[FOM] Predicativism and natural numbers

Charles Parsons parsons2 at fas.harvard.edu
Wed Jan 4 11:01:36 EST 2006

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

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

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