<< And, it appears that Goedel, to take an example, was a declared Platonist, but some logicians of note rejected Platonism of various kinds? ... >>
Yes, yes, of course, but this leads us from the history of mathematics to the history of philosophy which needs no discussion group because it can be covered in two lines,
round and round and round she goes, and where she stops no man knows.
But here is a question that has been bothering me for some time:
Beginning in the 19th century there arose serious doubts about the validity of fundamental concepts in mathematics, not only as theretofore about limits, but such fundamental things as counting. If we accept the most serious doubts, where does this leave us?
1. Can we develop a consistent mathematics on the remaining foundation? I.e. are the various objections consistent and not so serious as to destroy the possibility of any mathematics?
2. Is remaining mathematical rump sufficient to sustain the many applications of mathematics such as mathematical physics?
I think the answer to the first question is yes but am not at all sure about the second.