[FOM] on bill tait's answers to my questions (III)

Gabriel Stolzenberg gstolzen at math.bu.edu
Thu Mar 23 17:21:27 EST 2006

   This is the 3rd part of my reply to Bill Tait's answers of
March 16 to my questions of March 15.

   The following is part of Bill's answer to the question of whether,
if classical math didn't exist, constructive math would have to invent

> But constructive math (in your sense and self-conscious) would not
> only not have to, it indeed would not invent classical math as long
> as its aims remained constructive: an existence proof should yield
> an algorithm.

   Your conclusion is right but your reason is not.  Constructive
math doesn't need to invent classical math because it contains a
faithful representation of it--namely, the part devoted to seeing
what follows from LEM.  E.g., LEM => LEM.

   In the past, when I've made this banal but crucial observation,
the response has sometimes been curious.  E.g., "There must be a
trick."  "Constructivists don't want to prove consequences of LEM."
Really?  Constructivists want to make constructive proofs.  Period.
Including ones that have LEM as the antecedent of an implication.

>  What is important to me is conceptual clarity. I believe that the
> only way to understand the term 'meaning' (of expressions) is their
> public meaning, to be understood in terms of how they are correctly
> used. (The term 'correctly' here is indeed loaded; but I needn't go
> into this now. )

    I think that you do need to go into now.  Until you do, I'm
going to ignore what you say above.  Except for this: It should be
obvious that I am talking only about what you call "public meaning."

> The main point is that the locus of meaning cannot be (as you
> suggested in an earlier posting) in the mind. For the question
  would then be mandatory: Whose mind?

   I don't believe I ever suggested such a thing.  I talked about
mindsets, not about minds!  And I didn't talk about your mindset
(though I was tempted) or mine or anyone else's.  I talked about
two obviously (in your sense) "public" mindsets, the classical and
the constructive.

   Also, far from being mandatory, "Whose mind?" should be filed
under the heading of "bad questions."  But I needn't go into this

   To be continued.


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