FOM: FoM and Set Theory in Philosophy

Kanovei kanovei at
Wed Feb 28 12:28:48 EST 2001

>From: "A.P. Hazen" <a.hazen at>

>set theory is presented as THE foundation

[of mathematics]

This is not really what set theory intends for. 
Rather a layout to develop mathematics. 
A number, say \pi, can be consistently presented as a set 
(say, of all smaller rationals, which can also be viewed 
as sets of some kind, et cetera down to the empty set), 
so that all its mathematically known properties can be 
derived from this definition. 
It is not the same as \pi "ontologically" IS nothing but 
a certain set of rationals. 

Real foundational issues (as I see them) are 
1) how mathematical concepts emerge in the social life
2) what is their relation to "reality" (whatever that means)
3) is it by necessity or by occasion that (basic) mathematical 
   concepts are such as we know them ? 

How much of set theory or other mathematics one should know in 
order to analyse the issue philosophically depends only on the 
sort of objects one is going to consider -- thus, if this is 
cofunctor one should know what cofunctor is, if Woodin cardinal 
then what a Woodin cardinal is. There is no way to circumpass this. 


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