Fwd: Foundations and Foundationalism

[Harvey Friedman]

On Wed, Jun 15, 2022 at 2:23 AM Timothy Y. Chow <tchow at math.princeton.edu>
wrote:

> It is true that I am rather pessimistic about the prospects of replicating
> the success of foundationalism in mathematics in other arenas.  That
> mathematics is an outlier has been apparent for a very long time.  Ever
> since Euclid, it has been clear---in rough outline if not in full
> detail---that foundationalism (or something close to it) in mathematics
> ought to be possible.  As for foundationalism in any other philosophical
> arena, the entire history of Western philosophy can be regarded as a huge
> mountain of heuristic evidence that it is at best a very distant hope, and
> quite likely a wild goose chase.
>

I couldn't disagree more strongly with this. We seem to agree what
foundationalism means in mathematics and elsewhere, and we agree that it
has been a huge success in mathematics along the lines of classical f.o.m.

I also maintain that it has been a huge success also in computer science
and electrical engineering - both theoretical and applied. Of course, it
could be said that for the purposes of this discussion, computer science is
really mathematics.

I don't have the slightest doubt that the great success of foundationalism
in mathematics and computer science and electrical engineering can be had
in all of science and engineering and possibly in art as well. It's just
more difficult to accomplish than in mathematics.

The easiest extremely important target could be statistics, pure and
applied. Of course, there is some progress on this but it is very meager
compared to what we have in mathematics and computer science and electrical
engineering.

The reason that foundationalism is so difficult and slow to achieve is that
it requires very high levels of disparate abilities that rarely flourish
in a single individual. Whereas we all know people in mathematics
with uncanny power, and we also know perceptive scholars with
strong philosophical instincts, we don't know too many that not only have
both but also know how to use them together. The primary example from the
20th century that we all think of is of course Goedel. And in a different
realm, there is obviously Einstein.

The educational system is not helpful in many ways. Particularly
disappointing in this regard is the University environments and the grant
awards environment. What is needed is major incentives for deep
interactions at the most fundamental levels between different realms. There
are few rewards for doing long term projects like that until something
truly fundamental arises, which is expected to be more difficult, more
time consuming, and perhaps more controversial than ordinary research.

Harvey Friedman



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