FOM: RE: Quiz

F. Xavier Noria fxn at
Tue Mar 17 18:09:46 EST 1998

Moshe' Machover wrote:

>Let P be the proposition that the well-ordering theorem is first-order
>provable in (formalized) ZFC.
>Q1. Is P absolutely true now/always?

But, what does *true* mean in this context? I don't know what *be true*
could mean in mathematics. We can talk about, say, axioms, deduction
rules, formal systems, GEN Rule, MP Rule, E Rule, functional symbols,
PA-theorems, and such a things, but truth?
(BTW, what is a symbol indeed?)

My answer to this and the other questions about asteroid collision is:
P is first-order provable in (formalized) ZFC, that's all. This fact might
have nothing to do with truth.

Nevertheless, I think that the fact *P is first-order provable in
(formalized) ZFC* is, has been, and will be true. Its truth doesn't depends
on human existence, in spite of involving human concepts like ZFC.

Regards from Barcelona,
F. Xavier Noria

(Last-year-student of the Faculty of Mathematics, University of
Barcelona, who is very glad to read you. Internet is really great.)

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