FOM: meaning, significance, CH, Tragesser; some positive remarks
Robert S Tragesser
RTragesser at compuserve.com
Thu Dec 11 09:46:27 EST 1997
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From: Robert S Tragesser, 110440,3621
To: INTERNET:simpson at math.psu.edu, INTERNET:simpson at math.psu.edu
Date: Thu, Dec 11, 1997 08:44:23 AM
RE: FOM: meaning, significance, CH, Tragesser; some positive remarks
I've found valuable Steve Simpson's observations.
In a recent posting (Elementary proof, Reverse mathematics?) I
think I anticipate one or more of SS's criticism by drawing on an
observation of G-C Rota, that elementary proofs are related to
analyticity. I MEANT THE DISTINCTION BETWEEN ELEMENTARY AND NONELEMENTARY
PROOF TO BE WHAT I WAS LAMELY TRYING TO GET AT THROUGH MY INITIAL
MEANING/SIGNIFICANCE DISTINCTION.
I do not know what to say about Steve Simpson's claims about
accepted scientific usage. I did say that "meaning" and "significance" are
wobbly signifiers; what I should have been more explicit about is that I
have come to think that the important distinction which I was trying to get
at through those terms is between elementary and nonelementary proofs, so
that Steve Simpson's finding the issue of whether or not there can be a
nonelementary proof/disproof of CH interesting is what (and perhaps in the
end all) that I was driving at.
But concerning Steve's prickliness about violating accepted
scientific usages, I'd like to know where the tablets are on which these
are written ? Once years ago when I was considering various conceptions of
truth, Paul Teller objected to my using the word "truth" because Tarski
had written the book on truth -- what if one disagrees that Tarski had?
There is in any case surely a difference between someone using a
word like truth or significance as if they meant (but didn't) by it some
standard well-disti nguished thing and someone who puts up neon signs (like
I did) that I was using the terms meaning and significance to point to a
distinction which I hope the reader could see their way to independently of
my choice of words. But it was a happy result that I was (without my
initially being aware of it) pointing toward a distinction that was already
well appreciated -- elementary and nonelementary proofs.
rbrt tragesser
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