[FOM] Multiple types of foundation for mathematics (cognitive, biological, mathematical...)

[Aaron Sloman]

Some notes comparing and contrasting investigations into several different
kinds of foundation for mathematics, including cognitive,
biological/evolutionary, mathematical and metaphysical foundations:

http://www.cs.bham.ac.uk/research/projects/cogaff/misc/maths-multiple-foundations.html
(Also pdf)

Comments, criticisms, suggestions, and pointers welcome.

I would particularly welcome pointers to work on how biological evolution
was able to produce brains able to make ancient mathematical discoveries in
geometry and topology, e.g. leading to Euclid's Elements. Can those
processes be replicated in AI theorem provers?

The answers should refer to explanatory mechanisms not the competitive
advantages of having mathematical abilities.

Thanks.

Aaron Sloman
a.sloman at cs.bham.ac.uk
http://www.cs.bham.ac.uk/~axs