FOM: "Relativistic" mathematics?

Vladimir Sazonov sazonov at
Fri Oct 16 05:45:36 EDT 1998

Kanovei wrote:
> Sazonov:
> <There exists no unique mathematical (or arithmetical) world or a
> <universe (or standard model for arithmetic).
> True is [may be "if"? - V.S,] some sort of physical existence is being in mind.
> But: there exists a system of "physical" human knowledge
> i.e. knowledge of counting
> which unambiguously leads to {1,2,3,...} considered as
> *the* (unique) standard model for arithmetic.

It is said too shortly. I need more details to understand 
what do you mean by "human knowledge of counting". Say , 
I could guess that you mean just feasible numbers, or may 
be numbers in decimal notations (what is quite different!), 
i.e. actually finite strings of digits of feasible length. 
Or you mean also some more complicated (feasible?) terms 
involving eponentiation, Ackerman function, Friedman 
functions m(k), n(k), etc.? I do not know what is this 
"etc" and do not feel any solid ground. Even the "set"(?) 
of feasible numbers each of which seems to be a very 
concrete "thing" seems to me very umbiguous, nothing to 
say about the whole story on "all" imaginary infeasible numbers. 
I even do not know how to discuss about all of these matters 
without some formalism. As I wrote in my last posting to fom  
such "pure" ideas look, from my point of view, as amoeba 
without a skeleton. After formalization they become 
incomparably more definite, interesting and mathematical, 
but still vague in some respects. 

Vladimir Sazonov

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