Abstraction and Modest Reflection

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In “Neo-fregeanism: An Embarrassment of Riches” (Notre Dame J Formal Logic 44(1):13–48, 2003) Alan Weir introduces a number of formal constraints on abstraction principles that have become central to subsequent discussions of the Bad Company Problem, including stability and (Field and Caesar-neutral) conservativeness. In this essay we return to another notion introduced in that paper that has received much less attention—modest reflection—and we demonstrate that a natural version of this criterion is (i) a plausible constraint that acceptable abstraction principles must meet, (ii) distinct from all other such constraints proposed in the subsequent literature, yet (iii) intimately connected to a recent puzzle raised by Heck (and intimately connected to Heck’s own preferred solution to this puzzle).

Original languageEnglish (US)
Title of host publicationSynthese Library
PublisherSpringer Science and Business Media B.V.
Pages133-170
Number of pages38
DOIs
StatePublished - 2024

Publication series

NameSynthese Library
Volume484
ISSN (Print)0166-6991
ISSN (Electronic)2542-8292

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

Keywords

  • Abstraction
  • Conservativeness
  • Distractions
  • Logicism
  • Modest reflection
  • Monotonicity
  • Neo-logicism

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