What are Implicit Definitions?

Georg Schiemer, Eduardo Nicolás Giovannini

Publications: Contribution to journalArticlePeer Reviewed

Abstract

The paper surveys different notions of implicit definition. In particular, we offer an examination of a kind of definition commonly used in formal axiomatics, which in general terms is understood as providing a definition of the primitive terminology of an axiomatic theory. We argue that such "structural definitions" can be semantically understood in two different ways, namely (1) as specifications of the meaning of the primitive terms of a theory and (2) as definitions of higher-order mathematical concepts or structures. We analyze these two conceptions of structural definition both in the history of modern axiomatics and in contemporary philosophical debates. Based on that, we give a systematic assessment of the underlying semantics of these two ways of understanding the definiens of such definitions, by considering alternative model-theoretic and inferential accounts of meaning.

Original languageEnglish
Pages (from-to)1661-1691
Number of pages31
JournalErkenntnis: an international journal of analytic philosophy
Volume86
Issue number6
DOIs
Publication statusPublished - Dec 2021

Austrian Fields of Science 2012

  • 603113 Philosophy

Keywords

  • FREGE
  • Formal axiomatics
  • HILBERT
  • Implicit definitions
  • Inferential semantics
  • Model-theoretic semantics
  • Modern mathematics
  • Structural definitions

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