Jon S, List, 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.
JS: 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 relation of surrendering, considered as formally ordered dynamical dyadic relation, is a relation that can be expressed in the beta system of the EG. If μ is understood to involve an intention on the part of A, then it can't be expressed in those terms. In the Prolegomena, Peirce uses the modal tincture of Fur as a means of expressing intentions in the gamma system. The pattern of ermine (or the color yellow), is used to represent iconically that the area shaded expresses an intention on the part of the agent (see Don Roberts, 92-102). Understanding the character of the triadic relations that hold between the areas that are patterned or shaded one way to the other areas of the graph is not a simple matter. Hence the difficulties of sorting out the modal relations using the tinctures (or colors). In his monograph, Don Roberts attempts to revise the tinctures in order to overcome some of the concerns that Peirce raised about this manner of expressing modal relations in the gamma system. Given the complexities involved, I won't try to answer the question of whether the triadic relations involved are genuine or degenerate in some respects. 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. JS: 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: The initial description is underdetermined. The analysis he provides shows that Peirce was thinking of a transfer involving money and a contract, which means that the transfer was not simultaneous. Barter, as a form of exchange, is often simultaneous. When it is, that makes the exchange considerably simpler in character. That is one reason that exchange by barter may have preceded the development of formal systems of law. 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. JS: 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. JD: It does not follow from the simple fact that the analyses involve entia rationis that such creations of the mind may not represent something real. Notice how Peirce puts the point. In a tetradic relation, there are at most 10 triadic relations involved, whereas in a pentadic relation, there are at most 100 triadic relations involved. It does not follow from the claim that semiosis is continuous that there are, somehow, an unlimited number of triadic relations involved. Inserting a real triadic relation where, before, one was only a potentiality, can be done any number of times. In doing so, however, you've made a new relation. Yours, Jeff <http://twitter.com/JonAlanSchmidt> On Fri, May 10, 2019 at 10:44 PM Jeffrey Brian Downard <jeffrey.down...@nau.edu<mailto: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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