FOM: terminological foolishness? substantial issues
Stephen G Simpson
simpson at math.psu.edu
Mon Aug 24 16:43:14 EDT 1998
Martin Davis says that he and others are frustrated about my
interminable arguments over the precise meaning of various terms.
> In each case, Steve has apparently determined a unique correct
> useage with which to pound those quilty of wrong-think into
Have I pounded anyone into submission yet? Evidently Martin himself
is still in the defiant or "bloodied but unbowed" stage. :-)
Seriously Martin, I want to thank you for your many FOM postings,
which have unfailingly exhibited good sense and judgement.
However, I'd also like to point out that there may be more to these
terminological disputes than meets the eye.
> BOOLEAN RINGS vs BOOLEAN ALGEBRAS
> COMBINATORIAL STATEMENTS
I claim that each of these FOM threads has been concerned with one or
more substantial issues, not mere terminological foolishness.
1. Boolean rings vs Boolean algebras
The real issue here was, is mathematical logic to be relegated to the
ashcan of history, in favor of some specialized algebraic studies?
This arose from the discussion of another important f.o.m. issue: Is
there a coherent "categorical foundation" for mathematics, independent
of set-theoretic foundations?
2. Computability theory
The substantial issue here is: When the recursion theorists rejected
asymptotic complexity in the 1960's, were they missing out on a golden
opportunity to broaden their horizons? And this issue is part of some
larger issues: What does current research in recursion theory have to
do with foundations of mathematics? Does current research in
recursion theory exhibit the symptoms of decay described in Harvey's
"profound changes" posting (12 Aug 1998 02:24:08)?
3. Combinatorial statements
The substantial issue here is whether Harvey's research on finite
combinatorial independence results has actually achieved anything.
You and I agree that this research *is* exciting and *has* achieved a
lot, but we've also got Shoenfield pooh-poohing it on the grounds that
Con(ZFC) is just as combinatorial as Harvey's independent statements,
refusing to admit that there is any distinction whatsoever.
Martin, what do you have to say about these substantial issues? You
have already commented on 3, but what about 1 and 2?
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