[FOM] Alternative Foundations?

[Harvey Friedman]

I have some simple questions about "alternative foundations".

I think it might be useful to distinguish finite mathematics from general
mathematics.

1. Is there any form of "alternative foundations" that is new for finite
mathematics? Is this an important issue?

2. If so, how would you compare "alternative foundations" for finite
mathematics and "usual foundations" for finite mathematics, in terms of
their complexity - e.g., in terms of how difficult it is to learn, to
understand, to work with, to avoid errors in, etcetera? Is this an
important issue?

3. Same for 2, for general mathematics? Is this an important issue?

4. In the "usual foundations" there are a number of findings that have been
of great general intellectual interest, not only within mathematics, but
within philosophy, computer science, and arguably elsewhere. Is this the
case with "alternative foundations"? Is this an important issue?

5. In the "usual foundations", there are a number of results to the effect
that various constructions are unique in various senses. Is this the case
in "alternative foundations"? Is this an important issue?

Harvey Friedman
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