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    Priest, G. 2013. Mathematical pluralism. Logic Journal of IGPL, Vol. 21, Issue. 1, p. 4.


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

  • DUSTIN TUCKER (a1)
  • DOI: http://dx.doi.org/10.1017/S1755020309990359
  • Published online: 01 February 2010
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.

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*DEPARTMENT OF PHILOSOPHY, UNIVERSITY OF MICHIGAN, 435 SOUTH STATE STREET, ANN ARBOR, MI 48109–1003. E-mail:dtuck@umich.edu
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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
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