[FOM] Replies to Putnam

[Timothy Y. Chow]

Harvey Friedman wrote:

>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.
[...]
>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.

The defense of mainstream mathematics would surely be simply that 
mainstream mathematics *is* systematic knowledge.  If there is value in 
developing frameworks for systematic knowledge, then surely there is value 
in the accumulation of systematic knowledge?

Or do you implicitly believe that only certain *kinds* of systematic 
knowledge are worthwhile?  You didn't say so.

Mainstream philosophy could also be defended (though perhaps less 
convincingly) in your terms as follows: Philosophers accumulate persuasive 
arguments, where by "persuasive" I just mean that a significant number of 
people (not all people, of course) find themselves persuaded by them.
The systematic knowledge in question is just the collection of arguments 
(and in particular, is not any set of *answers to questions*).

>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.

Where can we read Mac Lane's views on the subject?  I tried searching the 
FOM Archives but got too many hits to sort through.

Tim