List: Like Gary R., I exchanged some additional off-List e-mails with André de Tienne, and once again he graciously granted permission to share some of his comments with the Peirce-L community. In this case, we discussed the different names for the relations among Peirce's categories, prompted by my on-List remark that Peirce's preferred term for "subsumption" (mentioned by Gary F.) was "involution" and Robert Marty's is "presupposition."
AdT: Marty derived his notion of presupposition not from Peirce but from Frege, who introduced a semantic presuppositional requirement that conditions the truth or falsity of such a statement as “Kepler died in misery” on the implicit assumption of the truth of the proposition “Kepler existed.” For the first proposition to have any truth value, what is stated in the second statement must be the case, and if so the first proposition is said to presuppose the second proposition. Should the second proposition turn out to be false, then the first proposition is neither true nor false, but merely nonsensical. Frege’s conception therefore was only related to truth dependency between propositions. But Peirce’s categories are not propositions, and thus they are not a matter of truth or falsity. They are general conceptions in a non-reciprocal order of “gradation”, each denoting a step or stage (logical or phenomenological or metaphysical) utterly distinct from the others, while in Frege this sort of categorial distinctness does not apply at all: the implicit assumption of a propositional truth is not what is at play. Besides, in his earliest text, Peirce associates the term “supposition” to “prescision” rather than “presupposition”, and that calls for terminological caution. AdT: The categories in 1867 were to be understood in terms of a gradation—a gradual passage consisting of three distinct and irreducible stages, each one of which was discovered, in one direction (from Being to Substance) through an act of inductive observation followed by a validating act (in the reverse direction) that manifested its indispensability as well as its non-reciprocal dependency. Supposition or prescision was that act of validation by virtue of the fact that prescision was not reciprocal: if A can be prescinded from B, B cannot be prescinded from A. A conditions B’s ability to represent, not the reverse (if that dependency is transitive throughout, then Substance [the manifold in need of representation or explanation] cannot be prescinded from Being [the expressed representation or explanation]). While experience moves from Substance to Being, categorial inductive inquiry moves from Being to Substance (prescision is unidirectional, but the passage works in both directions, one being first-intentional and the other second-intentional, so to speak). From Being one finds inductively that attached to the copula is always some qualitative predicate (itself monadic, dyadic, or triadic)—let’s call it Quality—but whether Quality deserves to be identified as a Category (or gradation stage) needs to be tested through an act of prescision: is it possible to suppose Being without Quality, but impossible to suppose Quality without Being? Well, yes, it is possible to attend to (prescind) Being while neglecting Quality, but one cannot attend to Quality while neglecting the copula, and this verifies both non-reciprocity and indispensability (prescision is thus an act of separation that combines logicality with practicability). Copulative Being therefore conditions Quality — in this sense that it arms it with a particular power to cast intelligibility about that which seeks intelligibility, Substance (the other two categories have each their own distinct and irreducible power). AdT: In that sense, one might say that Quality pre-supposes Being, in the sense that the supposition of Being without supposing Quality is possible. Any predicate supposes its own copulability, in other words, but that only means that it supposes (depends on) the independent supposability of the copula (or the possibility of independently attending to it). The interesting thing to observe is that, in the order of the passage from Substance to Being (thus the order of experience), Substance directly “determines” Representation (3rd), which then determines Relation (2nd, reference to correlates), which in turn determines Quality (1st), and then concludes in the full act of manifold-unifying predicative proposition (Being). The thing to keep in mind is that the pragmatic meaning of “determines” changes from stage to stage. AdT: For similar reasons I would not bring the conception of involution either into this mix when it comes to the relations among categories. The logical purposes that governed Peirce’s use of such terminology are too distinct, it seems to me. I responded by asking André to elaborate on his reasons for being hesitant to employ what I took to be Peirce's own term for the relations among his categories, "involution" AdT: The problem with “involution” is that Peirce’s conception of it is not defined in terms of “involvement”, a term too imprecise to be useful in such matters (vague or imprecise terms yield uncontrollable interpretants, unlike general terms which provide interpretants with a certain controlled latitude [the ability to pick and choose singulars or particulars falling within the area governed by the general term]; vague conceptions don’t provide enough clues to provide interpretants with any sort of authority to state what might follow from them, with the result that either interpretants shut up [appropriately] or state anything and everything with credulous abandon [e.g., conspiracy theories]). The term “involvement” is, like most terms, a mix of generality and vagueness, but it is mostly vague when left undefined. AdT: Peirce, on the other hand, did not leave the term “involution” undefined. It first appeared in his “Logic of Relatives” of 1870 (W2: 362, 377-79, 401-405, 429). The two main species of involution are called ordinary or progressive, and backward or regressive. In 1870 Peirce was not preoccupied with propositions but with classes, and it appears that involution yielded a notation (subscripts or superscripts) representing operation on predicate classes that were quantified (incrementally or decrementally). The act of involution appears to imply moves from wholes down to parts or vice versa within classes. Those two types of involution reappear briefly in 1876 as two kinds of “simple ligation” (W3: 186-188). They reappear in the Algebra of Logic of 1880 (W4: 204, and applied silently in subsequent pages), where Peirce abandoned classes in favor of propositions. They are not found in the 1885 essay, but in “Notes” related to the latter essay the concept of involution gets evoked with regard to the multiplication of propositions into themselves (W5: 192-195). If I am not mistaken the concept then disappears from Peirce’s logic, perhaps thanks to the constant evolution of his notation and progress on quantification. AdT: It remains that involution as Peirce used the term, progressive or regressive (notice the reciprocalness), has nothing to do with the categories or with prescision or with supposition, as far as my cerebral eyes can see. I am admittedly not very familiar with Peirce's earlier uses of "involution" for logical purposes. Instead, like Gary R. I mainly have in mind a few mentions in "The Logic of Mathematics: An Attempt to Develop My Categories from Within" (CP 1.484-495, c. 1896). As Vincent Potter summarizes in *Charles S. Peirce on Norms & Ideals*, "All the universes, then, are inseparably bound up although distinct, just as are the categories. They can be prescinded one from another in a definite logical sequence. Notice, however, that the order of involution and that of evolution are just the opposite. Thirdness or law involves Secondness or actuality and Firstness or potentiality; but potentiality evolves actuality and these two together evolve law." As for "subsumption," Peirce does not use it much either, and when he does, it is never for his categories--only for cases under laws (CP 1.485, 2.560, 2.574, 2.794), objects under concepts (1.559), premisses under a leading principle (2.465), and instances under classes (2.629, 5.183, 8.66). In fact, as far as I can tell, he never makes *any *assertion of the form, "3ns ____ 2ns and 1ns, and 2ns ____ 1ns," so we do not know for sure what verb (if any) he would insert in the blanks. That leaves me wondering if it might be a mistake to talk about his categories having direct relations to each other *at all*, since they are hypostatic abstractions--*entia rationis* that are created by thought *after *the acts of prescission that initially discern them in the phaneron. Instead, I am reminded again of Peirce's statement, "Perhaps it is not right to call these categories conceptions; they are so intangible that they are rather tones or tints upon conceptions'' (CP 1.353, 1885). Accordingly, Vincent Colapietro's self-described "insistence on the *heuristic function of the Peircean categories*" strikes me as very much on the mark. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
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