FOM: Reply to Friedman's ReplyToDavis (addendum)

[Martin Davis]

>>There are various things in mathematical practice that lead mathematicians
>>beyond what they are able to justify in terms of their contemporary
>>understanding. When this happens, a foundational problem arises. In the
>>happiest instances, foundational work will not only provide a satisfactory
>>explanation, but also will provide new directions for mathematical research.
>
>I agree that there are fruitful interpretations and reinterpretations of
>foundational developments along these lines. However, what specifically do
>you propose as a foundational problem that fits this mold now?

I'd suggest the success with classical open questions in descriptive set
theory using projective determinancy as an appropriate example. The
foundational issues that arise are the status of PD as an axiom of set
theory, its relation to large cardinal assumptions, etc.

Martin Davis