Jon S, List,
First, let me point out that I believe a number of arguments were offered in the post. The simplest argument was a mere colligation of separate points. The richer argument, I think, was explanatory in character. Having said that, let me try to comply with your request. Please be forewarned that the quote offered will not, by itself settle the matter. Rather, I provide a quote and ask how it might be interpreted. In "The Logic of Mathematics, an attempt to develop my categories from within", 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 Let's consider an example of a thoroughly genuine triadic relation. The example Peirce gives is an argument. Here is one such example: All men die; Enoch is a man; Therefore, Enoch dies. If we classify this sign according to the system in NDTR as a symbolic, argument, legisign, then what are its parts? Here are two different ways of thinking of the matter. 1. The premisses are a sign and the conclusion is the interpretant of those premisses. 2. The argument as a whole is a sign which may be interpreted in light of a further argument of which this is a part. Either way, we should be able to answer the following questions: a. Do symbolic arguments have parts? b. If they do, how are the parts related to make a whole? Normally, we think of individual things as having parts. My body, for instance, is a whole composed of several organs. My heart is in a particular location relative to my intestines. Are general things, like laws or symbols, wholes that consist of parts? Peirce's answer, I think, is yes. In fact, he felt a need to provide a much more general account of the relations between parts and whole just so that he could address such questions. He says: "I begin by defining a part of any whole, in a sense of the [term] much wider [than] any in current use, though it is not obsolete in the vocabulary of philosophy. In this broadest sense, [it] is anything that is (1) other than its whole, and (2) . . . such that if the whole were really to be, no matter what else might be true, then the part must under all conceivable circumstances itself really be, in the same 'universe of discourse,' though by no means necessarily in the same one of those three Universes with which experience makes us all more or less acquainted. Thus, light is a part of vision . . . . CP 7.535 Fn 6 Para 1/2 p 319 Note that the example he offers can be understood in a general way: light in the visible spectrum, generally understood, is a part of the process of vision, understood as a sort of law that governs all things having this capacity. The reading of the texts that I was exploring in the earlier email draws on this general account of how parts relate to wholes. In doing so, we get an understanding of how arguments are composed of propositions that serve as premisses and conclusions, and of how propositions are composed of terms. The predicate "terms" in the propositions are rhematic and are composed, in some sense, of iconic legisigns. The subject terms are composed, in some sense, of indexical legisigns. How far does this sort of analysis go? Peirce, I believe, takes a striking position when he asserts the following: The easiest of those which are of philosophical interest is the idea of a sign, or representation. A sign stands for something to the idea which it produces, or modifies. Or, it is a vehicle conveying into the mind something from without. That for which it stands is called its object; that which it conveys, its meaning; and the idea to which it gives rise, its interpretant. The object of representation can be nothing but a representation of which the first representation is the interpretant. But an endless series of representations, each representing the one behind it, may be conceived to have an absolute object at its limit. The meaning of a representation can be nothing but a representation. In fact, it is nothing but the representation itself conceived as stripped of irrelevant clothing. But this clothing never can be completely stripped off; it is only changed for something more diaphanous. So there is an infinite regression here. Finally, the interpretant is nothing but another representation to which the torch of truth is handed along; and as representation, it has its interpretant again. Lo, another infinite series. CP 1.339 We've considered this passage before. I remain interested in the portion that I've emphasized in boldface type. If symbolic legisigns, such as the argument above, are composed of parts that are, in themselves, general in character, then how should we understand the part-whole relationship in this case. Peirce suggests that the relationship works in a special way when we are considering something, like a symbol, whose parts are continuous, one with another. The argument has this character. On the one hand, we can consider it as an abstract general. In reality, though, the symbol lives as a habit of thought for the community of inquirers who have such beliefs about Enoch. As a living symbol, the argument is not made up of 10 symbolic terms. Rather, it is an embodied system of habits of thought that lives in a community. The parts of that system are continuous in their relations to each other and to the whole. How are the parts of a continuous thing related to a whole? This works differently than it does for those things that are aggregates of discrete