What’s so bad about second-order logic?

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Scopus citations

Abstract

Second-order logic is generally thought problematic by the philosophical populace. Philosophers of mathematics and logic may have sophisticated reasons for rejecting second-order logic, but ask the average philosopher-on-the-street what’s wrong with second-order logic and they will probably mumble something about Quine, ontological commitment, and set theory in sheep’s clothing. In this paper, I try to get more precise about exactly what might be behind these mumblings. I offer four potential arguments against second-order logic and consider several lines of response to each. Two arguments target the coherence of second-order quantification generally, and stem from concerns about ontological commitment. The other two target the expressive power of ‘full’ (as opposed to ‘Henkin’) second-order logic, and give content to the concern that second-order logic is in fact “set theory in sheep’s clothing”. My aim is to understand the dialectic, not take sides; still, secondorder logic comes through looking more promising than we might have initially thought.

Original languageEnglish (US)
Title of host publicationQuantifiers, Quantifiers, and Quantifiers
Subtitle of host publicationThemes in Logic, Metaphysics, and Language
PublisherSpringer International Publishing
Pages463-488
Number of pages26
ISBN (Electronic)9783319183626
ISBN (Print)9783319183619
DOIs
StatePublished - Jan 1 2015
Externally publishedYes

ASJC Scopus subject areas

  • Arts and Humanities(all)
  • Mathematics(all)
  • Social Sciences(all)

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  • Cite this

    Turner, J. (2015). What’s so bad about second-order logic? In Quantifiers, Quantifiers, and Quantifiers: Themes in Logic, Metaphysics, and Language (pp. 463-488). Springer International Publishing. https://doi.org/10.1007/978-3-319-18362-6_20