Jeff,
Interesting little anthology you've put together here, and it certainly shows Peirce referring to parts of signs (also parts of objects and of interpretants), and parts of an illative transformation. However I don't see a clear case here of Peirce referring to a part of a relation. The closest he comes is the one you put last, where he speaks of a part of a "spike" of a relation, which is still not a part of a relation. Generalizing from this sample, then, I think we can say that Peirce speaks often enough of parts of a sign, but does not speak of parts of a relation. If that's the case, I think it gives another reason why we should not say that a sign is a (triadic) relation, but that a sign relation is triadic - and its correlates should not be regarded as parts. Gary f. From: Jeffrey Brian Downard [mailto:jeffrey.down...@nau.edu] Sent: 22-Dec-17 13:33 To: jerry_lr_chand...@icloud.com; Helmut Raulien <h.raul...@gmx.de> Cc: Peirce List <peirce-l@list.iupui.edu>; John F Sowa <s...@bestweb.net> Subject: Re: Re: [PEIRCE-L] Lowell Lecture 3.6 Hello Gary F, John S, Helmut, Kirsti, List, I take John to be asking a good question about whether or how the part/whole distinction might or might not apply to the account of relations and relationships as it is applied in the normative science of semiotics. Given the context of our discussion, we can ask similar questions about how the distinction should be applied in the formal logic of the EG. In asking "what practical difference would it make," I take John to be asking the very same kind of thing that Peirce asked in his account of relations and relationships when he moves from the first (i.e., familiarity) and second (logical) grades of clarity, to a third pragmatic grade of clarity (see The Logic of Relatives starting at CP 3.456 and also 6.318 below). Starting with the texts, I see that Peirce applies the distinction in a number of places to the account of relations and relationships. Here are several relevant passages (note: words both underlined and in bold are my emphasis): 1. CP 2.316. Let us now proceed to compare the conclusions from the abstract definition of a Dicisign with the facts about propositions. The first conclusion is that every proposition contains a Subject and a Predicate, the former representing (or being) an Index of the Primary Object, or Correlate of the relation represented, the latter representing (or being) an Icon of the Dicisign in some respect. Before inquiring whether every proposition has such parts, let us see whether the descriptions given of them are accurate, when there are such parts. The proposition "Cain kills Abel" has two subjects "Cain" and "Abel" and relates as much to the real Objects of one of these as to that of the other. But it may be regarded as primarily relating to the Dyad composed of Cain, as first, and of Abel, as second member. This Pair is a single individual object having this relation to Cain and to Abel, that its existence consists in the existence of Cain and in the existence of Abel and in nothing more. The Pair, though its existence thus depends on Cain's existence and on Abel's, is, nevertheless, just as truly existent as they severally are. The Dyad is not precisely the Pair. The Dyad is a mental Diagram consisting of two images of two objects, one existentially connected with one member of the pair, the other with the other; the one having attached to it, as representing it, a Symbol whose meaning is "First," and the other a Symbol whose meaning is "Second." Thus, this diagram, the Dyad, represents Indices of Cain and Abel, respectively; and thus the subject conforms to our conclusion. 2. CP 4.173 A part of a collection called its whole is a collection such that whatever is u of the part is u of the whole, but something that is u of the whole is not u of the part. (174) It is convenient to use this locution; namely, instead of saying A is in the relation, r, to B, we may say A is an r to B, or of B; or, if we wish to reverse the order of mentioning A and B, we may say B is r'd by A. If a relation, r , is such that nothing is r to two different things, and nothing is r'd by two different things, so that some things in the universe are perhaps r to nothing while all the rest are r, each to its own distinct correlate, and there are some things perhaps to which nothing is r, but all the rest have each a single thing that is r to it, then I call r a one-to-one relation. If there be a one-to-one relation, r, such that every unit of one collection is r to a unit of a second collection, while every unit of the second collection is r'd by a unit of the first collection, those two collections are commonly said to be in a one-to-one correspondence with one another. . . . 3. CP 2.311 This latter Object may be distinguished as the Primary Object, the other being termed the Secondary Object. The Dicisign in so far as it is the relate of the existential relation which is the Secondary Object of the Dicisign, can evidently not be the entire Dicisign. It is at once a part of the Object and a part of the Interpretant of the Dicisign. Since the Dicisign is represented in its Interpretant to be an Index of a complexus as such, it must be represented in that same Interpretant to be composed of two parts, corresponding respectively to its Object and to itself [the Dicisign]. That is to say, in order to understand the Dicisign, it must be regarded as composed of two such parts whether it be in itself so composed or not. It is difficult to see how this can be, unless it really have two such parts; but perhaps this may be possible. Let us consider these two represented parts separately. The part which is represented to represent the Primary Object, since the Dicisign is represented to be an Index of its Object, must be represented as an Index, or some representamen of an Index, of the Primary Object. The part which is represented to represent a part of the Dicisign is represented as at once part of the Interpretant and part of the Object. 