Foundations and Foundationalism

Timothy Y. Chow tchow at
Sun Jul 10 16:11:20 EDT 2022

Harvey Friedman wrote:
> The reason I brought this up is that I was focused on the lack of a 
> working combination of mathematical and philosophical instincts and that 
> that combination is an essential component for major advances in 
> foundations of mathematics.
> Chow and also you are suggesting that this can be replaced by a 
> community or committee of people some of whom have strong mathematical 
> abilities but limited philosophical abilities, and some of who have 
> strong philosophical abilities but limited mathematical abilities. I'm 
> suggesting that that it never was effective and is not going to be 
> effective in coming up with path breaking foundational advances in the 
> foundations of mathematics.

I want to clarify that this is not at all what I intended to suggest. 
Here is what I wrote:

> If there is a way to settle disagreements, then there is no need to have 
> individuals who are geniuses in several dimensions at once.  Progress 
> can be achieved by a group.  Indeed, group progress is the way progress 
> has always been achieved, in any arena of human endeavor.

By a "group" I did not mean a "committee."  I meant a group that is many 
orders of magnitude larger than a committee; e.g., the set of all 
mathematicians throughout history.  If all the people in such a group are 
generally aligned, then someone can pick up where someone else left off a 
hundred years ago.  Friedman himself, here on FOM, has occasionally 
alluded to his own mortality.  Individual mortality is not fatal to 
progress if there is general corporate alignment.

In philosophy, it is the rule rather than the exception that new 
generations discard much of what previous generations accepted as settled.


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