Re: Peirce’s Categories • 15

Another point where the onrush of discussion and the impact of worldly distractions caused my train of thought to jump the track is here:

• Peirce List (1) (2) • RM • JA

RM:

First I note that the formulation “3ns involves 2ns, which involves 1ns” is very dangerous [as] it forgets that 2ns has its autonomy and 1ns too.  If you look at the podium [one] remains in the inner cylinder.  It seems to me that Peirce’s reproach to Hegel is:

“He has usually overlooked external Secondness, altogether.  In other words, he has committed the trifling oversight of forgetting that there is a real world with real actions and reactions.  Rather a serious oversight that.”

It is therefore important to prefer “3ns involves 2ns and 1ns, while 2ns involves 1ns” which preserves the autonomy of the Peircian categories so as not to encourage the idea of a possible peircean hegelianism.

JA:

I’ve been working on a comment about your first point but I’ll post it … when and if I manage to put it in respectable shape.  Just by way of a hint for now, the issue turns on whether we take involves or presupposes to be a dyadic relation and a transitive one at that, as we would if we pass from “3 involves 2” and “2 involves 1” to the conclusion “3 involves 1”.  That may be true for some concepts of involution or presupposition but I think the operative relation in this case is a thoroughly irreducible triadic relation, one whose properties do not reduce to the composition of two dyadic relations.

I think it will take a little more work to get clear about this.  I will go back to the draft remarks I was working on and see if I can bring them to bear on the question.

Resources

• Precursors Of Category Theory
• Survey of Precursors Of Category Theory

cc: Cybernetics • Ontolog • Peirce List (1) (2) • Structural Modeling • Systems Science