Constructive Math query.

Daryl wrote:

> Constructively, David is not justified in saying "Debatable" without
> actually providing a debate.

HAH! Very cute. (TF is clearly no constructivist in this sense!)


> No, it doesn't. "If A then B" *implies* "If we can prove A, then B",
> but the other way around is dubious.

Well clearly I am as much of a dunce here as David. *IF* one's brand
of constructivism is of the hard-nosed type that conflates truth
with provability, (which seems to have been widespread in the past,
recall my excerpt from Bishop), then I would have said it must be so.


> Take an example in which A is neither provable nor refutable.
> The interpretation "If we can prove A, then B" becomes vacuously
> true, in that case, but "If A then B" isn't vacuously true.

Well I would have thought that to a constructivist
(of this hard-nosed type) it WAS vacuously true.
Such a type would surely regard the "If A" part of your conditional
as equivalent to "If we can prove A" which he would deem false,
by noting the undecidability of A. So he would take your
conditional as vacuously true also. I see now that he would
also be required to admit that both A was false and ~A was false.
This would presumably not trouble him as asserting ~~A would
not require him to assert A.

Obviously I'm missing something trivial, but I doubt I'll ever
get it, I just can't seem to cotton to this phislosophical
constructivism, (as opposed to the strictly formal approach
of Bridges for example).

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Bill Taylor W.Taylor@xxxxxxxxxxxxxxxxxxxxx
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The intuitionist conflates existence with provability.
The Platonist conflates existence with consistency.
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