parts. In the same footnote quoted above, he says: "A perfect continuum belongs to the genus, of a whole all whose parts without any exception whatsoever conform to one general law to which same law conform likewise all the parts of each single part. Continuity is thus a special kind of generality, or conformity to one Idea. More specifically, it is a homogeneity, or generality among all of a certain kind of parts of one whole. Still more specifically, the characters which are the same in all the parts are a certain kind of relationship of each part to all the coördinate parts; that is, it is a regularity. CP 7.535 Fn 6 Para 2/2 p 319 Having considered these points, let us consider another general idea that is developed in "The Logic of Mathematics, an attempt to develop my categories from within". In the discussion of genuine triadic relations, he provides an account of genuinely triadic relations of quality in which two or more qualities (e.g., colors) are governed by a general law of quality (e.g., Newton's law of colors). Next, he provides an account of genuinely triadic relations of fact. The first laws that he considers are the laws of logic insofar as they govern facts in an objective manner, and then he considers the general laws of metaphysics and the law of time. Let us ask, how does the general law of logic govern facts? Peirce tells us that there are three clauses to the general law of logic, just as there are three clauses to the general law of metaphysics and the general law of time. The three clauses for the general law of logic can be separated as follows: a. The monadic clause is that fact is in its existence perfectly definite. Inquiry properly carried on will reach some definite and fixed result or approximate indefinitely toward that limit. Every subject is existentially determinate with respect to each predicate. b. The dyadic clause is that there are two and but two possible determinations of each subject with reference to each predicate, the affirmative and the negative. Not only is the dyadic character manifest by the double determination, but also by the double prescription; first that the possibilities are two at least, and second that they are two at most. The determination is not both affirmative and negative, but it is either one or the other. A third limiting form of determination belongs to any subject [with regard] to [some other] one whose mode of existence is of a lower order, [the limiting case involving] a relative zero, related to the subjects of the affirmation and the negation as an inconsistent hypothesis is to a consistent one. c. The triadic clause of the law of logic recognizes three elements in truth, the idea, or predicate, the fact or subject, the thought which originally put them together and recognizes they are together; from whence many things result, especially a threefold inferential process which either first follows the order of involution from living thought or ruling law, and existential case under the condition of the law to the predication of the idea of the law in that case; or second, proceeds from the living law and the inherence of the idea of that law in an existential case, to the subsumption of that case and to the condition of the law; or third, proceeds from the subsumption of an existential case under the condition of a living law, and the inherence of the idea of that law in that case to the living law itself. Thus the law of logic governs the relations of different predicates of one subject. Why three clauses? Are these the only general laws of fact that have three clauses? Or is Peirce offering these as examples that illustrate how every law operates in terms of three such clauses? The fact that the general law of quality also has three clauses leads me to hypothesize that, on Peirce's account, the latter may be the case. Working on that assumption, why are there three clauses for any of these general laws? When it comes to the manner in which general law-like things operate in the realm of genuine triadic relations, Peirce distinguishes in NDTR between three different sorts of lawlike things: Triadic relations are in three ways divisible by trichotomy, according as the First, the Second, or the Third Correlate, respectively, is a mere possibility, an actual existent, or a law. These three trichotomies, taken together, divide all triadic relations into ten classes. These ten classes will have certain subdivisions according as the existent correlates are individual subjects or individual facts, and according as the correlates that are laws are general subjects, general modes of fact, or general modes of law. CP 2.238 Once again, I've used boldface to highlight the relevant passage. I think it is plausible to suppose that the general law of logic has three clauses because the first clause governs general subjects (which in turn govern individual subjects), while the second clause governs general modes of fact (which in turn govern individual facts) and the third clause governs general modes of law (which in turn govern more specific laws that are part of a system of laws). As such, the classification of genuine triadic relations supplies part of the basis of a system of genuine triadic relations that can be used to explain how general laws govern individual subjects and facts in relation to the regularities in the possible qualities that each