Re: SUO: Re^n: Collections - Aggregation or Set
Chris Menzel <cmenzel@philebus.tamu.edu>:
>That said, there is one (and only one) clear thinking philosopher of
>mathematics that I know of who has respectably defended (not to say
>demonstrated) the view that sets of physical objects are themselves
>physical, viz., Penelope Maddy. The locus classicus here is her 1980
>paper "Perception and Mathematical Intuition," Philosophical Review 89
>(1980), pp. 163-196. Maddy is no crackpot -- she's head of the Logic
>and Philosophy of Science program at UC Irvine, author of two highly
>regarded Oxford Univ Press books on philosophy of mathematics, and she
>is a member of the American Academy of Arts and Sciences.
>
>The most interesting thing Maddy does in defense of the physicality
>thesis is to marshall neuroscientific evidence for the existence of
>"set detectors" that enable us to perceive sets of physical objects.
Wow. Neurological evidence in 1980? I wonder where she got it from.
They knew about retinal receptive fields, but Ive never come across
anything about set detectors. People didnt even know about neural
phase coding at that date.
>Such detectors, she argues, if they exist, provide a sound naturalistic
>basis for the possibility of set theoretic knowledge. After all, if
>sets really *are* completely abstract things, then they are causally
>inert and so (for the naturalist) a question remains as to how we can
>know anything about them. Maddy, who is both a mathematical realist
>about set theory and a scientific naturalist argues that her appraoch
>fills this epistemological gap.
I didnt know about this person or her work, I confess. I admire her
dedication: being simultaneously a mathematical realist and a
scientific naturalist is a pretty hard row to hoe.
Pat
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