FOM: Jurassic pebbles

[Kanovei]

<Date: Tue, 17 Mar 1998 09:26:45 -0800
<From: Vaughan Pratt <pratt at cs.stanford.edu>

<1. Would it be fair to infer from this that you believe that mathematics
<is not frozen in time but rather reflects what we know?

As it is clear that the amount of Math now and in 18 century 
is obviously different, I think what you are asking is whether 
(I believe that) if XXX is once put and properly recognized 
as a correct mathematical result, as the LT has been, then 

a) it will remain such (in the frameworks of the terrestrial 
   form of Mathematics ?) 

b) it always existed in the past. 

I would agree with a). 
My reason is that, at the very end, 
mathematics reflects the physical counting (including 
measurements as a form of counting: counting of measure 
units). And, since counting a very stable (or: absolutely 
stable) process (shall one add: in our universe), this, 
through many steps, results in the stability and 
unchangeability of our mathematics. 

However there can be reservations. For instnse, once they 
may think to change the whole setup of arithmetics to 
reflect the fact that the universe contains only finite 
amonut of particles. Who knows. 

b) Perhaps this depends on how you view the LT. If you 
think that the whole setup of arithmetic is in 1-1 way 
determined by the physical setup of the universe 
(there are reasons to think so), then PA, and LT as a 
logical consequence of PA, "always existed". In this sense, 
Lagrange only *discovered* rather than *created* the 
theorem (similarly to the discovery of Amerika by Columbus). 

However the existence of the LT as a social phenomenon 
begins from its proof by L. 

Vladimir Kanovei

PS. You comment (in another post) upon a letter of Harrington. 
Can you copy it for me (assuming it is a regular fom-list 
mailing), as I have not received it.