[FOM] Predicativism and natural numbers

[Charles Parsons]

At 7:33 PM +0100 1/3/06, Giovanni Lagnese wrote:

>Charles Parsons wrote:

>>  I'm not sure why you say the
>>  predicativist conception
>>  of _set_ is impredicative

>I mean the definition of set as the smallest collection inductively
>generated by some rules, as in Martin Loef's Intuitionistic (and
>"predicative") Type Theory.
>It's necessary to say "the smallest", so the concept of set is
>impredicative.

As you state it, the conception allows generalized inductive 
definitions, which would not have been admitted by classical 
conceptions of predicativity.

You will have to convince me that Martin-Loef admitted them as 
predicative. But others did, for example Lorenzen and Myhill in a 
paper in JSL 24, 1959. I try to mediate the issue in the last section 
of the 1983/1992 paper referred to in my first reply to you.

Charles Parsons