Jeff, List: JD: My strategy for interpreting these passages is to take Peirce at his word when he refers to the triadic relations that are involved.
Normally I would do likewise, which is why I find them so problematic. JD: In order to interpret "μ is the surrender by A of B" and "ν is the acquisition by A of D" as triadic and not merely dyadic relations, my hunch is that he is considering these actions as intentional in character. Maybe, but then how would you restate them as *explicitly *having three correlates, perhaps by presenting each as an EG? And would they then be *genuine *or *degenerate* triadic relations? JD: The case that you cite of an object being sold involves a transfer of money and a contract. The simpler case of exchange as barter with no contract is illustrative of how other kinds of relations may be involved when more general things, such as property laws and legal systems, are governing the intentional acts. There is no reference to a contract in the initial proposition, "S sells T to B for M"; and it is *isomorphic *with the allegedly simpler case, "A gives up B to C in exchange for D." In other words, it seems to me that "sells X for Y" is *logically *the same relation as "gives up X in exchange for Y." Do you disagree? Again, is an essential element somehow omitted if we analyze the tetradic relation of selling (or bartering) as a combination of only four triadic relations, two of giving (genuine) and two of exchanging (degenerate)? JD: How many triadic relations are involved in this process of a young child learning? Well, it appears to grow according to a power law. As such, it grows into a multitude that exceeds any system of numbers that is numerable or even any system that is abnumerable. Of course it does, because *real *semeiosis is *continuous*--it is not *composed *of discrete relations (prescinded predicates) and their discrete correlates (abstracted subjects) as expressed in definite propositions; those are all *artificial *creations of thought for the purposes of description and analysis. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Fri, May 10, 2019 at 10:44 PM Jeffrey Brian Downard < jeffrey.down...@nau.edu> wrote: > Jon S., List, > > My strategy for interpreting these passages is to take Peirce at his word > when he refers to the triadic relations that are involved. In order to > interpret "μ is the surrender by A of B" and "ν is the acquisition by A > of D" as triadic and not merely dyadic relations, my hunch is that he is > considering these actions as intentional in character. The object > surrendered and the agent who surrenders it are existing individuals in the > relation of agent and patient, but that existential description of the > individuals is part of an intentional action by A. As a general sort of > thing, the intention makes the action of surrendering triadic in > character--and so too with the action of A acquiring object D. > > The case that you cite of an object being sold involves a transfer of > money and a contract. The simpler case of exchange as barter with no > contract is illustrative of how other kinds of relations may be involved > when more general things, such as property laws and legal systems, are > governing the intentional acts. As a historical point, it is reasonable to > suppose that social conventions governing exchanges by barter developed > prior to any contracts or legal systems. Consequently, I think that the > proper analysis of every genuine triadic relation involves a correlate > that, itself, has the character of a general rule. As a correlate, that > intention, or property law, or what have you, may involve a general rule > that is part of a larger system of rules (such as a legal system). > > Having said that, the reason the number of triadic relations involved in > tetradic, pentadic and higher order relations goes up by a power of 10 is > not obvious to me. While it isn't obvious, here is a conjecture: Peirce > may be thinking about the operation of general laws and intentions as > conforming to a general model that applies to all genuinely triadic > relations. > > One such model is articulated in "The Logic of Mathematics, an attempt to > develop my categories from within". In that account of genuinely triadic > relations, the law of quality and most general laws of fact each involves > three clauses. The first clause governs each correlate considered in > itself. The second clause governs the dyadic relations between pairs of > correlates. The third clause governs the triadic relations between the three > correlates. It is possible that the operation of the three clauses involved > in such law might multiply the number of relations that may be involved in > tetradic, pentadic, sextadic (etc.) relations by a power of ten in each > case. The long explanations that he provides in this essay of the > triadic relations that are part of the laws of space and the laws of > physics may be illustrative of this general pattern. > > Generalizing on these points, I think that the *principles* of logic that > govern self-controlled acts of inference are, similarly, parts of larger > systems of logical rules. Something as straightforward as the rule > governing the first figure of the syllogism (the *nota notae*) is a rule > that is related, as part of a larger logical system, to the principles of > identity, non-contradiction, excluded middle, etc. The systematic > connections that hold between the underlying *laws* of logic are probably > richer and deeper than anything we are able to express in our little > theories of logic (*logica utens* or *logica docens*). As a result, the > analysis of the triadic relations that are involved in a symbolic > argument must take into account the relations that hold between the guiding > principle of the inference and the other rules that are essential to > inferences of that form. Peirce is offering an outline of how this might > work in his explanation of the three clauses that are part of the > general law of logic. > > In order to explain how our conceptions of the laws of logic--conceived as > principles that govern self-controlled acts of reasoning--might have > evolved in the human species, Peirce considers the simple case of a child > learning that hot stoves should not be touched. In "Faculties", > "Consequences" and "Further Consequences," Peirce starts with the child > forming a more or less deliberate intention to touch the stove. When the > child learns that it is not possible for him to hold his hand on the stove, > he learns that his parents were correct and his supposition was incorrect. > As such, it looks like there is a strategy that may be at work, which is to > explain how relatively simpler cases of intentional actions might later > give rise to new conceptions--including a conception of the leading > principle that governs the type of inferences that were involved in the > learning about the stove. > > Consequently, I think that some clarity could be achieved by applying the > analysis of the triadic relations that are involved in progressively more > complicated tetradic, pentadic, sextadic, etc. relations to simple > examples--such as that of a child learning how to engage more or less > self-controlled patterns of logical reasoning. My assumption is that the > child was already capable of thinking in a manner that conformed to the > laws of logic from an early age. The instinctive patterns of inference were > not subject to much self-control at the ages of 1 and 2, but the child was > learning how to use a conventional system of symbols (i.e., a natural > language) as a matter of habit. In time, what the child learned was how to > represent those laws to himself as principles. In turn, the child learned > to recognise what those principles, functioning as imperatives, > might require of him in terms of the future conduct of his inquiry. > > How many triadic relations are involved in this process of a young child > learning? Well, it appears to grow according to a power law. As such, it > grows into a multitude that exceeds any system of numbers that is numerable > or even any system that is abnumerable. The upshot of what I am suggesting > is that Peirce's observation that there may be a power law involved in > richer relations would explain his earlier assertions about the sort of > infinity and resulting continuity that is involved in the growth of our > cognitions. > > Yours, > > Jeff > Jeffrey Downard > Associate Professor > Department of Philosophy > Northern Arizona University > (o) 928 523-8354 >
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