[FOM] math/phil culture
friedman at math.ohio-state.edu
Fri May 2 03:47:33 EDT 2008
I want to try to make some perhaps thought provoking comments on
contemporary mathematics/ philosophy culture.
THESIS. Major Core Mathematicians generally produce major results
about intellectually minor issues. Major Core Philosophers generally
produce minor results about intellectually major issues. Major
Mathematical Philosophers and Major Philosophical Mathematicians
generally produce intellectually major results about intellectually
Today, core mathematicians and core philosophers are from profoundly
different cultures, with profoundly different attitudes towards
intellectual life, operating under profoundly different methodologies,
speaking profoundly different languages, etc.
THESIS. Major Mathematical Philosophy and Major Philosophical
Mathematics represent the only current hope for any kind of
intellectual reconciliation between Core Mathematicians and Core
Philosophers. Yet Mathematical Philosophy and Philosophical
Mathematics are both shunned by both the Core Mathematicians and the
Thus, what I am saying is that, in effect, the Core Mathematicians and
Core Philosophers have grown so very far apart, and incompatible, that
the proper balance of their perspectives and skills - represented so
well by Mathematical Philosophy and Philosophical Mathematics - is
proving entirely ineffective in moving them together.
I am now expecting a deep freeze where Major Mathematical Philosophy
and Major Philosophical Mathematics is going to become professional
extinct - in the sense that no longer can one gain a permanent
academic position on the basis of even Major Mathematical Philosophy
and Major Philosophical Mathematics.
So what do I think can be done about this?
1. There are some very key applications of the math/phil Interface
that I have no doubt will be unexpectedly successful and have a
profound effect on the World. This success will be obviously traced to
the Interface. I am thinking of SOFTWARE VERIFICATION and COMPUTER
ASSISTED EDUCATION. The former will utterly revolutionize software
development, and the latter will utterly revolutionize education, K-16.
2. We need to systematically investigate the most fundamental aspects
of the Interface. Instead, only those aspects of the Interface have
been seriously developed that carry the expectation of interest among
mathematical logicians. This is severely limiting. Of course, there is
no way to gain employment dealing with the truly fundamental aspects
of the Interface. So it is up to the people who already have regular
employment (or equivalent) to take up the challenge. Building up the
Interface systematically will help pull the Interface out of the
expected deep freeze, as a coherent and compelling subject for future
generations when the time is ripe.
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