[FOM] uniqueness of FOL

[meskew at math.uci.edu]

In a message dated August 25, 2013, Harvey Friedman wrote the following:

"For any of the usual classical foundational purposes, you need to be able
to get down to finite representations that are completely non problematic....

"Furthermore, first order logic is apparently the unique vehicle for such
foundational purposes. (I'm not talking about arbitrary interesting
foundational purposes). However, we still do not know quite how to
formulate this properly in order to establish that first order logic is in
fact the unique vehicle for such foundational purposes."

I would be interested to hear Dr. Friedman or others elaborate on why it
appears that FOL is uniquely suited for classical foundational purposes. 
I agree that it is well-suited, and that several other logics are not as
well-suited because they don't "get down to finite representations that
are completely non-problematic."  But what is the evidence that FOL is
uniquely suited for these purposes?  As Dr. Friedman said, we cannot
firmly establish this at present.  But if this thesis is "apparent," is
the evidence of an empirical nature, an intuitive nature, a philosophical
nature, or does it take the form of theorems about logics in general that
seem to support this broad thesis?

Thanks,
Monroe