[FOM] l basis of Intuitionism
Adriano Palma
Palma at ukzn.ac.za
Sun Jun 2 04:27:54 EDT 2013
This is indeed a good serious point. In my opinion intuitionism (within mathematics) was an unlikely and welcome success, precisely in spite of what (I take to be) its really poor philosophical basis.
It is an argument that would be long to run, and possibly of scant relevance to working mathematics.
I would suggest that in the case of intuitionism the work being done is highly successful because of the theories of computability which is one of the points at which the mathematical structures interact and interenengage with structures that are not mathematical at all (such as natural intellingences, brains, artificial computers, Turing Machines-implementation, and human psychology.) The argument tentative conclusion gives some support to two views: mathematics is mature, in the sense that it can do its work in progress within and without any philosophy (compare and contrast Newtonian classical mechanics is based on rather bizarre philosophies of action at a distance, absoluteness of time and space, "flows" and som such mirabilia) and it does beautifully the job of givlng singly the laws of something as arcane as a tidal wave, a cannon ball in motion, asteroids or planets (do not plese tell me it Is false, this is precisely the point: analogy = it is perfectly possible that there is no consciousness in anybody, a fortiori in any mathematician, that does split the original one-ness in two-ness [Brouwer's view since 1904] and yet, as correctly professor Bauer notes, intuitionism is mathematically fruitful)
Secondly, and more controversially, this can be a non reductio, indirect argument for a real independence of mathematics, by way of its objects being reachable inter-modally.
I shall be glad to expand, though I prefer not to tax my colleagues with reflections that are about the philosophy of mathematics and not mathematics itself.
Onward to finding out the truth about zeta functions.
With my best regards and thanks to what I leanr reading the posts.
palma, a
uKZn
From: fom-bounces at cs.nyu.edu [mailto:fom-bounces at cs.nyu.edu] On Behalf Of Andrej Bauer
Sent: 01 June 2013 09:23 PM
To: Foundations of Mathematics
Subject: Re: [FOM] Psychological basis of Intuitionism
I would just like to point out that there is a new generation of mathematicians who think that intuitionistic mathematics is worthwhile, not because of some philosophical conviction, but because it's better suited for what they do.
With kind regards,
Andrej
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