WittgensteinThemes from the Tractatus I:

Reality and Pictures of Reality

James Studd

FRW Lecture 7. Friday wk. 3, TT14

1 Two Lectures on the Tractatus

The 7 principal propositions of the Tractatus

1. The world is all that is the case.

2. What is the case—a fact—is the existence of states of affairs.

3. A logical picture of facts is a thought.

4. A thought is a proposition with sense.

5. A proposition is a truth-function of elementary propositions.

(An elementary proposition is a truth function of itself.)

6. The general form of a truth-function is [p, ξ,Npξq].

This is the general form of a proposition.

7. What we cannot speak about we must pass over in silence.

Week 3: Wittgenstein’s Logical Atomism, the Picture Theory

Week 5: Logic, the limits of expression; showing and saying.

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2 Logical Atomism

The opening of the Tractatus has an ostensibly metaphysical character:

1. The world is all that is the case.

2. What is the case—a fact—is the existence of states of affairs.

2.01. A state of affairs. . . is a combination of objects.

2.02. Objects are simple.

Let’s consider Wittgenstein’s elaboration on the various elements at face value:

Objects

Example of objects

Frege: ordinary things (chairs, people, . . . .); abstract things (numbers, . . . )

Russell: sense-data (the-brown-patch-chair-shaped-datum, . . . )

Wittgenstein: —

[Tractatus gives no examples; for the sake of exposition, we pretend ordinary things areobjects.]

Objects vs. relations

Frege and Russell: objects are sharply distinguished from relations.

Wittgenstein: —

The objects remains constant across possible situations

2.022 It is obvious that an imagined world, however different it may be from thereal one, must have something—a form—in common with it.

2.023 Objects are just what constitute this unalterable form.

States of affairs and facts

(a) ‘In a state of affairs, objects stand in a determinate relation to one another.’

(b) States of affairs vary from world to world

(c) Facts are existent states of affairs.

(d) Unlike Russell: no general facts; no genuine (existent) negative facts.

(‘negative facts’ (so called) are the non-existence of a fact. (2.06))

Example: James’s standing and James’s sitting are both states of affairs; only the formeris a fact.

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Possible situations

Possible situations consist of the possibility of existence and non-existence of states ofaffairs (see, e.g. 2.201–2.202)

2.061 State of affairs are independent of one another.

2.062 From the existence or non-existence of one state of affairs it is impossibleto infer the existence or non-existence of another.

4.27 For n states of affairs, there are Kn “ Σnv“0

`

nv

˘

possibilities of existenceand non-existence.

Of these states of affairs, any combinations can exist and the remindernot exist.1

A toy example: Suppose there are two states of affairs: Fa and Fb. Then, there are:

1 p“`

20

˘

q possible situation where neither exists.

2 p“`

21

˘

q possible situation where one exists.

1 p“`

22

˘

q 1 possible situation where both exist.

So the total number of possible situations is 4. (K2 “`

20

˘

``

21

˘

``

22

˘

“ 22)

The world

Wittgenstein elaborates:

1. The world is all that is the case.

1.1 The world is the totality of facts not of things

1.11 The world is determined by the facts, and by their being all the facts

Granted the invariance of objects, the world must clearly be more than their collection(else all possible worlds would be the same).

But why require that the facts be all the facts?

Russell: ‘You never can arrive at a general proposition by inference from particular propo-sitions alone.” (LA, 235.)

Suppose, for example, that you wish to prove . . . that ‘All men are mortal’. . . and say ‘A is man that is mortal’, ‘B is man that is mortal’, ‘C is a manthat is mortal’, and so on until you finish. You will not be able, in that way, toarrive at the proposition ‘All men are mortal’ unless you known when you havefinished. That is to say, that in order to arrive . . . at the general proposition,you must already have the general proposition ‘All men are among those I haveenumerated’. (ibid.)

Russell: there are general facts (and primitive knowledge of them).

Wittgenstein: no general facts. The truth and falsity of general propositions is determinedby the particular facts being all the facts.

1Recall`

nv

˘

is the number of ways of choosing v things from n things—i.e. the number of v-membered

subsets and n-membered set has. e.g.`

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˘

“ 3.

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3 Picture Theory

Wittgenstein: ‘We picture facts to ourselves.’ (2.1)

2.12 A picture is a model of reality.

2.131 In a picture the elements of the picture are representatives of objects.

2.15 The fact that the elements of a picture are related to one another in adeterminate way represents that things are related to one another in thesame way.

The picture theory of propositions

4.01 A proposition is a picture of reality

A propositions is a model of reality as we imagine it. (cf. 2.12)

3.22 In a proposition a name [simple sign (3.201)] is the representative of anobject. (cf. 2.131)

3.21 The configuration of objects in a situation corresponds to the configurationof simple signs in the propositional sign. (cf. 2.15)

A picture of the picture theory

How might we picture the state of affairs that Russell loves Wittgenstein.

Propositional sign (a fact)

form: Fhkkkikkkj

aRb P

Pictorial relationship Ó Ó π

Sense (a possible situation) Russell loves Wittgensteinloooooooooooooooomoooooooooooooooon

form: F

πpP q

• Other pictures (composed of words, sounds, action figures, . . . ) with the same logicalform can represent the same possible situation.

• Holding π fixed: bRa asserts that Wittgenstein loves Russell.

