Excerpt From: Monk, Ray. “Ludwig Wittgenstein - The Duty of Genius”
Wittgenstein’s attack on theory dominates his discussions with Schlick and Waismann during the Christmas vacation of 1930. ‘For me’, he told them, ‘a theory is without value. A theory gives me nothing.’ In understanding ethics, aesthetics, religion, mathematics and philosophy, theories were of no use. Schlick had, that year, published a book on ethics in which, in discussing theological ethics, he had distinguished two conceptions of the essence of the good: according to the first, the good is good because it is what God wants; according to the second, God wants the good because it is good. The second, Schlick said, was the more profound. On the contrary, Wittgenstein insisted, the first is: ‘For it cuts off the way to any explanation “why” it is good, while the second is the shallow, rationalist one, which proceeds “as if” you could give reasons for what is good’:
The first conception says clearly that the essence of the good has nothing to do with facts and hence cannot be explained by any proposition. If there is any proposition expressing precisely what I think, it is the proposition ‘What God commands, that is good’.Similarly, the way to any explanation of aesthetic value must be cut off. What is valuable in a Beethoven sonata? The sequence of notes? The feelings Beethoven had when he was composing it? The state of mind produced by listening to it? ‘I would reply’, said Wittgenstein, ‘that whatever I was told, I would reject, and that not because the explanation was false but because it was an explanation’:
If I were told anything that was a theory, I would say, No, no! That does not interest me – it would not be the exact thing I was looking for.Likewise the truth, the value, of religion can have nothing to do with the words used. There need, in fact, be no words at all. ‘Is talking essential to religion?’ he asked:
I can well imagine a religion in which there are no doctrinal propositions, in which there is thus no talking. Obviously the essence of religion cannot have anything to do with the fact that there is talking, or rather: when people talk, then this itself is part of a religious act and not a theory. Thus it also does not matter at all if the words used are true or false or nonsense.
In religion talking is not metaphorical either; for otherwise it would have to be possible to say the same things in prose.‘If you and I are to live religious lives, it mustn’t be that we talk a lot about religion’, he had earlier told Drury, ‘but that our manner of life is different.’ After he had abandoned any possibility of constructing a philosophical theory, this remark points to the central theme of his later work. Goethe’s phrase from Faust, ‘Am Anfang war die Tat’ (‘In the beginning was the deed’), might, as he suggested, serve as a motto for the whole of his later philosophy.
The deed, the activity, is primary, and does not receive its rationale or its justification from any theory we may have of it. This is as true with regard to language and mathematics as it is with regard to ethics, aesthetics and religion. ‘As long as I can play the game, I can play it, and everything is all right’, he told Waismann and Schlick:
The following is a question I constantly discuss with Moore: Can only logical analysis explain what we mean by the propositions of ordinary language? Moore is “Can only logical analysis explain what we mean by the propositions of ordinary language? Moore is inclined to think so. Are people therefore ignorant of what they mean when they say ‘Today the sky is clearer than yesterday’? Do we have to wait for logical analysis here? What a hellish idea!Of course we do not have to wait: ‘I must, of course, be able to understand a proposition without knowing its analysis.’
The greater part of his discussions with Waismann and Schlick that vacation was taken up with an explanation of how this principle applies to the philosophy of mathematics. So long as we can use mathematical symbols correctly – so long as we can apply the rules – no ‘theory’ of mathematics is necessary; a final, fundamental, justification of those rules is neither possible nor desirable. This means that the whole debate about the ‘foundations’ of mathematics rests on a misconception. It might be wondered why, given his Spenglerian conviction of the superiority of music and the arts over mathematics and the sciences, Wittgenstein troubled himself so much over this particular branch of philosophy. But it should be remembered that it was precisely this philosophical fog that drew him into philosophy in the first place, and that to dispel it remained for much of his life the primary aim of his philosophical work.
