[FOM] Replies to Putnam

[Harvey Friedman]

Hilary Putnam was recently in Columbus, Ohio in order to give the lead  
Plenary lecture at the Foundational Adventures conference, organized  
by Neil Tennant.

His talk concerned "Personal Reflections" arising out of our  
longstanding relationship that goes way back to 1964 when I was a  
Freshman at MIT.

At the end of Hilary's beautiful talk, he rightly thought it was  
appropriate to mention where he felt that he disagreed substantially  
with some of my viewpoints.

He mentioned two areas of disagreement. One concerns, generally  
speaking, philosophical methodology. The other concerns the value of  
category theory.

As I told Hilary later at the Conference, I feel that I have a much  
more nuanced position on these matters than what Hilary has attributed  
to me.

PHILOSOPHICAL METHODOLOGY

Hilary described my position roughly as

*the point of philosophy is to make philosophical questions precise  
and then attack them with scientific methods*

Hilary expressed strong disagreement with this viewpoint.

I think that the above position is defensible, but my own position  
that I put forth - particularly in private - is more nuanced.

My interests lie in the development of systematic knowledge. I am  
particularly focused on contexts where there is some understanding,  
which doesn't rise, or doesn't fully rise, to the level of systematic  
knowledge. Generally speaking, deep conceptual issues arise that need  
to be clarified in order to establish, or further establish, a proper  
framework for systematic knowledge.

My interest in philosophy is as a *tool* to be used to tackle deep  
conceptual issues that are essential for laying new frameworks for  
systematic knowledge.

I view philosophical thinking as an often essential tool in this  
regard. E.g., to identify crucial ambiguities, distinctions, primitive  
notions, as well as fundamental principles and questions.

I also view mathematical thinking as an often essential tool for  
formulation and the establishing of fundamental principles and facts.

In addition, I also view computer technology as an often essential  
tool for obtaining data, which can be used to test hypotheses and also  
to discover principles, questions, and concepts. I fully expect to use  
computer technology in an intense way for music theory.

Historically, some kinds of philosophical thinking has been  
particularly effective in the laying of new frameworks for systematic  
knowledge. Most scientists and engineers do not recognize this - at  
least not in these terms.

Particularly clear examples are present in the work of Aristotle,  
Bayes, Cantor, Descartes, Einstein, Frege, Goedel, Leibniz, Newton,  
Pascal, Russell, Turing, etcetera.

There are also many examples of philosophical thinking that are only  
partly successful in laying new frameworks for systematic knowledge. I  
am deeply interested in these partly successful or promising attempts.  
In these cases, it remains to be seen which parts of the work will  
come to fruition in this sense.

However, I do have some serious reservations about mainstream  
Philosophy - and equally serious reservations about mainstream  
Mathematics and mainstream Computer Science.

With regard to mainstream Philosophy, most of the philosophical  
thinking is directed at philosophical questions of intrinsic interest  
to mainstream philosophers - and NOT to the development of frameworks  
for systematic knowledge. My assertion that I am not interested in -  
or only casually interested in - the aspects of philosophy not aimed  
at the development of frameworks for systematic knowledge, is of  
course indisputable and merely autobiographical.

However, I can say something much more contentious. Although the great  
and essential use of philosophical thinking for the development of  
frameworks for systematic knowledge is, in my own view, beyond  
dispute, the value of other types of philosophical thinking not so  
aimed is very much in dispute in the general intellectual community. I  
have yet to see a convincing case for its value.

Similar challenges can be appropriately made to mainstream  
mathematics, and many other subjects. (I think that the challenge is  
readily met for foundations of mathematics, as it is comfortably  
thought of as a kind of applied mathematics with a clear external  
purpose, and with clear successes.) The usual defense of mainstream  
mathematics is that normal developments of mainstream mathematics lead  
to applied developments, with clear value in the development of  
frameworks for systematic knowledge. A similar defense can be made of  
mainstream philosophy. However, I have always found such blanket  
defenses insufficiently convincing.

This is a convenient place to stop my discussion. I look forward to a  
continuation of the discussion.

CATEGORY THEORY

Hilary described my position on category theory as attributing little  
or no value to it.

Hilary pointed out that many strong mathematicians consider category  
theory a particularly convenient way to formulate and help prove  
theorems.

Hilary implied that I disagreed with this assessment.

Actually, I agree totally with this assessment regarding the use of  
category theory.

My point of view is more nuanced: I strongly deny that category theory  
forms a philosophically coherent autonomous foundation for mathematics  
- in the sense that set theory forms a philosophically coherent  
autonomous foundation for mathematics. MacLane disagreed with this  
position. I suspect that Hilary Putnam agrees with my position on this.

For instance, Solomon Feferman has written substantially on this  
topic, and my reading of Feferman is that he agrees with my position  
on this.

Harvey Friedman