[FOM] Formalization Thesis: A second attempt
Vladimir Sazonov
vladimir.sazonov at yahoo.com
Thu May 27 18:10:29 EDT 2010
----- Original Message ----
> From: Timothy Y. Chow <tchow at alum.mit.edu>
> To: fom at cs.nyu.edu
> Sent: Tue, May 25, 2010 7:16:58 PM
> Subject: Re: [FOM] Formalization Thesis: A second attempt
> [Note
> to Sazonov: Of course, all this was figured out long ago and I am not
> offering anything "new" in the sense of original philosophical or
> mathematical research; what is perhaps "new" is the particular
> *pedagogical* idea of giving the Formalization Thesis a name. If you
> think there is no need to come up with a better way to explain these
> concepts to the non-specialist then I suspect you have not spent much time
> lately trying to do so.]
Of course things should be clarified again and again. But now,
after reading your last postings I read your Formalisation Thesis
(before looking at the end of this your posting) as:
A lot of contemporary mathematics is covered by ZFC.
I do not know who can doubt in this. May be only beginners
because of ignorance. This "fact" should be just demonstrated
step-by-step in the evident way during studying mathematics.
I also do not see that the term Thesis is appropriate here.
It alludes to some analogy with Church-Turing Thesis. But the latter
has a different form:
Intuitively computable = Turing computable.
The above formulation does not assert any equality.
"A lot of contemporary mathematics" is even more vague
than "Intuitively computable".
But you continue:
> So it's not a problem, from my perspective, to
> grant tentatively the possibility that ZFC (say) comprises EXACTLY the
> acceptable proofs. In fact, I daresay that a sizable fraction of my
> intended audience DOES think something like that, although they may not
> have articulated it explicitly.
Here I am in a shock since such restricting mathematics to ZFC
(even tentatively) or to anything like that seems to me absolutely
inappropriate. I highly agree on the extraordinary importance of
ZFC, but not to such a degree.
Vladimir
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