Mathematics and the Form of Life

‘It is fair to say that Wittgenstein brought about a revolution in philosophical perspective, making platonism – as traditionally presented – impossible. When a person can carry out a mathematical procedure correctly – for example, he can extend the series 2, 4, 6, 8…the platonist says he has learned to follow a rule or has apprehended a universal. We manifest our apprehension of a universal, our grasp of a rule, by at most a finite amount of behaviour, yet the grasp of a universal, or rule guarantees a potentially infinite amount of behaviour. Wittgenstein’s point is, roughly, that it is not because we have grasped a universal or rule that we behave in a certain way, but because we act in certain ways that we say that we have grasped a rule or universal. No rule or universal will guarantee that someone will not extend the series 2, 4, 6, 8, 17, 28, 1002, =, Δ…saying that at each step he is doing exactly what he did before. There is no such thing, Wittgenstein argued, as absolute sameness. A procedure is a case of doing the same thing again if it is a practice within what Wittgenstein called a ‘form of life’ – a community that shares perceptions of salience, routes of interest, feelings of naturalness – in which it is perceived as the same. If the platonist tries to step out of the form of life in order to tell those within how things really are, then he must come to grief. For outside the form of life there is nothing: no rules, no universals, no sameness, no reality.’ (Johnathan Lear, ‘Ethics, Mathematics and Relativism’, in ‘Essays on Moral Realism’, ed. Geoffrey Sayre-McCord, p. 87)

Stanley Jaki on a Theory of Everything

‘Herein lies the ultimate bearing of Gödel’s theorem on physics. It does not mean at all the end of physics. It means only the death knell on endeavours that aim at a final theory according to which the physical world is what it is and cannot be anything else. Gödel’s theorem does not mean that physicists cannot come up with a theory of everything or TOE in short. They can hit upon a theory which at the moment of its formulation would give an explanation of all known physical phenomena. But in terms of Gödel’s theorem such a theory cannot be taken for something which is necessarily true. Apart from Gödel’s theorem, such a theory cannot be a guarantee that in the future nothing essentially new would be discovered in the physical universe which would then demand another final theory and so on. Regress to infinity is no answer to a question that keeps generating itself with each answer. Gödel’s theorem means, among other things, that physicists who aim at reading God’s mind will not succeed, because they cannot read their own minds in the first place. A physicist, Paul Davies, who writes a book with the title The Mind of God, should be the object of pity and not the recipient of a prestigious prize for progress in religion. Gödel’s theorem remains a serious assurance to all physicists that their minds will forever be challenged by ever fresh problems. With a recourse to logic they would also know what to think of efforts to derive the very specific constants of physics from non-specific considerations. Insofar as mathematics works with numbers, it will remain steeped in specifics all of which raise the question: Why such and not something else? It is that question which keeps the mind awake, or rather is raised by minds not prone to slumber.’