[lbo-talk] "Theory's Empire," an anti-"Theory" anthology

Tayssir John Gabbour tayssir.john at googlemail.com
Wed May 28 11:55:02 PDT 2008


On Wed, May 28, 2008 at 6:35 PM, Jerry Monaco <monacojerry at gmail.com> wrote:
> Just a side-note: I am not sure if anyone follows debates in the
> philosophy of mathematics. Mathematicians tend toward philosophical
> idealism and for good reason. Various mathematical theories seem to
> come upon us as pre-existing objects. Personally, I am anti-Platonic
> idealism in everything except mathematics. In mathematics I think
> Platonic idealism is in fact another name for Real Materialism. Or
> put it another way... the numbers exist independent of human
> experience of the theoretical entities we used to describe the
> numbers.

Have you looked at Reuben Hersh's _What is Mathematics, Really_, and his proposed alternative, humanism? He claims:

Humanism sees that constructivism, formalism and platonism each

fetishizes one aspect of mathematics, insists that one limited

aspect is mathematics.

This account of mathematics looks at what mathematicians do. The

novelty is conscious effort to avoid falsifying or idealizing.

If we give up the obligation of mathematics to be a source of

indubitable truths, we can accept it as a human activity. We give

up age-old hopes, but gain a clearer idea of what we are doing,

and why.

1. Mathematics is human. It's part of and fits into human culture.

2. Mathematical knowledge isn't infallible. Like science,

mathematics can advance by making mistakes, correcting and

recorrecting them. (This fallibilism is brilliantly argued in

Lakatos's Proofs and Refutations.)

3. There are different versions of proof or rigor, depending on

time, place and other things. The use of computers in proofs is a

nontraditional rigor. Empirical evidence, numerical

experimentation, probabilistic proof all help us decide what to

believe in mathematics. Aristotelian logic isn't always the only

way to decide.

4. Mathematical objects are a distinct variety of social-historic

objects. They're a special part of culture. literature, religion

and banking are also special parts of culture. Each is radically

different from the others.

Music is an instructive example. it isn't a biological or physical

entity. Yet it can't exist apart from some biological or physical

realization -- a tune in your head, a page of sheet music, a high

C produced by a soprano, a recording, or a radio broadcast. Music

exists by some biological or physical manifestation, but it makes

sense only as a mental and cultural entity.

What confusion would exist if philosophers could conceive only two

possibilities for music -- either a thought in the mind of an

Ideal Musician, or a noise like the roar of a vacuum cleaner.

... and he goes onto build this case, explaining that there's a "backstage" to mathematics which mainstream philosophy don't know about, where the makeup comes off, and things are less cut-and-dried as the orderly arrays or theorems would lead us to believe:

The purpose of separating front from back isn't only to keep

customers from interfering with the cooking. It's also to keep

them from knowing too much about the cooking.

Everybody down front knows the leading lady wears powder and

blusher. They don't know exactly how she looks without them.

Diners know what's supposed to go into the ragout. They don't know

for sure what does go into it.

Traditional philosophy recognizes only the front of

mathematics. But it's impossible to understand the front while

ignoring the back.

Incidentally, I once mentioned other math/philosophical books on this list, and I have a weird feeling you'd like Gian-Carlo Rota's book: http://mailman.lbo-talk.org/2007/2007-September/018355.html

Tayssir



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