Against Second-Order Logic: Quine and Beyond

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Abstract

Is second-order logic logic? Famously Quine argued second-order logic wasn’t logic but his arguments have been the subject of influential criticisms. In the early sections of this paper, I develop a deeper perspective upon Quine’s philosophy of logic by exploring his positive conception of what logic is for and hence what logic is. Seen from this perspective, I argue that many of the criticisms of his case against second-order logic miss their mark. Then, in the later sections, I go beyond Quine to develop a novel case that quantification into polyadic predicate position, understood as requiring quantifiers to range over relations, isn’t intelligible.
Original languageEnglish
Title of host publicationHigher Order Metaphysics
EditorsPeter Fritz, Nicholas K. Jones
Place of PublicationOxford
PublisherOxford University Press
Chapter11
Pages378-401
Number of pages24
ISBN (Print)9780192894885
Publication statusPublished - 21 Mar 2024

Keywords

  • 2nd order logic
  • Quine

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