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Background
Background
Ludwig Wittgenstein was born into a very wealthy family in Vienna, Austria. With regular visits from the likes of Brahms and Mahler, their family home was a cultural centre in the city of Vienna, which was itself a centre of culture, science, art, and music.
He went to the same primary school in Linz as Adolf Hitler. He initially went to Manchester university where he invented an early kind of jet engine, from there he went to Cambridge to study logic under Bertrand Russell.
When the First World War broke out, he went to fight in the Austrian army, often volunteering for the most dangerous assignments. He was eventually taken prisoner.
During the war he filled notebooks with the ideas that became his first master-work Tractatus Logico-Philosophicus.
The world is everything that is the case.
What is the case (a fact) is the existence of states of affairs.
A logical picture of facts is a thought.
A thought is a proposition with a sense.
A proposition is a truth-function of elementary propositions. (An elementary proposition is a truth-function of itself.)
The general form of a proposition is : [p, ξ, N(ξ)] This is the general form of a proposition.
Whereof one cannot speak, thereof one must be silent.
- The world is everything that is the case.
He conceived of the world as being ‘the totality of facts, not things’ and the totality of facts determines what is the case and what isn’t.
He ends proposition 1 with an odd statement:
1.21 Each item can be the case or not the case while everything else remains the same.
2. What is the case (a fact) is the existence of states of affairs.
2. What is the case (a fact) is the existence of states of affairs.
In the second proposition, Wittgenstein introduces, what’s known as ‘the picture theory of language’. Propositions are a picture of reality, and the way in which the parts of that proposition can be combined is determined by the form of representation.
2.1 We make to ourselves pictures of facts.
2.11 The picture presents the facts in logical space, the existence and non-existence of atomic facts.
2.12 The picture is a model of reality.
…
2.15 That the elements of the picture are combined with one another in a definite way, represents that the things are so combined with one another.
This connexion of the elements of the picture is called its structure, and the possibility of this structure is called the form of representation of the picture.
2.151 The form of representation is the possibility that the things are combined with one another as are the elements of the picture.
2.1511 Thus the picture is linked with reality; it reaches up to it.
2.1512 It is like a scale applied to reality.
3. A logical picture of facts is a thought.
3. A logical picture of facts is a thought.
In proposition 3, Wittgenstein distinguishes between the essential and accidental features of a proposition. There are obviously many ways of saying the same thing, but the essential feature is the thing that is common to them all.
3.34 A proposition possesses essential and accidental features.
Accidental are the features which are due to a particular way of producing the propositional sign. Essential are those which alone enable the proposition to express its sense.
3.341 The essential in a proposition is therefore that which is common to all propositions which can express the same sense.
And in the same way in general the essential in a symbol is that which all symbols which can full the same purpose have in common.
3.3411 One could therefore say the real name is that which all symbols, which signify an object, have in common. It would then follow, step by step, that no sort of composition was essential for a name.
A thought is a proposition with a sense.
A thought is a proposition with a sense.
In proposition 4, Wittgenstein attempts to elucidate the nature of logic and how our propositions connect with reality.
Wittgenstein thinks that most philosophical problems occur because we don’t have a decent grasp on the logic of our language.
4.003 Most propositions and questions, that have been written about philosophical matters, are not false, but senseless. We cannot, therefore, answer questions of this kind at all, but only state their senselessness. Most questions and propositions of the philosophers result from the fact that we do not understand the logic of our language.
(They are of the same kind as the question whether the Good is more or less identical than the Beautiful.)
And so it is not to be wondered at that the deepest problems are really no problems.
4.0031 All philosophy is Critique of language (but not at all in Mauthner's sense). Russell's merit is to have shown that the apparent logical form of the proposition need not be its real form.
…
4.03 A proposition must communicate a new sense with old words. The proposition communicates to us a state of affairs, therefore it must be essentially connected with the state of affairs.
And the connexion is, in fact, that it is its logical picture. The proposition only asserts something, in so far as it is a picture.
…
4.11 The totality of true propositions is the total natural science (or the totality of the natural sciences).
Wittgenstein introduces the concept of a truth table to demonstrate the nature of the connections between propositions. The truth table demonstrates how the truth-conditions are limits on the possible combinations of propositions.
4.31 The truth-possibilities can be presented by schemata of the following kind (“T” means “true”, “F” “false”. The rows of T's and F's under the row of the elementary propositions mean their truth-possibilities in an easily intelligible symbolism).
