Path: utzoo!attcan!uunet!husc6!bloom-beacon!hubcap.UUCP!steve From: steve@hubcap.UUCP (""Steve" Stevenson") Newsgroups: comp.ai.digest Subject: Re: undecidability Message-ID: <19880807031816.0.NICK@HOWARD-JOHNSONS.LCS.MIT.EDU> Date: 7 Aug 88 03:18:00 GMT Sender: tytso@bloom-beacon.MIT.EDU Organization: The Internet Lines: 32 Approved: ailist@ai.ai.mit.edu Path: hubcap!steve From: "\"Steve\" Stevenson" Newsgroups: comp.ai.digest Subject: Re: undecidability Date: Thu, 4 Aug 88 09:09 EDT References: <19880803191849.8.NICK@HOWARD-JOHNSONS.LCS.MIT.EDU> Organization: Clemson University, Clemson, SC Lines: 23 From a previous article, by asg@pyuxf.UUCP: > In a previous article, John B. Nagle writes: >> Goetz writes: >>> [Goedel's incompleteness ... unbounded number of axioms] >> Always bear in mind that this implies an infinite system. >> There are times when I wonder if it is time to displace infinity from >> its place of importance in mathematics.... > Actually, infinity arises in basic set theory, ... But isn't this the point? The nominalists/finitist won't let you get to that step. Take for example your mythical perfect(?) computer programmer. To such a person, the discussion of infinity in any guise is lost: there just aren't any infinite processes (by almost anybody's) definition. Intuitionist as a little better - only countable infinity allowed. The foundational issue is whether or not it is legit to propose successor and related things as legit bases for mathematics. That's John's point: The canon of infinity may not be all that good an idea.-- Steve (really "D. E.") Stevenson steve@hubcap.clemson.edu Department of Computer Science, (803)656-5880.mabell Clemson University, Clemson, SC 29634-1906