Precursors Of Category Theory • Discussion 1


JA:  In the logic of Aristotle categories are adjuncts to reasoning designed to resolve ambiguities and thus to prepare equivocal signs, otherwise recalcitrant to being ruled by logic, for the application of logical laws.  The example of ζωον illustrates that we don’t need categories to make generalizations so much as we need them to control generalizations, to reign in abstractions and analogies that are stretched too far.

EB:  Aristotelian categories are “adjuncts to reasoning”?

I’ve been exploring a particular type of commonality or continuity in the way categorical references function in various systems of categories from Aristotle, through Kant and Peirce, to contemporary mathematical category theory.  The following posts give the background on that.

  • Precursors Of Category Theory • (1) (2) (3)

Viewing the discussion of Excluded Middle and Non-Contradiction in the light of Peirce’s observations about their relation to the General and the Vague, the upshot is that elements of natural language, indeed, all species of representation in the wild, do not as a rule obey the usual laws of logic, but violate them in various ways.  It is only after signs and symbols have been categorized, their equivocations “driven down” or “reduced” by reference to the appropriate category, that they become subject to logical laws.



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This entry was posted in Abstraction, Ackermann, Aristotle, C.S. Peirce, Carnap, Category Theory, Hilbert, Kant, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Relation Theory, Saunders Mac Lane, Sign Relations, Type Theory and tagged , , , , , , , , , , , , , , , , . Bookmark the permalink.

1 Response to Precursors Of Category Theory • Discussion 1

  1. Pingback: Survey of Precursors Of Category Theory • 2 | Inquiry Into Inquiry

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