[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
period?
Notes:
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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