Precursors Of Category Theory • Discussion 3

Take your place on The Great Mandala
As it moves through your brief moment of time.
Win or lose now you must choose now
And if you lose you’re only losing your life.

Peter Yarrow

Re: Ontolog ForumAlex Shkotin

I like Kant’s criticism of Aristotle versions of categories.

“Finding these basic concepts — such a proposal was worthy of such an astute thinker like Aristotle.  But since he did not have any principle, he picked them up as they came across to him, and first typed ten concepts, which he called categories (predicates).  Then it seemed to him that he found five more such concepts, which he added to the previous ones under the name of post-predicate.  However, his table was still insufficient.”  (Kant, Critique of Pure Reason, §10.  About Pure Rational Concepts, or Categories).

Dear Alex,

My sketch on Precursors Of Category Theory shows a big ellipsis under the heading for Kant.  I meant to get back to him, as I used to do every half-decade or so, but it’s been a long time since I kept to that schedule.  Kant is a lodestar in the Peircean constellation — Peirce’s “New List of Categories” invokes his guidance on the function of concepts just as he tries his own hand at the wheel.  I quoted that passage in my selections from Peirce.

Selection 1

§1.  This paper is based upon the theory already established, that the function of conceptions is to reduce the manifold of sensuous impressions to unity, and that the validity of a conception consists in the impossibility of reducing the content of consciousness to unity without the introduction of it.  (CP 1.545).

§2.  This theory gives rise to a conception of gradation among those conceptions which are universal.  For one such conception may unite the manifold of sense and yet another may be required to unite the conception and the manifold to which it is applied;  and so on.  (CP 1.546).

C.S. Peirce, “On a New List of Categories” (1867)

To be continued …



cc: CyberneticsOntolog ForumPeirce ListStructural ModelingSystems Science

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 3

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

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.