might come to possess. (Side note: please understand that I am not going through these steps for no reason. Rather, I’m developing a line of interpretation of the classification of relations that can be used, for instance, in metaphysics to understand the explanations Peirce offers in his metaphysical writings such as “The Law of Mind” and “Man’s Glassy Essence”). Let me try to summarize these points. How do laws govern the changes in the properties of individual objects? The manner in which laws appear to work on this Peircean account is not simple. That is, it is not simply a matter of having a law as one correlate of a triadic relation that governs the relations between two other correlates which consists of either (a) the properties of two individual objects or (b) the properties of objects involved in two individual facts. In some sense, that is what laws do--but they don't operate so simply. Rather, the first clause of the law of logic governs the regularities of general objects. The second clause governs the regularities of general facts. The third clause in the law governs the regularities of general laws. Those laws of general modes of subjects, general modes of facts and general modes of laws, in turn, govern existing individuals and the possible characteristics they might come to possess--and any changes in the laws that govern those individuals and their properties as the laws themselves evolve over time. So too, I think, when it comes to the way the representations of the laws of logic in thought might govern symbolic arguments that are subject to higher degrees of self-control as embodied in the habits of living communities of inquirers. Spelling that out would take some work. I'll stop here to see if there are questions about the general line of interpretation I'm offering of the three clauses that are parts of the general laws listed above. As before, I recognize that there may be more than one way to interpret these texts. Having said that, I'm trying to explain what I find attractive in an approach that takes symbols to have, as the first correlate of a thoroughly genuine triadic relation, internal parts that are themselves genuinely triadic in character, and so on for the parts of those parts without end. --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________ From: Jon Alan Schmidt <[email protected]> Sent: Monday, April 15, 2019 2:55:36 PM To: [email protected] Subject: Re: Re: [PEIRCE-L] Peirce Monument Jeff, List: Please provide specific quotes from "The Logic of Mathematics" (or other writings of Peirce) to support your claim that "any sign that is general in character ... have the nature of genuine triadic relations." If that were the case, then what would be the three correlates of such relations? Instead, my understanding is that the triadic relation is that of representing or (more generally) mediating. CSP: I will say that a sign is anything, of whatsoever mode of being, which mediates between an object and an interpretant; since it is both determined by the object relatively to the interpretant, and determines the interpretant in reference to the object, in such wise as to cause the interpretant to be determined by the object through the mediation of this "sign." (EP 2:410; 1907) This is reflected by the first EG in the attachment. As Peirce stated here, there are also dyadic relations between the Object and the Sign, and between the Sign and the Interpretant--namely, that of determining--but the triadic relation cannot be reduced to these. The second EG in the attachment is my initial attempt to diagram this--in accordance with the dyadic relations, "the flow of causation" is from Object to Sign to Interpretant; but although the Object also determines the Interpretant, it does so only through the mediation of the Sign. JD: You have focused on the first three clauses. What is implied in the 4th and fifth? ... For any interpretant that has a general nature, it will itself be a genuine triadic relation in its nature. I do not see anything in any of the five clauses from CP 2.242 to warrant treating either a Sign or an Interpretant as a triadic relation, rather than a correlate of such a relation. On the contrary, clause 1 states plainly that "A Representamen [such as a Sign] is the First Correlate of a triadic relation," and clause 4 states just as plainly that "the possible Interpretant is determined to be the First Correlate of the same triadic relation to the same Object" (emphases added). JD: In the process of representation, correlate A functions as a sign in relation to some real interpretant C, where that interpretant C, in turn, serves as a sign in relation to some further object D [to some] interpretant E. What does interpretant C represent to E as a sign? For one thing, it represents object B is the same object as D (or B corresponds to D in some way). My reading is instead that Interpretant C simply has B as its Object, just like Sign A; there is no need to posit "some further object D." The difference is that Interpretant C is determined by Object B through the mediation of Sign A. Likewise, Interpretant E has B as its Object, but Interpretant E is determined by Object B through the mediation of Interpretant Sign C. This is reflected by the third EG in the attachment. JD: What is more, the kind of genuine triadic relation that interpretant C embodies ... Signs are embodied in their Replicas (1903) or Instances (1906), but where did Peirce ever say that a relation can be embodied? JD: Thus far, I've argued that all legisigns, and a fortiori, all symbols have the character of being, themselves, genuine triadic relations. What is more, I've argued that all symbolic signs are, in themselves, thoroughly genuine triadic relations. You have offered these assertions, but so far I am frankly not seeing any arguments for them. Again, CP 2.242 seems quite explicit that Signs and Interpretants are correlates, not triadic relations, genuine or otherwise. 