John S, Jon S, List,
JohnS: To clarify these issues, search CP for every occurrence of "A gives B". Jeff D: Here is one passage that is particularly germane to the question at hand. When Peirce claims that giving is a genuinely triadic relation, I take note of the fact that in the "Logic of Mathematics, an attempt to develop my categories from within" the intentional act of one person giving something to another person under a law is classified, on my reading of the text, as a paradigmatic example of thoroughly genuine triadic relation. Consider the following passage: I now come to Thirdness. To me, who have for forty years considered the matter from every point of view that I could discover, the inadequacy of Secondness to cover all that is in our minds is so evident that I scarce know how to begin to persuade any person of it who is not already convinced of it. ... Analyze for instance the relation involved in 'A gives B to C.' Now what is giving? It does not consist [in] A's putting B away from him and C's subsequently taking B up. It is not necessary that any material transfer should take place. It consists in A's making C the possessor according to Law. There must be some kind of law before there can be any kind of giving, -- be it but the law of the strongest. But now suppose that giving did consist merely in A's laying down the B which C subsequently picks up. That would be a degenerate form of Thirdness in which the thirdness is externally appended. In A's putting away B, there is no thirdness. In C's taking B, there is no thirdness. But if you say that these two acts constitute a single operation by virtue of the identity of the B, you transcend the mere brute fact, you introduce a mental element . . . . The criticism which I make on [my] algebra of dyadic relations, with which I am by no means in love, though I think it is a pretty thing, is that the very triadic relations which it does not recognize, it does itself employ. For every combination of relatives to make a new relative is a triadic relation irreducible to dyadic relations. Its inadequacy is shown in other ways, but in this way it is in a conflict with itself if it be regarded, as I never did regard it, as sufficient for the expression of all relations. My universal algebra of relations, with the subjacent indices and and, is susceptible of being enlarged so as to comprise everything; and so, still better, though not to ideal perfection, is the system of existential graphs. CP 8.331 In this passage, Peirce says that the relation of giving does not consist merely in the following two facts: 1. A's putting B away from him, and 2. C's subsequently taking B up. On the analysis offered at CP 1.474, I agree that both of these facts--considered as individual facts about existing objects--are dyadic in character. Both facts may, by particularization, be evolved into a dyadic triad. Note that the particularization requires a further evolution of the dyadic relations involved in each fact into a dyadic triad. Those same facts can also be analyzed as being parts of intentional actions. Insofar as there is a mental component involved in each, both are genuinely triadic in their character because the existential facts are now considered to be governed by general habits of thought. What is more, Peirce notes that B does need not be an existing object. It might, for instance, be a piece of intellectual property, such as the rights of ownership to a patented invention. As such, I believe that this passage provides a basis for analyzing some acts of giving as involving three genuinely triadic relations. 1. The intentional action μ which consists in A surrendering B 2. The intentional action η which consists in C acquiring B 3. Μ<https://en.wikipedia.org/wiki/%CE%9C> is the performance of μ with the intent of bringing about η under a Law of some kind. In offering this analysis, I accept the general point that a genuinely triadic relation a combination of two or more individual facts concerning existential objects under some genuine third that, as a general, governs the interaction of the two. My suggestion is that a thoroughly genuine triadic relation also involves three genuinely triadic relations that are brought together by a genuinely triadic relation. What is special about representations, Peirce says, is that they are not governed by mere laws of fact. Peirce says: Genuine triads are of three kinds. For while a triad if genuine cannot be in the world of quality nor in that of fact, yet it may be a mere law, or regularity, of quality or of fact. But a thoroughly genuine triad is separated entirely from those worlds and exists in the universe of representations. Indeed, representation necessarily involves a genuine triad. For it involves a sign, or representamen, of some kind, outward or inward, mediating between an object and an interpreting thought. Now this is neither a matter of fact, since thought is general, nor is it a matter of law, since thought is living. CP 1.480 My interest here is to clarify Peirce's suggestion that questions about the origins of life can be better understood if we ask about the origins of genuinely triadic relations. The same, I think, would have to hold for explaining the origins of intelligent and self-controlled processes of thought. As such, I'd like to ask how we might explain the evolution of thoroughly genuine triadic relations--such as an intentional act of giving under a living law, where each of the correlates is itself understood to be genuinely triadic in its character. What is special about some triadic relations that enables further homeostasis, growth, and reproduction in the relations themselves? --Jeff
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