jrs at math.duke.edu
Wed Aug 26 15:34:46 EDT 1998
Martin Davis writes that the dispute over whether ConZFC is a finite
combiatorial statement has gone on too long, and I agree completely. Let
me explain as briefly as I can why I entered into the dispute and why I
failed to get my point across.
The original point of dispute was whether Harvey's proof of the
independence of a tree principle was a significant foundational advance
over Godel's proof of the independence of ConZFC. Steve said that it was
because the tree principle was a finite combinatorial principle
(henceforth f.c.p.) and ConZFC was not. I challenged him to provide a
definition of f.c.p. from which it would be clear that ConZFC was not an
f.c.p.; we could then sensibly argue about whether f.c.p. was a
significant founatioal concept. The nearest thing to a definition in his
reply was that "a combinatorial principle is a principle about the
arrangement of objects in patterns". I replied that I thought ConZFC was
a c.p. in this sense. In his reply, he did not state whether his
statement was a definition of c.p. or whether he thought ConZFC fit this
definition. But he did give reasons for thinking ConZFC was not a
f.c.p. They revolved the fact that ConZFC was not understandable within
the context of finite combinatorics. I replied that he was replacing
f.c.p. by understandable f.c.p., and that the latter was not a suitable
concept for our purposes, since the word understand is inherently vague.
I think this is confirmed by the discussions of Steve and Neil Tennent
about whether ConZFC is understandable (or graspable); they seem to be
more about the meaning of understandable than the nature of ConZFC.
I regret to say that the reply of Steve to Martin's communication, at
least in the last part, showed him at his worst. It was full of
unsupported statements laced with emotional and prejudicial words and
phrases. Rather than argue this in detail, I will list some quotes from
his reply, putting these words and phrases in caps; I leave it to other
readers to decide whether this contribute to rational discourse or heap
ridicule and contempt on those who disagree with him. I do not think
Steve wants to ridicule anyone; I think the use of such phrases is due to
the conviction that his opinions are true and important and his despair
that he has difficulty convincing others whom he respects as logicians to
agree to this. I only wish he could see that this sort of argument is
the worst way to convince people of anything.
>is mathematical logic to be relegated to the ASHCAN OF HISTORY, in
favor of some SPECIALIZED algebraic studies.
>When the recursion theorists REJECTED asymptotic complexity, were
they missing out on a GOLDEN OPPORTUNITY to BROADEN THEIR HORIZONS?
>Does current research in recursion theory exhibit SYMTOMS OF DECAY?
>we've got Shoenfield POOH-POOHING it ..., REFUSING TO ADMIT that
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