[FOM] Ask Dr. Bill
gstolzen at math.bu.edu
Tue Mar 14 17:26:43 EST 2006
I've composed a list of questions for Bill Tait in the hope
that his answers will enable me to finally understand his take
on the issues that we've been discussing.
-3. True or false? A classical existence proof is often a
good first step towards getting a construction.
-2. True or false? A classical existence proof is often an
annoying distraction from getting a construction.
-1. Among classical mathematicians, constructive math is the
study of what can be proved without omniscience. How does your
own interpretation of it as a part of classical math differ from
0. If classical math didn't exist, would constructive math
have to invent it?
1. Why is it important to you that a statement about real
numbers in constructive math mean the same thing as the formally
identical statement in classical math?
2. Why would it be a bad idea for a mathematical community to
have a paradigm shift in which it replaces its old metaphysics
with a new one?
3. Do you believe that classical math provides the big picture
but that in constructive math we have difficulty seeing the forest
for the trees?
4. Why do you dislike the interpretation of classical math as the
part of constructive math in which we investigate how it helps to be
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