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 Mon, Apr 15, 2019 at 10:40 AM Jeffrey Brian Downard <[email protected]<mailto:[email protected]>> wrote: Hello Jon S, List, Does the sign itself constitute a triadic relationship? You say, No. It is the first correlate of a triadic relation, but it is not itself a triadic relation. Let me adopt the other side of the argument and see what points I can marshall in its favor. First, I'd like to point out that any sign that is general in character: (i.e., all legisigns, and therefore all symbols) have the nature of genuine triadic relations. Legisigns have that nature in themselves. Symbolic legisigns have that nature in themselves and in the relation that holds between sign and object. That much follows from the account of genuine triadic relations offered in a number of places, including "The Logic of Mathematics, an attempt to develop my categories from within." Furthermore, consider the following definition of a sign offered in NDTR: A Representamen is the First Correlate of a triadic relation, the Second Correlate being termed its Object, and the possible Third Correlate being termed its Interpretant, by which triadic relation the possible Interpretant is determined to be the First Correlate of the same triadic relation to the same Object, and for some possible Interpretant. A Sign is a representamen of which some interpretant is a cognition of a mind. Signs are the only representamens that have been much studied. (1903 - C.P. 2.242) Let's separate the clauses: 1. A Representamen is the First Correlate of a triadic relation, 2. the Second Correlate being termed its Object, 3. and the possible Third Correlate being termed its Interpretant, 4. by which triadic relation the possible Interpretant is determined to be the First Correlate of the same triadic relation to the same Object, 5. and for some possible Interpretant. You have focused on the first three clauses. What is implied in the 4th and fifth? For those interpretants that really are general signs in relation to some further object and interpretant, what is the character of such a sign? For the sake of the argument, let's set to the side interpretants that are, in themselves, mere possibles or mere existents. For any interpretant that has a general nature, it will itself be a genuine triadic relation in its nature. Let me ask: why is this important for the sake of offering explanations of how signs and interpretants function in the process of semiosis? As we try to answer this question, let us shift the focus of our attention from the anatomy to the physiology of signs and explain what is essential to their proper functioning. In the process of representation, correlate A functions as a sign in relation to some real interpretant C, where that interpretant C, in turn, serves as a sign in relation to some further object D interpretant E. What does interpretant C represent to E as a sign? For one thing, it represents object B is the same object as D (or B corresponds to D in some way). What is more, Peirce suggests, C represents the relation that A holds to B to interpretant E. C cannot really serve the function of representing such features about A and B to E without itself being genuinely triadic in character. What is more, the kind of genuine triadic relation that interpretant C embodies is not a genuine triadic relation of quality (i.e., what he calls a law of quality) or a genuine triadic relation of fact (i.e., a law of fact). Rather, it is what Peirce calls a thoroughly genuine triadic relation. These sorts of relations are special in that the general character of C, in serving the function of both an interpretant in relation to A and as a sign in relation the further interpretant E, is not a mere law. That is, it is not simply a rule having some sort of generality or some sort of necessity. Rather, as a representamen, C has the character of a living general--one that has life and is capable of growth. This is something that C itself possess as a sign. Thus far, I've argued that all legisigns, and a fortiori, all symbols have the character of being, themselves, genuine triadic relations. What is more, I've argued that all symbolic signs are, in themselves, thoroughly genuine triadic relations. One reason they must have this character is that it is essential for serving, in turn, the function as a symbolic sign in relation to some further object and interpretant. What should we say of signs that are, in their nature, iconic qualisigns (tones) or indexical sinsigns (tokens)? Without arguing the point, I would like to point out that they are always capable of serving as parts of larger inferences. I'll leave it at that. --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354
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