• Varying π: aRb can express any possible situation with logical form F

(A) A picture (or propositional sign) P is fact: the fact that the elements e1, e2, . . . of thepicture (constituent simple signs) are arranged accord to the pictures’ pictorial form(proposition’s logical) form F . (2.14, 3.14)

(B) The elements e1, e2, . . . of P stand in a pictorial relation π to things in the worldπpe1q, πpe2q, . . .. (2.1513–4)

(C) P represent the possible situation πpP q that the depicted things πpe1q, πpe2q, . . . arearranged according to the form F . (2.15, 2.2, 2.201)

(D) P is a correct picture (a true proposition) if πpP q is how things actually are. (2.21)

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4 Motivations for the Picture theory

Russell and Wittgenstein:

• Empty names (which don’t represent any object) are meaningless.

• False propositions (which don’t represent any fact) are meaningful.

How can we explain this difference?

Russell ‘Desdemona loves Cassio’ can’t express the fact that Desdemona loves Cassio. Shedoesn’t; so there’s no such fact. (LA, 225)

Frege’s solution: posit thoughts

• Empty names may be meaningful by virtue of expressing a sense.

• False propositions may be meaningful by expressing a thought.

Frege: thoughts neither belong to the subjective inner world, nor the external world

A third realm must be recognized. What belongs to this corresponds withideas, in that it cannot be perceived by the senses, but with things, in thatit needs no bearer to the contents of whose consciousness to belong. Thusthe thought, for example, which we expressed in the Pythagorean theorem istimelessly true, true independently of whether anyone takes it to be true. Itneeds no bearer. It is not true for the first time when it is discovered, but islike a planet which, already before anyone has seen it, has been in interactionwith other planets. (‘The thought’, 302)2

Worry: how, then, do we come to grasp thoughts? How do we access the third realm?

Russell’s solution: the multiple relation theory of judgment

Although the fact that Desdemona loves Cassio does not exist; it’s constituents do.

Russell (1910): Othello believes that Desdemona loves Cassio iff Othello stands in thebelieving relation to: Dedemona, the relation loves, and Cassio.

Analogously (we might suggest): The sentence ‘Desdemona loves Cassio’ says that Desde-mona loves Cassio iff the sentence stands in the saying relation to: Dedemona, the relationloves, Cassio.

2Mind 65 (1956) [1918], 289–311.

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Wittgenstein objects

3.141 A proposition is not a blend of words.—(Just as a theme in music is nota blend of notes.)

A proposition is articulate.

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

Consider the difference between the following:

(1) Desdemona, loves, Cassio

(2) Desdemona loves Cassio

• The list of words (1) merely lists entities: Desdemona, the relation loves, and Cassio.

• The sentence (2) says something about how these constituents fit together: namely,that Desdemona loves Cassio.

How can (2) achieve this?

Russell (1910): hard to see how (2) improves on (1).

Russell (1913): Bring in logical forms too. Othello’s belief is not just a relation to Desde-mona, loves, and Cassio, but also the logical form of the proposition.

Worry: a return to the third realm?

Wittgenstein’s response

3.1431 The essence of a propositional sign is very clearly seen if we imagine onecomposed of spatial objects (such as tables, chairs, and books) instead ofwritten signs.

Then the spatial arrangement of these things will express the sense of theproposition.

3.1432 Instead of, ‘The complex sign “aRb” says that a stands to b in the relationR, we ought to put, ‘That “a” stands to “b” in a certain relation says thataRb.

3.21 The configuration of objects in a situation correponds to the configurationof simple signs in the propositional sign.

(A) The crucial point is that while (1) is a list; (2) is a fact.

(B) We need not be acquainted with a third realm of forms in order to see how theconstituents fit together.

(C) The propositional sign itself shows us this in its logical form.

(D) It is not the list of words that says that Desdemona love Cassio; it is the fact that“Desdemona” stands to “Cassio” in a certain relation—e.g. respectively flanking theleft and right of the expression “loves”—says that Desdemona loves Cassio.

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5 A case for atomism

Russell and Wittgenstein both endorse the possibility of analysis:

4.221 It is obvious that the analysis of propositions must bring us to elementarypropositions which consist of names in immediate combination.

Why is this obvious?

Russell: analysis is necessary to explain how we can understand propositions. They must—after analysis—consist only of constituents with which we are acquainted.

Wittgenstein: simple objects are a precondition for meaningful expression.

Wittgenstein case for atomism

2.021 Objects make up the substance of the world. That is why they cannot becomposite.

2.0211 If the world had no substance, then whether a proposition had sense woulddepend on whether another proposition was true.

2.0212 In that case we could not sketch any picture of the world (true or false)

4.061 A proposition has a sense that is independent of the facts.

Pears on Wittgenstein’s case for atomism

(P1) ‘If there were any complex things named in the complete analyses of ordinary factualsentences, then the analysing sentences would have sense only if certain other sentence. . . were true.’

(P2) ‘But the sense of a sentence about a complex thing cannot possibly depend on thetruth of another sentence about its components. ’

So (C) Only simple things are named in complete analyses.3

In support of (P1)

Consider φa, and suppose a is complex: e.g. b-standing-in-R-to-c.

• Wittgenstein: this has sense (depicts a possible situation) only if a denote an object.

• But: a denotes an object only if bRc

So φ has sense only if bRc is true.

In support of (P2): why can’t bRc be a condition on φa having sense?

Pears: sense-conditions are ineffable. But what. . . ‘bRc’ says is evidently not ineffable.

Next time: why does Wittgenstein take sense-conditions to be ineffable?

3David Pears The False Prison, vol 1 (OUP, 1987), pp. 66ff.

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