FOM: constructivist philosophy
Thomas Forster
T.Forster at dpmms.cam.ac.uk
Sun Jun 4 12:11:57 EDT 2000
> For example, we know that Bishop has stated (rather vehemently) that
> nonconstructive existence proofs constitute fraud. Why? If we prove
> the absurdity of (forall x) not Phi(x), why does Bishop think this is
> not a proof (or at least very strong evidence) that (exists x) Phi(x)?
Typically a nonconstructive existence proof gives one a constructive proof
of not-not there exists. What I tell my students is that nonconstructive
existence proofs should be regarded not a fraud but as *prophecy*. (This fits
well with the S4 interpretation as a tense logic, too, which is cute). It's
perfectly reasonable to be dissatisfied with nonconstructive existence proof:
if you are the knight in shining armour seeking the key to the dungeon
wherein is incarcerated by the wicked dragon the weeping princess, a
nonconstructive existence proof for the key is of no immediate use, tho'
it presumably gives you heart to keep trying. It all depends what you're
trying to do. (I tell them that too). Apparently the philosophers call
this `cohabitationism'.
Thomas
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