Lainaus "John F. Sowa" <sowa@xxxxxxxxxxx>: (01)
> What Chaitin called quasi-empirical is closely related to what
> Wolfram called computationally irreducible. Following is a note
> I wrote in a different thread. (02)
Hilary Putnam uses the term quasi-empirical with at least slightly
different meaning in [1]. For example, calculus can be taken as
quasi-empirical mathematics: it works perfectly with or without any
mathematical proofs of it, although empirical proofs are available. (03)
Of course, the availability of a mathematical proof does not harm
anybody, especially if the proof is constructive and does not appeal
to anything transfinite. When calculus is 'proved' by using
infinitesimals and/or the limit procedure (in the sense that something
that is infinitely far is reached), I don't consider that that sort of
a proof makes calculus any more reliable. (04)
Avril (05)
[1] Hilary Putnam. What is Mathematical Truth? Historia Mathematica 2,
1975, p.529-543. Reprinted in [2] p.49-65. (06)
[2] Thomas Tymoczko: New Directions in the Philosophy of Mathematics:
An Anthology. Princeton University Press, 1998. (07)
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