Precursors of Category Theory : 1

A few years back I began a sketch on the Precursors of Category Theory, aiming to trace the continuities of the category concept from Aristotle, thorough Kant and Peirce, Hilbert and Ackermann, to contemporary mathematical use.  Perhaps a few will find these notes of use in the current context.

Precursors of Category Theory


Now the discovery of ideas as general as these is chiefly the willingness to make a brash or speculative abstraction, in this case supported by the pleasure of purloining words from the philosophers:  “Category” from Aristotle and Kant, “Functor” from Carnap (Logische Syntax der Sprache), and “natural transformation” from then current informal parlance.

— Saunders Mac Lane, Categories for the Working Mathematician, 29–30.

This entry was posted in Ackermann, Aristotle, C.S. Peirce, Carnap, Category Theory, Hilbert, Kant, Logic, Mathematics, Peirce, Peirce List, Relation Theory, Saunders Mac Lane, Semiotics, Type Theory and tagged , , , , , , , , , , , , , , . Bookmark the permalink.

5 Responses to Precursors of Category Theory : 1

  1. By the bye, have you encountered Leo Corry’s Modern Algebra and the Rise of Mathematical Structures?

  2. (Not sure this comment posted the first time; sorry if this is a repeat.) I was wondering if you were aware of Leo Corry’s Modern Algebra and the Rise of Mathematical Structures? Corry provides a very carefully cited and detailed discussion of the changes in contemporary algebraic theory that led up to the development of Category Theory.

    • Jon Awbrey says:

      Thanks for the reference. I was not acquainted with that and will definitely look into it as I continue this inquiry. The notion I had was to trace links between mathematical and philosophical uses of categories that are not normally noted in either field.

      By the way, any relation to I.N. Herstein?

      • “any relation to I.N. Herstein?” — Not in any meaningful sense. Some members of my family have done a bit of genealogy and there do not appear to be any connections with I.N.’s family line (which I believe is from Czechoslovakia) for at least 5 generations back. However, on the list of ironies: I moved to Chicago within a year of his death and took my classes in Abstract Algebra at DePaul from his ex-wife (Barbara Cortzen.)

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

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