Jon S, List, JD: 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).
JS: Yes, but the attachment of any EG to the surface on which it is scribed does not constitute an increase of its valency. "A surrenders B" and "A acquires D" are dyadic relations, whether their EGs appear on Metal (actuality) or Fur (intention). A triadic relation is one that requires a Spot with three Pegs to represent it. Again, what third correlate would you identify in order to treat these relations as triadic? JD: The EGs are formal systems of mathematical logic. Taken alone, the systems do not provide adequate answers to the philosophical questions we are asking. Rather, they can be used as toolsets. Peirce is trying to improve these toolsets for the sake of doing philosophy with the aim of ensuring that they do not misrepresent what we seek to clarify. I take myself to be starting with a question about some phenomena drawn from common experience. Such data are the proper starting point, Peirce suggests, for all philosophical inquiries. Consider a case of somebody giving something to another person. That is pretty common. Other philosophers have made much of these sorts of experiences. Witness the essay written by Emerson on the topic. In the phenomenological analysis of the experience of such activities, what kinds of relations are involved? This, I think, is prior to and different in some respects from asking the question of what kinds of logical relations are involved in our general conception of giving. In the cases we've been considering of giving, exchanging and selling, I take Peirce to be starting with a more or less particular case in mind--and he is filling in the details of that case as he goes. You seem to be suggesting that the details don't matter. My reply is that they do for the sake of the phenomenological analysis. We can apply the EGs--considered as mathematical toolsets--in the phenomenological analysis of features drawn from our common experience and in the logical analysis of common conceptions. It may be more at home in the latter case than in the former, but it appears to be useful in both areas of inquiry. Consider the converse way of looking at the relations between the EGs and phenomenology. Peirce often is drawing on the phenomenological analysis of common experience as he develops and refines the EGs. He explicitly says that the analysis of common phenomena such as the practice of counting and the activity of moving a particle from a point on a piece of paper are guiding the formulation of the postulates for mathematical systems of number theory, topology. The same is true in the development of the conventions (i.e., permissions, precepts and postulates) of the EGs. You claim that "the attachment of any EG to the surface on which it is scribed does not constitute an increase of its valency." The question, I take it, was whether the EGs represent different kinds of relations in the case of "A gives up B" (as scribed in the beta system) as compared "A intends to give up B" (as scribed in the gamma system). In the gamma system, the intention of A giving up B is represented in an area of that is colored yellow to represent its modal character as something that is or was intended. On my interpretation of such a graph in the gamma system, the differently colored areas of the sheet represent different kinds of relations as compared to an existential dyadic relation that is represented by spots and lines of identity in the beta system. In addition to the relations between the different shaded areas that are represented on one side of the SA, there are also the relations to what is represented on the other side and/or on other deeper sheets in a book with different modal characteristics. My assumption is that, just as a cut may take us from one sheet to another that is deeper, the shading may also represent relations that penetrate down into those sheets that lie below. My approach to interpreting these different sheets is to think of them as 2-dimensional slices through a multidimensional topological space. I'll leave the implications of such a reading to the side. JD: You say: "'A surrenders B' and 'A acquires D' are dyadic relations, whether their EGs appear on Metal (actuality) or Fur (intention). A triadic relation is one that requires a Spot with three Pegs to represent it." As you can tell, I see things differently. One does not need to consider the intricacies of the gamma system to understand the main point I am trying to make. Compare these two assertions: "A shot B in the heart and he died" and "If A shoots B in the heart, then B will die." What is the upshot of scribing both in the beta system? In particular, what is the import of representing the conditional by a scroll? I take the expression of the conditional to involve a genuinely triadic relation because there is a law that governs the relation. The generality of that relation is expressed iconically in terms of the relation between three spaces: the area that is bounded by the innermost part of the scroll, the area that is bounded by the outermost part of the scroll, and the area that is outside of both. The scroll is needed to represent the genuinely triadic character of such relations because the generality of the conditional cannot be adequately expressed in terms of the spots and lines of the beta system alone. JD: 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. JS: A contract is not essential to the relation of selling, and my understanding is that time has no bearing on logical relations. I still have a hard time seeing how bartering is any simpler than selling, other than the peculiar aspect of money being transferred rather than another item. JD: The contract was a part of Peirce's example. We shouldn't ignore those parts of the examples that appear to be essential to understanding his points. They are his examples, after all. My understanding is that the temporal order of A giving up B and then C acquiring B has a lot to do with our understanding of such phenomena. The dynamical dyadic relation of agent and patient, as a formally ordered relation, may depend on such a temporal ordering. If C tried to acquire B before A had given it up, then it wouldn't be a gift, would it? See the points made above about the differences between phenomenological analyses, which may involve temporally ordered relations, and logical analyses, which may abstract from those relations. Note that some logical systems do take temporal relations into account. Does the gamma system enable one to represent relations of tense?Consider what Peirce says about Metal as a representation of what is actually the case: "Different states of things may all be Actual and yet not Actual together" [Ms 295, p.44]. One way that things that are actually the case are not actual together is if they happened at different times. 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. JS: I did not suggest otherwise. My point was that the number of different relations that we obtain from analysis is arbitrary to some degree, because we are using something discrete to represent something that in itself is continuous. JD: I take the EGs to be topological in character. As a formal system, they are based on the notion of relations of composition and transformation that hold between areas on a sheet of assertion that is, itself, continuous. Various discontinuities are introduced onto the sheet to represent what is existing and discrete as individuals, but the continuity of this type of logical system is central and not peripheral. Yours, Jeff On Sat, May 11, 2019 at 12:42 PM Jeffrey Brian Downard <jeffrey.down...@nau.edu<mailto:jeffrey.down...@nau.edu>> wrote: 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
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