*From*: Robert.Paul@xxxxxxxxxxxxxxxxxx (Robert Paul)*To*: lit-ideas@xxxxxxxxxxxxx*Date*: 19 Dec 2004 16:16:47 PST

M. Chase writes: I'm sure Robert is aware of Hilary Putnam's work on quantum logic, which dates from the 1960's. In "Is logic empirical?" in R. Cohen and M. P. Wartofski (eds.), Boston Studies in the Philosophy of Science (Dordrecht, Holland: D. Reidel, 1968). Reprinted as "The logic of quantum mechanics" in H. Putnam, Mathematics, Matter and Method, Cambridge University Press (1976) he writes inter alia Logic is as empirical as geometry. We live in a world with a non-classical logic. -------------------------- M. Chase is too kind. However, paraphrasing authority--in this case Putnam (who was re-working Quine)--is no substitute for actual argument and examples. It is often said that quantum physics and its logic have somehow shown that the law of the excluded middle [not-(p and not-p)] must be abandoned; that it is 'false'; or that (as one of Andreas' sources suggests) it no longer (!) applies to 'reality' or to 'the world we live in.' Putnam wants to claim that the propositions of logic are every bit as empirical as 'Mike has two euros in his pocket.' His reason for claiming this would seem to be that one can imagine examples in which (some forms of) _applied_ mathematics do not, in the case of certain quantum phenomena, 'work' when the traditional law of the excluded middle is invoked. (I say 'invoked' because the claim is that it cannot, in the end, be _used_.) And this may well be true: let's just stipulate that it is true, and that the logic and mathematics of quantum physics must resort to other devices. However, whether certain forms of _applied_ mathematics 'work' in a quantum universe, is not itself a mathematical or logical claim. It is an empirical claim, on all fours with 'That elephant won't fit into the trunk of that Volkswagen.' It tells us nothing about which models or modes of applied mathematics do 'work' in everyday life (counting change, charging someone with bigamy, dividing a plate of cookies 'evenly'); and it needs to be argued that anything that is true of applied mathematics is true of pure mathematics 'in general.' As long as I'm making bold claims about areas in which I scarcely dare to tread I'll suggest something more: the results of Putnam (Quine; Brouwer; the 'later' Wittgenstein) depend upon our being able to make assertions in a natural language and to deduce consequences from them. If those who are ready to ascend to the New World of logic believe that once there they can throw away their ladders, so be it. In the meantime, for Putnam, as for anyone, setting out valid arguments is impossible without a belief in the law of non-contradiction. As Aristotle said, 'You might reject this; but you can't argue with me about it.' [Metaphysics, somewhere] Robert Paul The Reed Institute ------------------------------------------------------------------ To change your Lit-Ideas settings (subscribe/unsub, vacation on/off, digest on/off), visit www.andreas.com/faq-lit-ideas.html

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