nLab Tools for the advancement of objective logic

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• William Lawvere,

  Tools for the advancement of objective logic: closed categories and toposes,

  in J. Macnamara, Gonzalo Reyes (Eds.),

  The Logical Foundations of Cognition,

  Oxford University Press 1993

  (Proceedings of the Febr. 1991 Vancouver Conference “Logic and Cognition”), pages 43-56, 1994.

  (pdf)

which argues that “objective logic” in the sense of Georg Hegel‘s Science of Logic should be understood as being captured by universal constructions of category theory/topos theory, whereas the “subjective logic” is to be understood as ordinary deduction/inference about objects such constructed.

The text explicitly discusses formalization in categorical logic of Hegelian concepts such as

• abstract general, concrete general and particular by categorical theories (Lawvere theories) and their models;

• unity of opposites by adjoint modalities.

Various related suggestions are implicit in other texts by Lawvere, see at William Lawvere – Mathematics related to philosophy

Contents

1. Categorical Refinement of a Hegelian Principle

2. Deepening, Metrics, Unity and Identity of Adjoint Opposites

3. Realization of Plans

4. Detailed Models of Becoming

category: reference