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INTENSIONALITY AND PARADOXES IN RAMSEY’S ‘THE FOUNDATIONS OF MATHEMATICS’

Published online by Cambridge University Press:  05 February 2010

DUSTIN TUCKER
DUSTIN TUCKER*
Affiliation:
Department of Philosophy, University of Michigan
*
*DEPARTMENT OF PHILOSOPHY, UNIVERSITY OF MICHIGAN, 435 SOUTH STATE STREET, ANN ARBOR, MI 48109–1003. E-mail:[email protected]
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Abstract

In ‘The Foundations of Mathematics’, Frank Ramsey separates paradoxes into two groups, now taken to be the logical and the semantical. But he also revises the logical system developed in Whitehead and Russell’s Principia Mathematica, and in particular attempts to provide an alternate resolution of the semantical paradoxes. I reconstruct the logic that he develops for this purpose, and argue that it falls well short of his goals. I then argue that the two groups of paradoxes that Ramsey identifies are not properly thought of as the logical and semantical, and that in particular, the group normally taken to be the semantical paradoxes includes other paradoxes—the intensional paradoxes—which are not resolved by the standard metalinguistic approaches to the semantical paradoxes. It thus seems that if we are to take Ramsey’s interest in these problems seriously, then the intensional paradoxes deserve more widespread attention than they have historically received.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 3 , Issue 1 , March 2010 , pp. 1 - 25
Copyright
Copyright © Association for Symbolic Logic 2010

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