[FOM] 486:Naturalness Issues

Arnon Avron aa at tau.ac.il
Thu Mar 22 10:58:23 EDT 2012

The notion of "natural" mathematical proposition seems to me
anything but natural, and at best depending on the fashion
at some particular time - no more.

Instead of repeating past arguments, let me ask a few simple questions:

1) Was the question whether the Non-Euclidean Geometries 
   are consistent a "natural" mathematical question?

   Is it now?

2) Was Cohen's theorem about the consistency of ZF+\neg CH a "natural"
   mathematical theorem? 

   Is it now?

3) Was the question whether ZF is consistent a "natural" mathematical
   question at the beginning of the 20th century? Was it "natural"
   at least for Hilbert?

   Is it now?

4) Which mathematical theorems have greater g.i.i (a concept I do
   think is extremely important): consistency theorems or some
   current theorems in "core" mathematics? 

   Is g.i.i. a legitimate criterion for being "natural"?

Arnon Avron

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