[FOM] Quine and the Principle of Abstraction
Chris Gray
cpgray at library.uwaterloo.ca
Wed Sep 16 10:43:03 EDT 2009
The predicate substituted for 'F' must be 'is not an element of' or 'is
not an element of itself' and for the very reason that you site. A
predicate may have more occurrences of the arguments than follow the
schematic letter it replaces.
For instance, 'knows Jones and Smith plays squash with' giving:
(Ey) (x) (x is an element of y iff (x knows Jones and Smith plays squash
with x))
Chris Gray
Alex Blum wrote:
> 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?
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