[FOM] Quine and the Principle of Abstraction

Alex Blum blumal at mail.biu.ac.il
Mon Sep 14 02:39:22 EDT 2009

Quine seems to derive Russell's Paradox from:  

                         (Ey)(x)(x is an element of y iff Fx)

by substituting the sentence 'x is not an element of' for 'F', to get 
for 'Fx', 'x is not an element of x'. Methods of Logic. (Revised edition 
'64 p.249, 3rd edition '72 p.253). But doesn't this violate the 
restriction: "Variables free in the predicate must not be such as to be 
captured by quantifiers in the schema into which the predicate is 
substituted." Quine. M of L. 3rd ed., p.148?


Alex Blum


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