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, second-order logic comes through looking more promising than we might have initially thought.

Original languageEnglish (US)
Title of host publicationSynthese Library
PublisherSpringer Science and Business Media B.V.
Pages463-487
Number of pages25
DOIs
StatePublished - 2015

Publication series

NameSynthese Library
Volume373
ISSN (Print)0166-6991
ISSN (Electronic)2542-8292

Keywords

  • Continuum Hypothesis
  • Epistemic Obligation
  • Genuine Consequence
  • Ontological Commitment
  • Topic Neutrality

ASJC Scopus subject areas

  • History and Philosophy of Science
  • History
  • Language and Linguistics
  • Logic

Fingerprint

Dive into the research topics of 'What’s So Bad About Second-Order Logic?'. Together they form a unique fingerprint.

Cite this