Evening Note for Monday, October 12

Thought for the Evening: TRS Triads

A recurring pattern in the history of Western philosophy is what might be called a Term-Relation-System  (TRS) triad, a collection of three in which the second and third member 'build' on the one(s) before. The oldest TRS triad is found in logic: Term, Proposition, Argument. Logical terms are put in relation to each other to make propositions; propositions are put together into a system that we call an argument. 

Term, Proposition, Argument is the root triad for most of the TRS triads in the history of philosophy, although we should perhaps keep an open mind for finding TRS triads outside of the family. One very different triad that could perhaps be seen as a TRS triad, but which is surely not related historically, is the old liberté, fraternité, egalité. One could very plausibly see this as identifying something pertaining to the individual, thus liberty as a term, which interacts with other liberties of other individuals to get fraternity as the relation, and then fraternity is structured into a system, equality. Certainly the equality in the slogan is intended to be systematic, not just a happenstance of equality between individuals, but a system in light of which individuals are equal.

There are no doubt others; it would be interesting to go through Bonaventure's endless triads and see which, if any of them, count as TRS triads and which don't. (Could one, true, good, for instance, be considered a TRS triad? How about number, weight, measure? Does faith, hope, love admit of an account that makes it a TRS triad, or is it some other kind of triad?) But the real heyday of the TRS triad in Western philosophy begins with Kant, who makes significant and deliberate use of them. The reason is that Kant sees our grasp on the world as structured by judgment, and the three kinds of judgment are Categorical, Hypothetical, Disjunctive, and Kant quite clearly characterizes these in a TRS way (which is, I think, entirely consistent with how they had been understood throughout the history of the theory of judgment). Because judgment is so important and Kant thinks of it as involving a TRS triad, TRS triads keep showing up in Kant's work. For instance, Kant gives twelve pure concepts of the understanding, which are, so to speak, the map for how we understand the world:

Quantity: Unity, Plurality, Totality 
Quality: Reality, Negation, Limitation
Relation: Inherence, Causation, Community
Modality: Possibility, Existence, Necessity

When you look at the characterizations of these, Quantity and Relation are both quite clearly understood in TRS terms. Because of Relation, we can consider something like Substance, Law, System as a TRS triad, because in a sense relation establishes these as features of our understanding of the world; this makes a lot of sense, given how Kant understands each. Quality and Modality are trickier, but I think there's at least an argument that they should also be understand as a building triad.

But there are other cases in Kant. I think there's a very strong argument that Kant's three major formulations of the categorical imperative -- the Law of Nature formulation, the End in Itself formulation, and the Kingdom of Ends formulation form a TRS triad.

Kant, however, is not the only one who makes important use of TRS triads. Peirce does, as well. Peirce likes triads in general, and often discusses logic, so it is not surprising to find TRS triads in his work, but he very definitely builds them.  The most obvious example, derived directly from Term, Proposition, Argument, is the Rheme, Dicent, Delome classification of signs; Peirce pretty clearly intends this to be a more general form of Term, Proposition, Argument, applicable to every kind of sign, and even will often use 'Argument' instead of 'Delome'. Given the analogies between this triad and the other two important triads of Qualisign, Sinsign, Legisign and Icon, Index, Symbol, these classifications seem to be TRS triads as well. If we can read Possibility, Existence, Necessity as a TRS triad for Peirce as well as Kant, this would clinch the argument, since many of Peirce's triads are structured in such a way as to be Possibility, Existence, Necessity triads of one form or another. 

(One could, however, argue that Possibility, Existence, Necessity is a distinct kind of triad which can overlap with TRS triads. It's easy to relate Possibility as a Term-modality and Necessity as a System-modality, because that is closely tied to how we explain them to begin with -- the necessary is that which is found in all possibles -- but it's much harder to get a grasp on Existence as a Relation-modality, because Existence doesn't seem obviously reducible to just possibilities in relation. Existence is not really in between Possibility and Necessity; it is more fundamental than either, at least in how we think of them. Perhaps we are being too literal, though, and the real middle here is something that might be more accurately called Truth, in the ontological sense, as a relation between possibles.)

Various Links of Interest

* James Hankins, Pietas, at First Things

* Ashok discusses Gerard Manley Hopkins's "As Kingfishers Catch Fire"

* John Farrell reviews Mark Shea's The Church's Best-Kept Secret

*  Patrick O'Donnell, Introducing the concept of rasa in Indian aesthetics and philosophy of art, at ReligiousLeftLaw.com 

* Barbara Castle, Awakening to Virtue: Confessions of a Well-Read, Unlucky Good Girl

*  Emrys Westacott, The Venerable Prejudice against Manual Labour

* John Marenbon, Why Read Boethius Today?

Currently Reading

Ahmet Midhat Efendi, Felâtun Bey and Râkım Efendi
Declan Finn, Crusader