[FOM] math/phil culture

[Harvey Friedman]

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  
major issues.

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  
Core Philosophers.

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.

Harvey Friedman