It was the contradictions in Frege’s logic discovered by Russell that had first excited Wittgenstein’s philosophical enthusiasm, and to resolve those contradictions had seemed, in 1911, the fundamental task of philosophy. He now wanted to declare such contradictions trivial, to declare that, once the fog had cleared and these sorts of problems had lost their nimbus, it could be seen that the real problem was not the contradictions themselves, but the imperfect vision that made them look like important and interesting dilemmas. You set up a game and discover that two rules can, in certain cases, contradict one another. So what? ‘What do we do in such a case? Very simple – we introduce a new rule and the conflict is resolved.
They had seemed interesting and important because it had been assumed that Frege and Russell were not just setting up a game, but revealing the foundations of mathematics; if their systems of logic were contradictory, then it looked as if the whole of mathematics were resting on an insecure base and needed to be steadied. But this, Wittgenstein insists, is a mistaken view of the matter. We no more need Frege’s and Russell’s logic to use mathematics with confidence than we need Moore’s analysis to be able to use our ordinary language.
Thus the ‘metamathematics’ developed by the formalist mathematician David Hilbert is unnecessary.fn1 Hilbert endeavoured to construct a ‘meta-theory’ of mathematics, seeking to lay a provably consistent foundation for arithmetic. But the theory he has constructed, said Wittgenstein, is not metamathematics, but mathematics: ‘It is another calculus, just like any other one.’ It offers a series of rules and proofs, when what is needed is a clear view. ‘A proof cannot dispel the fog’:
If I am unclear about the nature of mathematics, no proof can help me. And if I am clear about the nature of mathematics, then the question about its consistency cannot arise at all.The moral here, as always, is: ‘You cannot gain a fundamental understanding of mathematics by waiting for a theory.’ The understanding of one game cannot depend upon the construction of another. The analogy with games that is invoked so frequently in these discussions prefigures the later development of the ‘language game’ technique, and replaces the earlier talk of ‘systems of propositions’. The point of the analogy is that it is obvious that there can be no question of a justification for a game: if one can play it, one understands it. And similarly for grammar, or syntax: ‘A rule of syntax corresponds to a configuration of a game … Syntax cannot be justified.’
But, asked Waismann, couldn’t there be a theory of a game? There is, for example, a theory of chess, which tells us whether a certain series of moves is possible or not – whether, for instance, one can checkmate the king in eight moves from a given position. ‘If, then, there is a theory of chess’, he added, ‘I do not see why there should not be a theory of the game of arithmetic, either, and why we should not use the propositions of this theory to learn something substantial about the possibilities of this game. This theory is Hilbert’s metamathematics.’
No, replies Wittgenstein, the so-called ‘theory of chess’ is itself a calculus, a game. The fact that it uses words and symbols instead of actual chess pieces should not mislead us: ‘the demonstration that I can get there in eight moves consists in my actually getting there in the symbolism, hence in doing with signs what, on a chess-board, I do with chessmen … and we agree, don’t we?, that pushing little pieces of wood across a board is something inessential’. The fact that in algebra we use letters to calculate, rather than actual numbers, does not make algebra the theory of arithmetic; it is simply another calculus.
After the fog had cleared there could be, for Wittgenstein, no question of meta-theories, of theories of games. There were only games and their players, rules and their applications: ‘We cannot lay down a rule for the application of another rule.’ To connect two things we do not always need a third: ‘Things must connect directly, without a rope, i.e. they must already stand in a connection with one another, like the links of a chain.’ The connection between a word and its meaning is to be found, not in a theory, but in a practice, in the use of the word. And the direct connection between a rule and its application, between the word and the deed, cannot be elucidated with another rule; it must be seen: ‘Here seeing matters essentially: as long as you do not see the new system, you have not got it.’ Wittgenstein’s abandonment of theory was not, as Russell thought, a rejection of serious thinking, of the attempt to understand, but the adoption of a different notion of what it is to understand – a notion that, like that of Spengler and Goethe before him, stresses the importance and the necessity of ‘the understanding that consists in seeing connections'.
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