Re: The Law of the Excluded Middle again (long)


And - I'm sorry if this question has already been
answered, but
I'm getting punch-drunk from the way this thread has
gone, and
my memory may be starting to fail me - if it /is/ a
false hope,
then what kind of value, if any, does a
constructivist see in
non-constructive arguments? Are they simply invalid,
therefore
establishing nothing? Or, less drastically, must the
construct-
ivist somehow "suspend disbelief", and regard
non-constructive
arguments as an attractive but wildly speculative and
basically
nonsensical kind of fiction (or even a kind of
abstract music)?
Or is there some way of using them to give
information useful to
the constructivist, which involves some non-trivial
intellectual
work, and is not anything like as straightforward as
"mentally
replacing every statement P ... by ~~P"?
--

Every statement P is already logically equivalent to
~~P. No mental replacement necessary.

So far as how one who prefers a constructive argument
should regard a non-constructive argument, what has
that got to do with mathematics? Most so called
classical theorems (Bishop showed) can be proved
constructively, anyway. As for those that haven't been,
all the constructivist demands is less faith and more
method.

Tom


Angus Rodgers
(twirlip@ eats spam; reply to angusrod@)
Contains mild peril
.

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