[FOM] Unrestricted Quantification and Paradox

Robert Smith rsmithjr at covad.net
Wed Jun 6 11:54:01 EDT 2007

General prohibitions against "self-reference" are untenable IMHO.

Consider recursive functions in mathematics/computer science, such as the
standard definition of "factorial".  Such definitions obviously include self
reference, but a proper recursive definition contains basis cases that
terminate the recursion and does not result in unbounded recursion.

One might argue that the problem with the "liar paradox sentence":

	This sentence is false.

is not so much that it is "self-referential", or that it involves a
"semantic" or "meta-linguistic" notion such as truth.  It is simply that
there is an unbounded recursion.  The following pseudo-code program blows
the push-down stack:

		return(not liar());

Bob Smith
Stanford University

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