FOM: rigidity

[Kanovei]

>Date: Fri, 15 Feb 2002 11:23:41 -0700
>From: Randall Holmes <holmes at diamond.boisestate.edu>

>>
Friedman objects to infinitesimals on the grounds that one cannot
give an example.  

Note that it is impossible to give an example of a point in classical
Euclidean geometry. 
>>

I think the "example" here is not intended (by HF) to mean that 
a certain formal theory proves unique existence of something.  
It looks like there is a big domain of mathematics 
(core mathematics?) 
whose objects of study admit an application to physical 
quantities, shapes, other observable phenomeha, directly 
or indirectly, and either in some rather absolute sense 
(numbers) or as soon as a coordinate system of some kind 
is fixed (curves), in such a way that a uniqueness of some 
kind can be observed. 

For instance, Borel sets of reals do admit such an application 
(less explisit than in the case of natural numbers), 
while infinitesimals, urelements in NFU, Woodin cardinals don't. 

The Euclidean geometry in coordinateless version is a combinatorial 
theory whose objects (for instance a triangle with equal sides) 
are easily identifiable. 

V.Kanovei