SUO: Re: Mapping from the Frying Pan to the Fire
Jon,
Mathematics has always been an embarrassment for
professed nominalists because mathematicians truly
believe in the existence of all kinds of abstract forms,
which were Plato's original inspiration for his heaven.
> ... that divinest of abstractions,
> just to name names, a set.
I regard geometry and arithmetic as far more divine
than set theory. And I regard the project of trying
to reduce all other mathematical forms to sets as
a misguided plot on the part of closet nominalists.
They tried to tame the wild and wooly Platonic forms
by replacing all of them with just one well behaved
house pet called a set. Quine is one of the worst
offenders.
> Why do people with some reputed training in the 20th
> century excuse for logic have so much trouble grasping
> a simple fact of simple mathematics? Inasmuch as they
> seem to be otherwise healthy intellects, I have no choice
> but to put it down to the deleterious effects of the
> particular logical tools they use.
No. They were corrupted by the same person who drove
Ludwig Boltzmann to suicide: Ernst Mach -- that darling
of the Vienna Circlers, who married Peirce's logic to
Mach's positivism.
Bottom line: The greatest evil in logical positivism
lies in the noun, not the adjective.
John