Re: mystification and categorification

[Mike Oliver <moliver@unt.edu>]

Vaughan Pratt wrote:

> Quite right.  I would add to this "and satisfying the expected equations."
> The "nasty sets" of which Steve speaks fail to satisy such expected
> equations as 2^2^X ~ X.  (The power set of a set is a Boolean algebra,
> for heaven's sake.  Why on earth forget that structure prior to taking the
> second exponentiation?  Set theorists seem to think that they can simply
> forget structure without paying for it, but in the real world it costs
> kT/2 joules per element of X to forget that structure.  If set theorists
> aren't willing to pay real-world prices in their modeling, why should we
> taxpayers pay them real-world salaries?  Large cardinals are a figment of
> their overactive imaginations, and the solution to consistency concerns is
> not to go there.)

I will answer you in a Popperian key:  Large cardinals are falsifiable,
and are not yet falsified.  They may in fact be figments of our imaginations,
but then why do they keep on *working*?  Could be just a coincidence -- but
so could all other observation; that way lies the nullification of science
in general.

It's an illusion, by the way, to think that you can be rid of concerns about
consistency by dumping large cardinals, that you can thus achieve a priori
justification for apodictic certainty.  That doesn't exist even for the
natural numbers; Ed Nelson is quite right on this point.

As to the question of taxpayer funding, I will not attempt to justify
it (I'm a libertarian in politics), but will merely note that many
taxpayers probably feel that way about *all* pure mathematics.