play –

it doesn’t ‘contain’ anything – it has no ‘self’

the so called ‘outer function F’ and ‘the inner function F’ are either two different functions – or the one function reasserted –

if they are different functions – then they should be distinguished in the notation i.e. F and F¢

if they are one in the same – then the reassertion is logically irrelevant –

and the notation F(F(fx)) –  is a confused mess

3.334. The rules of logical syntax must go without saying, once we know how each

individual sign signifies.

how we know how each individual sign signifies – is rule governed –

and the rules must be stated – if there is to be a game

3.34. A proposition possesses essential and accidental features.

Accidental features are those that result from the particular way in which the

propositional sign is produced. Essential features are those without which the

proposition could not express its sense.

a proposition is a proposal – open to question – open to doubt – and uncertain

any proposed feature of a proposition – is open to question –

the sense of a proposition – is open to question – open to doubt – and is uncertain

3.341. So what is essential in a proposition is what all propositions that can express

the same sense have in common.

And similarly, in general, what is essential in a symbol is what all symbols that can

serve the same purpose have in common

the sense of a proposition – is open to question – open to doubt – and is uncertain

what propositions have in common – is logical uncertainty

in a game context – what is ‘essential’ in a symbol – is that it is rule-governed

3.3411. So one could say that the real name of an object was what all symbols that

signified it have in common. Thus, one by one, all kinds of composition would prove

to be unessential to a name.

the ‘real name’ of an object / proposition – is whatever name it is given

there is nothing essential to a name

3.342. Although there is something arbitrary in our notations, this much is not

arbitrary – that when we have determined one thing arbitrarily, something else is

necessarily the case. (This derives from the essence of notation.)

any proposal – or any aspect of any proposal – is open to question – open to doubt – and is uncertain

there are entrenched propositional practises – and rule-governed propositional games –

necessity is a propositional game – a rule governed game

notation – has no essence

3.3421. A particular mode of signifying may be unimportant but it is always important that it is a possible mode of signifying. And it is generally so in philosophy: again and again the individual case turns out to be unimportant, but the possibility of each case discloses something about the essence of the world.

any mode of signifying is valid –

what is important – or unimportant – is a question of propositional / philosophical fashion

in the absence of proposal – our world is unknown

any proposal put – makes known –

our world is propositional –

‘the world’ – is what is proposed –

what is proposed – is open to question – open to doubt – and is uncertain –

the world has no essence

3.343. Definitions are rules for translating from one language into another. Any

correct sign-language must be translatable into any other in accordance with such

rules; it is this they all have in common.

translation is a definition game – a rule governed propositional game

that is to say – to achieve a translation – you follow the rules proposed –

if you don’t follow the rules – you don’t translate

and yes what different sign games have in common is these translation rules

you can of course engage in the logical activity of question – of doubt – and of exploring the uncertainty of the proposed rules of translation

doing this though – is not playing the game –

it is not translating

3.344. What signifies in a symbol is what is common to all the symbols that the rules of logical syntax allow us to substitute for it.

yes – the symbol represents a rule governed propositional game –

if the game is a ‘logical syntax game ‘ then the game is governed by the rules of logical syntax

the rules of logical syntax determine symbolic substitution

you can question the rules of logical syntax – but this is a logical activity –

it is not playing the substitution game

3.3441. For instance, we can express what is common to all notations for truth

functions in the following way: they have in common that, for example, the notation

that uses '~p' ('not p') and 'pvq' ('p or q') can be substitutes for any of them.

(This serves to characterize the way in which something general can be disclosed by

the possibility of a specific notion.)

truth functional analysis is a rule governed sign-game – a rule governed propositional game

there are substitution rules in this game

if you play such a rule governed game – you play according to the rules –

if you don’t follow the rules – you don’t play the game –

‘something general can be disclosed  by the possibility of a specific notation’ –

the ‘something general’ that is disclosed – is the game –

the rule governed propositional game

3.3442. Nor does analysis resolve the sign for a complex in an arbitrary way, so that it

would have a different resolution every time that it was incorporated in a different

proposition.

analysis here is rule governed and is integral to the game – as played

3.4. A proposition determines a place in logical space. The existence of this logical

space is guaranteed by the mere existence of the constituents – by the existence of the

proposition with sense.

we can talk about propositions – without the notion of logical space

I think that the notion of logical space – is an unnecessary underpinning of propositional action –

however – if it has its use – it has its use –

but the use is rhetorical – not logical

3.41 The propositional sign with logical co-ordinates – that is the logical place.

the propositional sign with logical co-ordinates – is a proposal

3.411. In geometry and logic alike a place is a possibility; something can exist in it.

a place is a proposal

3.42. A proposition can determine only one place in logical space: nevertheless the

whole of logical space must already be given by it.

(Otherwise negation, logical sum, logical product, etc., would introduce more and

more elements – in co-ordination.)

(The logical scaffolding surrounding a picture determines logical space. The force of a proposition reaches through logical space.)

this ‘whole of logical space’ idea – just strikes me as mystical –

as little more than rhetorical packaging

what is given by a proposal – by a proposition – is open to question – open to doubt and uncertain

negation – logical sum – logical product – are rule governed propositional actions –

propositional games

propositions exist and function in proposed propositional contexts – structures – and in propositional games

3.5. A propositional sign, applied and thought out, is a thought.

a propositional sign – applied – is a proposal – applied

the proposal – is open to question – open to interpretation – open to description –

its application – is open to question – open to doubt – and uncertain

a proposal can be described as a thought

© greg . t. charlton. 2018.