[FOM] Platonism and metamathematics

[Vaughan Pratt]

Is there anything Platonic about metamathematics, e.g. as envisaged by 
Kleene (*Introduction to Metamathematics*, NH, 1952), or Rasiowa and 
Sikorski (*The Mathematics of Metamathematics*, 1963), or Halmos 
(*Algebraic Logic*, 1962), or Tarski (cf. Blok and Pigozzi's "Alfred 
Tarski's Work on General Metamathematics", JSL 53:1, 36-50), etc?

If not then what makes it less Platonic than mathematics?

If so then how does one go about differentiating the Platonism of 
mathematics from that of metamathematics?

Or is there no difference?

Vaughan Pratt