4.442 Thus e.g.
is a propositional sign.
…
If the sequence of the truth-possibilities in the schema is once for all determined by a rule of combination, then the last column is by itself an expression of the truth-conditions. If we write this column as a row the propositional sign becomes: (TTT)(p, q), or more plainly: (TTFT)(p, q).
…
4.46 Among the possible groups of truth-conditions there are two extreme cases.
In the one case the proposition is true for all the truth-possibilities of the elementary propositions. We say that the truth conditions are tautological.
In the second case the proposition is false for all the truth possibilities. The truth-conditions are self-contradictory.
In the first case we call the proposition a tautology, in the second case a contradiction.
4.461 The proposition shows what it says, the tautology and the contradiction that they say nothing.
The tautology has no truth-conditions, for it is unconditionally true; and the contradiction is on no condition true.
Tautology and contradiction are without sense.
(Like the point from which two arrows go out in opposite directions.)
(I know, e.g. nothing about the weather, when I know that it rains or does not rain.)
…
4.462 Tautology and contradiction are not pictures of the reality. They present no possible state of affairs. For the one allows every possible state of affairs, the other none.
…
4.463 The truth-conditions determine the range, which is left to the facts by the proposition.
(The proposition, the picture, the model, are in a negative sense like a solid body, which restricts the free movement of another: in a positive sense, like the space limited by solid substance, in which a body may be placed.)
…
5. A proposition is a truth-function of elementary propositions. (An elementary proposition is a truth-function of itself.)
5. A proposition is a truth-function of elementary propositions. (An elementary proposition is a truth-function of itself.)
In proposition 5, things get particularly fruity.
A big theme of this proposition is an attack on the view of causality.
Firstly, he shows how all the rules of inference can be shown in truth-tables. This shows that there is nothing else that is required to show the possible combinations of propositions - we don’t need extra ‘laws of inference’.
5.101 The truth-functions of every number of elementary propositions can be written in a schema of the following kind:
(TTTT)(p, q) Tautology (if p then p, and if q then q) [p ⊃ p . q ⊃ q]
(FTTT)(p, q) in words: Not both p and q. [∼(p . q)]
(TFTT)(p, q) If q then p. [q ⊃ p]
(TTFT)(p, q) If p then q. [p ⊃ q]
(TTTF)(p, q) p or q. [p ∨ q]
(FFTT)(p, q) Not q. [∼q]
(FTFT)(p, q) Not p. [∼p]
(FTTF)(p, q) p or q, but not both. [p . ∼q : ∨ : 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) p and q. [p . q]
(FFFF)(p, q) Contradiction (p and not p; and q and not q.) [p . ∼p . q . ∼q]
…
5.132 If p follows from q, I can conclude from q to p; infer p from q.
The method of inference is to be understood from the two propositions alone.
Only they themselves can justify the inference.
Laws of inference, which —as in Frege and Russell— are to justify the conclusions, are senseless and would be superfluous.
There is no need for anything on top of this. So we can’t really ask, for example, why it’s the case that…
If P then Q
P
∴ Q
According to the view that Wittgenstein is attacking, science produces ‘laws’ which then somehow guarantee a logical entailment, but what Wittgenstein wants to show is that the connections are all part of the form of representation - they are ‘internal relations’.
What appears to be a necessity that exists outside the form of representation is in fact a logical/linguistic necessity - the truth of the conclusion follows from the premises.
5.133 All inference takes place a priori.
5.134 From an elementary proposition no other can be inferred.
5.135 In no way can an inference be made from the existence of one state of affairs to the existence of another entirely different from it.
5.136 There is no causal nexus which justifies such an inference.
5.1361 The events of the future cannot be inferred from those of the present.
Superstition is the belief in the causal nexus.
5.1362 The freedom of the will consists in the fact that future actions cannot be known now. We could only know them if causality were an inner necessity, like that of logical deduction. The connexion of knowledge and what is known is that of logical necessity.
(A knows that p is the case is senseless if p is a tautology.)
The mysterious ‘I’
The mysterious ‘I’
Another theme of proposition 5 is the nature of ‘I’ —the subject of experience. Wittgenstein argues that the subject of experience does not exist in the world, but is the limits of the world.
5.632 The subject does not belong to the world but it is a limit of the world.
5.633 Where in the world is a metaphysical subject to be noted?
You say that this case is altogether like that of the eye and the eld of sight. But you do not really see the eye.
And from nothing in the eld of sight can it be concluded that it is seen from an eye.
