[FOM] Re: Sharp mathematical distinction between potential andactual infinity?

Vladimir Sazonov V.Sazonov at csc.liv.ac.uk
Tue Sep 30 16:13:08 EDT 2003

"Timothy Y. Chow" wrote:

> I confess that my sympathies lie with P here; I tend to think that
> if we take skepticism towards N seriously, then we also need to take
> "Kripkensteinian" skepticism towards rules seriously, and this leads
> quickly to a wildly, and in my opinion unacceptably, ultraskeptical
> view of virtually all mathematics and logic.

and in a next message he explained what is "Kripkensteinian" 
skepticism towards rules. I omit this. 

Dear Timothy Y. Chow, 

An answer to the above notes on the need to take 
"Kripkensteinian" skepticism (without even knowing what it is) 
have been already done by me in a reply to YOUR previous message. 
Did you read it? (Harvey Friedman have replied to other aspects 
of this skepticism.) 

And in your reply to Friedman (Tue, 30 Sep 2003 10:51:46 -0400 (EDT)) 
you continue to ignore my answer. I assert (and have already argued) 
that skepticism towards N does not lead to skepticism towards rules. 

Thus, I should repeat that place (just several lines):

Sazonov, Mon, 29 Sep 2003 21:06:41 +0100
Re: [FOM] Sharp mathematical distinction between
               potential and actualinfinity?

"Additional essential point is that WE DO NOT NEED any theory of 
formal systems to use their rules: we only need to be well trained 
for that. (Likewise, we do not need any theory of bicycles to ride.) 
These notes allow us to avoid any serious infinite regress in 
understanding the nature of mathematical rigorous reasoning." 

It is essentially this way all of us studied mathematics at school 
and at our universities. This is the real mathematical practice. 
Of course there are people who are unable even to follow 
mathematical proofs (rules) as you described this 
in "Kripkensteinian" skepticism. And so what? 

This is my argumentation. But what is yours? Just declaring? 
I cannot consider seriously this your new caricature 
("Kripkensteinian" skepticism) - I do not know on which prototype, 
as well as your claim that "it is a reductio ad absurdum argument". 
You are reducing to absurd some imaginary opponent. 
I am a real one having nothing general with your imaginary. 

I guess, you are actually mixing syntax with (informal) semantics 
and mathematics with metamathematics. 


Vladimir Sazonov

Dear FOMers,

I also should conclude that I am highly unsatisfied by that 
level of mutual (mis)understanding and ignoring what have been 
already said which we can see so often here in FOM. 
Is not this a real reason for discussions "with no expectation 
of resolution" (quoted from the posting of H. Friedman to 
the same posting of Timothy Y. Chow on "Kripkensteinian" 

I do not exclude myself. Sometimes I have no time to reply 
to some postings addressed to me what could be considered by 
others as ignoring their opinions. I am really sorry for that. 
I hope that this or other way I have actually replied (or will 
reply) in some indirect way. 

Vladimir Sazonov

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