4. CP 4.564 In the first place, the most perfectly analytical system of representing propositions must enable us to separate illative transformations into indecomposable parts. Hence, an illative transformation from any proposition, A, to any other, B, must in such a system consist in first transforming A into AB, followed by the transformation of AB into B. For an omission and an insertion appear to be indecomposable transformations and the only indecomposable transformations. That is, if A can be transformed by insertion into AB, and AB by omission in B, the transformation of A into B can be decomposed into an insertion and an omission. 5. CP 3.493 For the purpose of this algebra, I entirely discard the idea that every compound relative consists of an antecedent and a consequent part. I consider the circle round the antecedent as a mere sign of negation, for which in the algebra I substitute an obelus over that antecedent. The line between antecedent and consequent, I treat as a sign of an "operation" by itself. It signifies that anything whatever being taken as correlate of the first written member -- antecedent or consequent -- and as first relate of the second written member, either the one or the other is to be accepted. 6. CP 6.318. I have, since 1870, written much about the logic of relations. In those writings, I have usually restricted the terms "relations" and "relationships" to existential relations and relationships. By a relationship I understand the conception of a fact about a set of things abstracted from the representation of the things themselves or, in other words, a predicate which requires more than one subject to complete a proposition, or conception of a fact. A "relation" only differs from a "relationship" in that one of the subjects is regarded as being taken account of first, and is usually called the subject nominative, while the others are called the direct and indirect objects. In other words a relation is a predicate requiring one subject nominative and one or more objects in a definite sequence. In my earlier papers [in Volume 3] I use the conception of relation chiefly; in my later ones that of relationship. The difference is little more than trifling. An existential relation or relationship is distinguished from others by two marks. In the first place, its different subjects all belong to one universe; which distinguishes it very strikingly from such relations as that which subsists between a thing and its qualities, and that which subsists between portions of matter and the form into which they are built; as for example between the cells of a living body and the whole body, and often times between the different singulars of a plural and the plural itself. In the second place, an existential relation or relationship differs from some other relations and relationships in a respect which may be described in two ways, according as we employ collective or distributive forms of expression and thought. Speaking collectively, the one logical universe, to which all the correlates of an existential relationship belong, is ultimately composed of units, or subjects, none of which is in any sense separable into parts that are members of the same universe. For example, no relation between different lapses of time -- say, between the age of Agamemnon and that of Homer -- can be an existential relation, if we conceive every lapse of time to be made up of lapses of time, so that there are no indivisible units of time. 7. CP 3.576. By a seed (granum) of an existential relation is to be understood an existing individual which not only stands in that relation to some correlate, but to which also some relate stands in that relation. By a spike of a relation is to be understood any collection of seeds of it of which it is both true that every one of them stands in that relation to some one of them; and it is also true that to every one seed of the spike some seed of the spike stands in that same relation. Thus, two spikes of the same relation may have common seeds, or one may even be a part of another. A simple spike is a spike not containing any other spike as a part of it. Looking at these seven passages, it seems clear to me that Peirce is applying the distinction between part and whole to the relations and relationships that are found in the science of semiotics and in the formal logic of the EG. What is more, he applies the distinction in his both his logical (i.e., 2nd level of clarity) and in his pragmatic (i.e., 3rd level) definitions and explanations of how the correlates are related to one another in both degenerate and genuinely dyadic and triadic relations. Having said that, he is being remarkable careful about when and how the distinctions should be applied. It is possible that Peirce is mistaken in applying the distinction between part and whole the way he does to semiotic relations and relationships but, for my part, I don't see anything that stands out as a clear error on his part. As such, my aim is to follow his lead in the proper use of these terms--at least when I'm trying to interpret his texts. Yours, Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354
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