Definitions

from Wiktionary, Creative Commons Attribution/Share-Alike License

  • n. The quality of being categorical.

Etymologies

from Wiktionary, Creative Commons Attribution/Share-Alike License

categoric +‎ -ity

Examples

  • (Discussion of Hellman 1989 will be reserved for Section 5.2, when the notion of categoricity is introduced.) 4.5 Fictionalism

    Philosophy of Mathematics

  • In turn, Dedekind is much more explicit and clear than Frege about issues such as categoricity, completeness, independence, etc., which puts him in proximity with a “formal axiomatic” approach as championed later by Hilbert and Bernays

    Dedekind's Contributions to the Foundations of Mathematics

  • It is closer in kind to what is termed "categoricity" in formal semantics, a categorical theory being one whose models are all isomorphic to one another.

    Einstein's Philosophy of Science

  • Often acknowledged in that connection are: his analysis of the notion of continuity, his introduction of the real numbers by means of Dedekind cuts, his formulation of the Dedekind-Peano axioms for the natural numbers, his proof of the categoricity of these axioms, and his contributions to the early development of set theory

    Dedekind's Contributions to the Foundations of Mathematics

  • In Dedekind's case, completeness is to be understood in a semantic sense, as based on categoricity; similarly, consistency is to be understood semantically, as satisfiability by a system of objects

    Dedekind's Contributions to the Foundations of Mathematics

  • One of the main consequences of the completeness theorem is that categoricity fails for Peano arithmetic and for Zermelo-Fraenkel set theory.

    Kurt Gödel

  • Gödel in his review (1934c) of Skolem's paper also does not mention this fact, rather observing that the failure of categoricity for arithmetic follows from the incompleteness theorem.

    Kurt Gödel

  • Against this account, however, it may be pointed out that it seems that the categoricity of intended models for real analysis, for instance, cannot be ensured in this manner.

    Philosophy of Mathematics

  • Predicability, then, is not a sufficient condition of categoricity, but non-predicability is a sufficient disqualification.

    Medieval Theories of the Categories

  • It played a major role in debates over the ontology of general relativity and was an important part of the background to the development of the modern concept of categoricity in formal semantics (for more on the history, influence, and demise of the principle of univocalness, see Howard 1992 and 1996).

    Einstein's Philosophy of Science

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