[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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