[FOM] Resources on the empirical foundations of mathematics

[Andrew Boucher]

> On Tue, Jan 10, 2006 at 03:02:12PM -0800, Richard Haney wrote:
>> And, for example, I am interested
>> in exploring how much interesting, useful mathematics can be done by
>> allowing oneself, when talking about natural numbers, to talk only
>> about natural numbers less than or equal to some unspecified, rather
>> large natural number.


I have looked at second-order arithmetic without the successor axiom  
(the assumption that there is always a next natural number).  This  
makes no contrary assumption about the existence of an (unspecified)  
large natural number, so it is weaker than what you have in mind.    
Quite a lot of arithmetic can be done:  Euclidean Algorithm, Unique  
Prime Factorization, Quadratic Reciprocity, presumably Fermat's Last  
Theorem.  You can find papers on the subject near the bottom of my  
web page (the ones in pdf format) www.andrewboucher.com/papers/ 
index.htm.
>