Newsgroups: comp.ai.philosophy
Path: cantaloupe.srv.cs.cmu.edu!das-news2.harvard.edu!news2.near.net!news.mathworks.com!udel!gatech!swrinde!pipex!uknet!festival!edcogsci!jeff
From: jeff@aiai.ed.ac.uk (Jeff Dalton)
Subject: Re: rereRe: The end of god
Message-ID: <CzFn0u.7LF@cogsci.ed.ac.uk>
Sender: usenet@cogsci.ed.ac.uk (C News Software)
Nntp-Posting-Host: bute-alter.aiai.ed.ac.uk
Organization: AIAI, University of Edinburgh, Scotland
References: <1994Nov3.203014.2198@oracorp.com> <39civ5$288@mp.cs.niu.edu>
Date: Thu, 17 Nov 1994 22:12:30 GMT
Lines: 35

In article <39civ5$288@mp.cs.niu.edu> rickert@cs.niu.edu (Neil Rickert) writes:

>>I would say that truth of a statement is only meaningful given an
>>*interpretation* of the terms in the statement. However, in the case
>>Jim is talking about, I believe that it is clear that the
>>interpretation of "is consistent" in the statement "S is consistent"
>>is to be the same interpretation of "is consistent" as in the
>>assumption "Suppose that S is a consistent axiomatic system."
>
>Basically, you are accepting a Platonist view, and insisting that,
>even if I deny Platonism, the notion of truth must still be based on
>your Platonist view.  I reject that.

What's Platonist about the paragraph above?  Or were you talking
about something further back?

>>>One cannot say "it most certainly is true".  Instead, one can only say
>>>"In the formal system S' it most certainly is true."
>
>>Formal systems don't determine the truth of statements, they determine
>>the provability of statements.
>
>If one has a theory of truth based on formal systems, then truth has
>no meaning outside a formal system.  All you are doing is denying the
>possibility of such a notion of truth.  To a mathematical formalist,
>for example, there is no other notion of mathematical truth.

Then why are the incompleteness results such an issue (not to
mention completeness and soundness)?  If truth and proof are
the same, all these issues vanish.

Or do you have some notion of truth in a formal system that's
other than proof from the axioms of that system?

-- jeff
