Jon S, Gary F, John S, List,
Let me offer a brief response to the objection Jon S. raised earlier. JD: I take the expression of the conditional (i.e., expressed in the EGs by a scroll) to involve a genuinely triadic relation because there is a law that governs the relation. Jon S: What is the warrant for taking every relation that is governed by a law to be genuinely triadic on that sole basis? On the contrary, most (if not all) dyadic relations that we encounter in experience are governed by laws in some way, but we still classify them as dyadic because they have exactly two correlates; the law itself is not a third correlate. CSP: Any dynamic action--say, the attraction by one particle of another--is in itself dyadic. It is governed by a law; but that law no more furnishes a correlate to the relation than the vote of a legislator which insures a bill's becoming a statute makes him a participator in the blow of the swordsman who, in obedience to the warrant issued after conviction according to that statute, strikes off the head of a condemned man. (CP 6.330; 1908) Jon S: Even a degenerate dyadic relation is governed by a law; e.g., the hardness of a diamond consists in the truth of the conditional proposition that if it were to be rubbed with another substance, it would resist scratching. Are there any passages in Peirce's writings where he characterized a relation with exactly two correlates as triadic? Jeff D: Most of the relations that we encounter in experience are rich and complex. Consider the experience of one billiard ball A colliding with another B in accordance with the law of inertia LI. We can abstract from the law of inertia and attend solely to the dynamical relation between A and B as existing individuals. There is a fact about each. A is in motion, and then it collides with B, which was stationary. As a result, B moves. That can be treated as a dynamical dyadic relation that is formally ordered such that A is agent and B is patient. Considered in this way, we treat the dyadic relation between them as a mere matter of brute force. Alternately, we can consider the relation between the fact that A was moving and B was stationary, and then the later fact that B was put into motion as a result of the collision as being governed by the law of inertia (LI). According to Peirce's classification of relations in "The Logic of Mathematics,...), this is a genuinely triadic relation of fact. All such genuinely triadic relations of fact are governed by some kind of law. On my interpretation of the text, the law of inertia functions as the third correlate in the triadic relation. We can analyze the relation in a number of ways, here is a simple version: A determines B to accelerate in accord with LI. A fuller analysis would involve a closer look at LI. Newton's account of this law takes the following form: Force of inertia=mass*acceleration. How does the law of inertia govern the relations between the facts concerning A and B? The first fact attributes qualities to each (i.e., each billiard ball has a position at the first time, such that A is in motion heading towards the other ball and B is not in motion). The second fact attributes a different set of qualities to each. The law governs the changes in those facts so that there is a general regularity that governs other possible interactions between any masses of this type. Notice what Peirce says about inertia as a dynamical law insofar as it is explained by Newton in his theory of physics: As to the common aversion to recognizing thought as an active factor in the real world, some of its causes are easily traced. In the first place, people are persuaded that everything that happens in the material universe is a motion completely determined by inviolable laws of dynamics; and that, they think, leaves no room for any other influence. But the laws of dynamics stand on quite a different footing from the laws of gravitation, elasticity, electricity, and the like. The laws of dynamics are very much like logical principles, if they are not precisely that. They only say how bodies will move after you have said what the forces are. They permit any forces, and therefore any motions. Only, the principle of the conservation of energy requires us to explain certain kinds of motions by special hypotheses about molecules and the like. Thus, in order that the viscosity of gases should not disobey that law we have to suppose that gases have a certain molecular constitution. Setting dynamical laws to one side, then, as hardly being positive laws, but rather mere formal principles, we have only the laws of gravitation, elasticity, electricity, and chemistry. Now who will deliberately say that our knowledge of these laws is sufficient to make us reasonably confident that they are absolutely eternal and immutable, and that they escape the great law of evolution? The main difference that I see between the law of inertia and the law of gravity is that, on Peirce's account, the former is governed by (if you will) a logical law of deductive demonstration. As such, the law is taken to be unchanging in its form. The law of gravity, on the other hand, might very well continue to evolve. For instance, gravitational "constant" in Newton's version of the law might be evolving. Furthermore, it's being an inverse square law and not an inverse of a 2.1 power might not be fixed. Rather, the inverse power relation (as a function of distance) might be evolving. The fundamental law governing the evolution of the law of gravity is, on Peirce's account, the one law of mind. On my reading of this text, we can understand that law to be an objective manifestation of the one law of logic. In this case, the third clause that is governing the law of gravity is not one of deductive demonstration. Rather, it is one that brings abductive and inductive patterns of inference to bear on the ongoing formation of the spatial and temporal habits in their relations to the distribution of mass both locally and globally (e.g., understood in terms of the paths that are possible through a given space). There appears to be a difference between the operation of these laws. The law of inertia is, at this point in the history of the universe, relatively static and dead. For the most part, it operates in an efficient, mechanical, linear, conservative manner. The law of gravity, on the other hand, continues to evolve. As a law, it appears to have some sort of life. Is the claim that the law of inertia seems to govern the motions of masses in a manner that is akin to a form of logical demonstration, while the law of gravity seems to govern the relations between space and mass in a manner that is akin to a form of logical abduction and/or induction testable as a hypothesis? My hunch is that it is a testable hypothesis. Yours, Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________ From: Jon Alan Schmidt <jonalanschm...@gmail.com> Sent: Sunday, May 12, 2019 11:57 AM To: peirce-l@list.iupui.edu Subject: Re: [PEIRCE-L] Triadic and Tetradic relations Jeff, List: JD: I take the expression of the conditional to involve a genuinely triadic relation because there is a law that governs the relation. What is the warrant for taking every relation that is governed by a law to be genuinely triadic on that sole basis? On the contrary, most (if not all) dyadic relations that we encounter in experience are governed by laws in some way, but we still classify them as dyadic because they have exactly two correlates; the law itself is not a third correlate. CSP: Any dynamic action--say, the attraction by one particle of another--is in itself dyadic. It is governed by a law; but that law no more furnishes a correlate to the relation than the vote of a legislator which insures a bill's becoming a statute makes him a participator in the blow of the swordsman who, in obedience to the warrant issued after conviction according to that statute, strikes off the head of a condemned man. (CP 6.330; 1908) Even a degenerate dyadic relation is governed by a law; e.g., the hardness of a diamond consists in the truth of the conditional proposition that if it were to be rubbed with another substance, it would resist scratching. Are there any passages in Peirce's writings where he characterized a relation with exactly two correlates as triadic? 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. EGs represent the relations of (ter)coexistence and (ter)identity as continuous--we can always add another Graph to the Sheet of Assertion, and we can always add another branch to any Line of Identity--but they do not represent the process of semeiosis as continuous. Instead, they represent a hypothetical instantaneous state of an Argument, and the transformation to a subsequent state is always by means of discrete steps. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt<http://www.LinkedIn.com/in/JonAlanSchmidt> - twitter.com/JonAlanSchmidt<http://twitter.com/JonAlanSchmidt> On Sat, May 11, 2019 at 10:22 PM Jeffrey Brian Downard <jeffrey.down...@nau.edu<mailto:jeffrey.down...@nau.edu>> wrote: 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
----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
