Mathematics as a part of neuroscience

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Evgenii Rudnyi

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Apr 8, 2012, 1:03:07 PM4/8/12

to embryo...@googlegroups.com

Along my search on how to deal with mathematics, I have found one paper
and let me start with a quote

"Materialists believe that mathematical objects exist only materially,
in our brains.[3] Mathematical objects are believed to correspond to
physical states of our brain and, as such, should ultimately be
explicable by neuroscience in terms of biochemical laws. Stanislas
Dehaene suggests that human brains come equipped at birth with an
innate, wired-in ability for mathematics.[4] He postulates that, through
evolution, the smallest integers (1, 2, 3 . . .) became hard-wired into
the human nervous system, along with a crude ability to add and
subtract. A similar position is defended by George Lakoff and Rafael
Nunez, who seek to explain mathematics as a system of metaphors that
ultimately derive from neural processes.[5] Penelope Maddy conjectures
that our nervous system contains higher order assemblies that correspond
to thoughts of particular sets.[6] She posits that our beliefs about
sets and other mathematical entities come, not from Platonic ideal
forms, but, rather, from certain physical events, such as the
development of pathways in neural systems. Such evolutionary
explanations seek to derive all our mathematical thoughts from purely
physical connections between neurons."

3. Cf. Jean-Pierre Changeux and Alain Connes, Conversations on Mind,
Matter, and Mathematics (Princeton, N.J.: Princeton University Press,
1995), 13.

4. Stanislas Dehaene, The Number Sense: How the Mind Creates Mathematics
(Oxford: Oxford University Press, 1997).

5. George Lakoff and Rafael Nunez, Where Mathematics Comes From (New
York: Basic Books, 2000).

6. Penelope Maddy, Realism in Mathematics (Oxford: Oxford University
Press, 1993).

What do you think, does it sounds plausible from a biology viewpoint?

In the paper, there are other suggestions

http://www.csc.twu.ca/byl/matter_math_god.pdf

but I am not sure if they are really better. This is the problem with
mathematics that bothers me at the moment. Any better idea?

Evgenii

P.S. I have created a slide for my problem on two mathematicians - see
slide 26 in