Re: Peirce’s Categories • 15

Understanding another person’s thought can be difficult.  Understanding the way another understands a third person’s thought, all the more so, even if that third person is not so formidable a thinker as Charles Sanders Peirce.  Measures of misunderstanding may be moderated if all thoughts and thinkers are guided by common objectives but the proof of the pudding is in the partaking, as they say.  So let’s step carefully and focus on the task of determining whether category theories, old and new, make good tools for understanding sign relations.

The interaction recorded in my last post continued as follows:

• Peirce List • RM • JA

RM:

I do not see how we can talk here about an operative relationship that would be a triad relationship.  It is not anything other than the composition of two morphisms and I do not ask for more.  3, 2, and 1 are the “place names” and “involves” are arrow names that I usually call alpha and beta.  Now if you think about the determinations in the sign, I have always assumed after much study of the 76 definitions, this idea that the composition of applications captures the presence in the mind of each of the elements of the sign, in such a way that they are themselves ipso facto connected by a triadic relationship.  There is a relationship of tricoexistence that is established as in this case evoked by Peirce:  “It predicates the genuinely Triadic relationship of tricoexistence, ” (CP 2.318, unfortunately there is a hole in my PDF of CP right after and I [left] my paper edition at the library of my university, inaccessible at the moment).

We have a mutual incomprehension?

JA:

I don’t often join the debates over sign classification so frequently animating the animadversions of the Peirce List.  As more the observer than the participant I see the same pattern over and over, with occasional hints but never any hue of resolution fast enough to last and satisfy every dyehard.

Situations of that sort are no novelty in philosophy, or politics, or even math and science on occasion.  And when they occur it is usually because the “place to stand” from which the subject appears in its proper light has yet to be reached by every viewer.

So I’ll back up a little and say how I see things from where I am.

Resources

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

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