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Virgil
Posts:
8,833
Registered:
1/6/11


Re: Matheology � 221
Posted:
Feb 13, 2013 3:44 PM


In article <d615f15f73b54f2997a5c60b42644010@fw24g2000vbb.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.de> 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 > 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 relaxed, > 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", nCategoryCafe, Sept. > 30, 2011] > > Regards, WM 



