[FOM] definition of N without quantifying over infinite sets

[Thomas Forster]

The significance of FFF - Friedman's Finite 
Form of Kruskl's theorem is of course that it is a fct about N probable
only by reasoning about infinite sets.

When explaining this to my students I of course have to anticipate that 
the inductive definition of N involves quantifying over ininite sets - 
after all if you contain 0 and are closed under S then you are infinite, 
so i employ a definition that i learned from Quine: set theory and it 
logic.   You are a natural number iff every set containing you and closed 
under predecessor contins 0.  This doesn't involve quantification over 
infinite sets.

Did Quine invent this?  If not, who did?

        Thomas Forster



       www.dpmms.cam.ac.uk/~tf; 01223-337981 and 020-7882-3659