[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. 



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