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Topic: Matheology § 221
Replies: 3   Last Post: Feb 14, 2013 4:24 PM

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Posts: 8,833
Registered: 1/6/11
Re: Matheology � 221
Posted: Feb 13, 2013 3:44 PM
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In article
WM <> wrote:

> Matheology § 221
> As I get older I seem to be getting more and more relaxed about
> foundational issues. I¹m happy to see people formalize and explore all
> imaginable attitudes toward the foundations of mathematics. I feel
> confident that the more interesting axiom systems will eventually
> attract more researchers, while the less interesting ones will remain
> marginal. I am not eager for one system to prevail over all others Š
> nor do I feel any desire for systems I dislike to go completely
> extinct. It¹s a lot like my fondness for biodiversity. I enjoy the
> diversity of life, and am very happy there are tigers, and would be
> sad for them to go extinct, even though I wouldn¹t want a bunch
> running around in my back yard.
> In particular, I¹m glad there are ultrafinitists, because I suspect
> that only someone with views like that could be motivated to prove the
> inconsistency of (say) Peano arithmetic, and seek plausible strategies
> for doing it.

Competent ultrafinitists might well produce something mathematicly
useful , but incompetent ones, like WM, can only serve as bad examples.

> If everyone believes Peano arithmetic is consistent, and it¹s not,
> we¹re in big trouble because it¹ll take us a long time to discover it.
> So we need a few lonely people working on the other side of this
> issue. I don¹t think they¹ll succeed, but I¹m glad they¹re trying.
> Even if they don¹t succeed, there could be some interesting concepts
> and theorems that only they are likely to find.
> Finally, I don¹t expect these people to take the same Œrelaxed,
> balanced¹ attitude that I have. I suspect that only someone with
> strong opinions could possibly be motivated to spend a lot of time
> developing ultrafinitism, or trying to prove the inconsistency of
> Peano arithmetic. Expecting them to share my relaxed attitude is a bit
> like expecting a tiger to be an environmentalist.
> [John Baez: "The Inconsistency of Arithmetic", n-Category-Cafe, Sept.
> 30, 2011]
> Regards, WM


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