[FOM] The defence of well-founded set theory

Vladimir Sazonov V.Sazonov at csc.liv.ac.uk
Thu Oct 6 16:37:26 EDT 2005

Quoting Andrej Bauer <Andrej.Bauer at andrej.com>:

> I would like to offer a criticism not of set-theory itself, but of the
> idea that having a single powerful foundation of mathematics is a good
> thing.

The following seems is in the line of some recent posts 
on non-uniqueness of mathematical foundation. 

Of corse, mathematics is not about one platonistic style world. 
It is about numerous formal systems describing numerous imaginary 
worlds and styles of intuition and reasoning possibly not reducible 
one to another. 

Wherefrom could it follow at all that one such formalism and one style 
of intuition, even so great as classical set theory (ZFC), will or 
should absolutely dominate forever or even only in some historical 


1. "Formal" should be understood in a wide sense of this word 
assuming rather formalisability in principle than absolutely 
formal "engineering" as in computer programming.  

2. "Not reducible" assumes various senses of this word. 

In fact, this is nothing else as a wide formalistic view 
on mathematics (at least how I understand it). 

Vladimir Sazonov

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