FOM: concepts, sets

[Neil Tennant]

  I was interested in Steve Simpson's reply to my email, which was intended
  to elicit some 'philosophical' reactions from the mathematicians on the
  list. I would hasten to add that I myself do *not* subscribe to Quinean
  holism as described in my email---but it's pretty widespread in the 
  philosophical community.
  
  One point in response to Steve: if one is prepared to give the well-founded
  structure of all the concepts of mathematics, why restrict one's scope
  just to the basic ones? Why not exhibit the whole caboodle, all the way up
  to (and beyond) "symplectic manifold"? For that way, at least, one bears
  out the claim that the chosen class of *basic* concepts can really support
  the weight required of them.
  
  Also, by casting one's net more widely over all definable concepts, one might
  uncover interesting alternative definitions (just as there might be, in the
  well-founded structure of claims, interesting alternative proofs).
  
  On a different point, in reply to Vaughan Pratt's email in which he says
  that he thinks all sets are ordinals: What?! What about, for example,
  {2} or {3,7}? Can one no longer have such sets?
  
  Neil Tennant