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From: weemba@brahms.BERKELEY.EDU (Matthew P. Wiener)
Newsgroups: net.ai,net.philosophy
Subject: Re: A halting problem: a meaty response
Message-ID: <11585@ucbvax.BERKELEY.EDU>
Date: Tue, 28-Jan-86 21:00:17 EST
Article-I.D.: ucbvax.11585
Posted: Tue Jan 28 21:00:17 1986
Date-Received: Thu, 30-Jan-86 05:27:51 EST
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In article <1070@mmintl.UUCP> franka@mmintl.UUCP (Frank Adams) writes:
>In article <11452@ucbvax.BERKELEY.EDU> weemba@brahms.UUCP (Matthew P. Wiener) writes:
>>
>>There are problems now known which are believed forever insoluble.
>
>Just a note here -- this discussion gives examples of problems which are
>*believed* forever insoluble.  This is not the same as being *known* to
>be insoluble.  There does not seem to be any way to know that a problem
>is definitely insoluble (as distinct from undecidable in a formal system).

I don't quite understand this note, so I'll try to rephrase it.  Nobody *knows*
whether Peano arithmetic is consistent, but everyone (well, almost everyone :-)
*believes* it is.  If one day someone proves it is not, then everyone will, in
fact, *know* it is inconsistent.  The same comment applies to the higher and
higher axioms of infinity I discussed in the >> article, with a spectrum of
lower and lower confidence/reasonableness/Anschauung/?????? in the axioms.

My misunderstanding (have I just expanded his note??) seems to come from the
mere existence of the note.   "this discussion gives examples of problems
which are *believed* forever insoluble" -- can anyone give me an example of
a discussion, *any* discussion, where one *knows* as opposed to *believes*??
(Cf. Lewis Carroll's version of Achilles and the Tortoise.)

ucbvax!brahms!weemba	Matthew P Wiener/UCB Math Dept/Berkeley CA 94720