Opis

• Tytuł:
  Category Theory and Set Theory as Theories about Complementary Types of Universals
• Twórca:
  Ellerman, David
• Opis:
  Instead of the half-century old foundational feud between set theory and category theory, this paper argues that they are theories about two different complementary types of universals. The set-theoretic antinomies forced naïve set theory to be reformulated using some iterative notion of a set so that a set would always have higher type or rank than its members. Then the universal u F = {x | F(x)} for a property F(.) could never be self-predicative in the sense of uF ∈ uF . But the mathematical theory of categories, dating from the mid-twentieth century, includes a theory of always-self-predicative universals – which can be seen as forming the “other bookend” to the never-self-predicative universals of set theory. The self-predicative universals of category theory show that the problem in the antinomies was not self-predication per se, but negated self-predication. They also provide a model (in the Platonic Heaven of mathematics) for the self-predicative strand of Plato’s Theory of Forms as well as for the idea of a “concrete universal” in Hegel and similar ideas of paradigmatic exemplars in ordinary thought.
• Dostępność obiektu:
  Dostęp otwarty
• Prawa:
  Prawa autorskie (c) 2017 Logic and Logical Philosophy
• Data:
  2016.08.05
• Typ:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion
• Język:
  angielski
• Źródło:
  Logic and Logical Philosophy; Vol. 26 No. 2 (2017): June; 145-162;
  Logic and Logical Philosophy; Tom 26 Nr 2 (2017): June; 145-162;
  2300-9802;
  1425-3305
• Format:
  application/pdf
• Wydawca:
  Uniwersytet Mikołaja Kopernika w Toruniu
• Relacja: https://apcz.umk.pl/LLP/article/view/LLP.2016.022/9503
• Temat i słowa kluczowe:
  universals;
  category theory;
  Plato’s Theory of Forms;
  set theoretic antinomies;
  universal mapping properties;
  logic
• Identyfikator: https://apcz.umk.pl/LLP/article/view/LLP.2016.022
• Dostawca danych:
  Akademicka Platforma Czasopism
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