5.6331 For the field of sight has not a form like this:
5.634 This is connected with the fact that no part of our experience is also a priori.
Everything we see could also be otherwise.
Everything we can describe at all could also be otherwise.
There is no order of things a priori.
...
5.641 There is therefore really a sense in which in philosophy we can talk of a non-psychological I.
The I occurs in philosophy through the fact that the world is my world.
The philosophical I is not the man, not the human body or the human soul of which psychology treats, but the metaphysical subject, the limit not a part of the world.
6. The general form of truth-function is: [p, ξ, N(ξ)]. This is the general form of proposition.
6. The general form of truth-function is: [p, ξ, N(ξ)]. This is the general form of proposition.
6.44 It is not how the world is that is mystical, but that it is.
6.45 The contemplation of the world sub specie aeterni is its contemplation as a limited whole. The feeling of the world as a limited whole is the mystical feeling.
This says nothing else than that every proposition is the result of
successive applications of the operation N′
(ξ) to the elementary
propositions.
All propositions of logic are of equal rank; there are not some which are essentially primitive and others deduced from these.
( TLP 6.127)
The [principle] of causality is not a [principle] but the form of a [principle].
( TLP 6.32)
with a sufficiently fine square [mesh] and now say of every square that it is white or black.
( TLP 6.341)
Newtonian mechanics, for example, brings the description of the universe to a unified form. Let us imagine a white surface with irregular
black spots. We now say: Whatever kind of picture these make I can always get as near as I like to its description, if I cover the surface with
a sufficiently fine square mesh and now say of every square that it is white or black. In this way I shall have brought the description of the surface to a unified form.
( TLP 6.341)
In his discussion of the net metaphor, Wittgenstein makes an enigmatic set
of remarks concerning the way in which different meshes (or nets) from the
natural sciences compare with each other. He writes:
This form is arbitrary, because I could have applied with equal success
a net with a triangular or hexagonal mesh. It can happen that the
description would have been simpler with the aid of a triangular mesh;
that is to say we might have described the surface more accurately with
a triangular, and coarser, than with the finer square mesh, or vice versa,
and so on. To the different networks correspond different systems of
describing the world.
( TLP 6.341)
And now we see the relative position of logic and mechanics. (We could
construct the network out of figures [meshes] of different kinds, as out
of triangles and hexagons together.) That a picture like that instanced
above can be described by a network of a given form asserts nothing
about the picture. (For this holds of every picture of this kind.) But this
does characterize the picture, the fact, namely, that it can be completely
described by a definite mesh of definite fineness.
So too the fact that it can be described by Newtonian mechanics
asserts nothing about the world; but this asserts something, namely,
that it can be described in that particular way in which as a matter of
fact it is described. The fact, too, that it can be described more simply
by one system of mechanics than by another says something about the
world.
( TLP 6.342)
Whereof one cannot speak, thereof one must be silent.
The world is everything that is the case.
What is the case (a fact) is the existence of states of affairs.
A logical picture of facts is a thought.
A thought is a proposition with a sense.
A proposition is a truth-function of elementary propositions. (An elementary proposition is a truth-function of itself.)
The general form of a proposition is : [p, ξ, N(ξ)] This is the general form of a proposition.
(of all propositions, some happen to be true, and of those that are left, some happen to be not true… (It just happens that this is the case)).
Whereof one cannot speak, thereof one must be silent.
Superficially, this looked like a book about Logic - a continuation of the project of Frege and Russell. But Wittgenstein insisted that the Tractatus is ‘a machine for becoming decent’.
Imagine all possible propositions. Some of these happen to be true, and some of them happen not to be.
They are all possible. There is no necessity in the relationships between them. Wittgenstein even abandons causal necessity… Causal necessity is not a kind of necessary connection, but merely a kind of conjunction. We cannot, via deduction, establish any more facts, because all possibilities might exist.
And so, The facts about the world are thus contingent. No proposition is of any more importance than any other… There is no hierarchy of facts, no mechanism of necessity.
If there is no mechanism of necessity, then all of the ‘values’ that you impose on the world are no more important than other contingent facts.
The Tractatus is ‘a machine for becoming decent’.
What we consider to be meaning is often just constraint
So… ‘it is not how the world is that is mystical, but that it exists.’
Ethics is clarity – recognizing that the filter that we impose on the world, hides that which is truly mystical.
Tasks:
Tasks:
Try to explain why the Tractatus was a ‘machine for becoming decent’.
Do you agree with what he said?
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