FOM: Platonism v. social constructivism

[Reuben Hersh]

>>  
>Dear Prof. Tennant:  First let me quote your astonishing dictum:

"...any social-institutional factors shaping the

> history of mathematics as thus far developed by human beings is

> IRRELEVANT to the truth of Platonism (or any other philosophy of

> mathematics opposed to social constructivism). The same goes for

> whatever social-institutional factors might have shaped the history of

> mathematics in any other extra-terrestrial civilization. "

	I refrain from any extra-terrestrial arguments.  According to the 

first sentence, since history runs up to the present, all 

social-institutional factors in present day mathematics 

are IRRELEVANT to the truth of Platonism.

I agree with that, if I can rephrase it:  to a

devout Platonist, no social-institutional (or social non-institutional)

factors in present or past mathematics can shake his/her Platonist

convictions.  

	However, my project was not primarily to convert Platonists.  Rather, I

sought to explain in what sense pure mathematics exists, without

resort to transcendental ideology.  I concluded that it exists as

part of society and culture, historically evolved.  

This proposal isn't new.  It goes back to White and Durkheim.  It does 

not conflict with the common knowledge, that simple 

measuring and counting deal with physical reality.  Advanced mathematics 

grows from simple measuring and counting, stimulated by social 

needs and human curiosity, with many an assist from physical applications.

As you say truly, "Just because it's we who do the thinking doesn't 

mean that what we are thinking about depends entirely on us."

	If you try with an open mind to make a philosophical 

analysis of mathematics, how can you begin without 

looking at what is actually going on, and where it came from?

Well, if you're already in touch with a transcendent REALITY, the 

natural yearning of the soul (or of Reason) to unite with that reality 

makes actual life experience IRRELEVANT.  

	The trouble is that two thinkers, both in touch with transcendent 

Reality, may give different reports of what it says.  Thus, the proliferation 

of schismatics.  Another trouble is that any dicta about 

real mathematical life that may come down from transcendent Reality may 

not have much legitimacy for us low-level types who aren't in touch with 

it.  

Reuben Hersh