FOM: use of 'platonism' in f.o.m.

[Robert Black]

Martin Davis suggests that the modern use of 'platonism' in f.o.m. derives
from Gödel, citing his 1933 Cambridge address.  But if that's where it
comes from, it really comes from Carnap, since Gödel is repeating there
something from his 1932 review of Carnap's 1931 'The logicist foundations
of mathematics' where Carnap attacks Ramsey's defence of inpredicative
definitions as 'not far removed from a belief in a platonic realm of ideas
which exist in themselves, independently of if and how finite human beings
are able to think them' and as 'theological mathematics' (cited from the
translation in the Benacerraf/Putnam collection).

However, this usage (and Gödel's in 1992/3) is clearly *pejorative*
(perhaps the term was just hanging around with this pejorative sense in
Göttingen/Vienna in the 30s).  What is more interesting is when 'platonism'
becomes not a word of abuse but a positive position.  And here I suspect
the important influence is indeed Bernays' 1934 'Sur le platonisme dans les
mathématiques' (also in Benacerraf/Putnam).  Without himself supporting
platonism, Bernays in effect sets out varying degrees of it as the
alternative to constructivism.

Rather later, but the key influence in the present-day use of the term
amongst philosophers, is Quine's 1948 'On What There Is', where he
associates the logicism of Frege, Russell, Whitehead, Church and Carnap
with 'the Platonic doctrine that universals or abstract entities have being
independently of the mind'.  This paper provides an account of what it is
to commit oneself to the existence of abstract entities which, whether one
agrees with it or not, still provides the point of departure for all more
recent philosophical writing on the topic.

Robert Black
(Lecturer in Philosophy, University of Nottingham.  Principal research
interest:  philosophy of mathematics)