Gary F., Ben, Franklin, List, Off the top of my head, I would think that there is a straightforward way of interpreting the passage: “every proposition and every argument can be regarded as a term”. What is, at one stage of inquiry, a fully formed and isolated proposition (i.e., medadic in form), can be, a later stage, a term-like part of a larger proposition. It will function as a rheme when the medadic proposition gains a new bonding site and is then connected to other things in a larger proposition or argument. The same is true for an argument. Whole arguments can be embedded as parts in a larger proposition and thereby function as rhemes in relation to the other parts of a proposition. Doesn't this take place, for instance, when a number of perceptual judgments are colligated into a single premiss in a larger argument? Each perceptual judgement is initially expressive of a proposition. Later, when they are colligated into a single premiss, each perceptual judgment is really functioning as a rheme in a larger proposition--which is really a premiss in a larger argument.
Or, let's put the point more precisely in the terms of the mature sign theory. Every triadic relation that is formed between qualisign, immediate object and immediate interpretant is, as a triad, something that can (as a token) function as an indexical sinsign in relation to a dynamical object and dynamical interpretant. Together, these two connected and nested triads compose a perceptual judgment. In turn, a number of these perceptual judgments can be colligated together to form the content of the symbolic legisign that is brought into relation to the dynamical object and final interpretant in an argument. Putting things in such terms doesn't always help to make the points much clearer. As such, I've attached a couple of diagrams that I'm using to think about the relations between the signs, objects and interpretants in the classification of the 66 different kinds of signs and sign relations. My suggestion is that the triad on the left is joined to the triad in the middle by serving as the sign term, and the same holds true for the relation between the triad in the middle and the triad on the right. I've tried to picture this in the second diagram using colored and dashed circles to show that the triad one the left is serving as the sign in the triad to its right. The process I've sketched by nesting the dashed circles is an overly simplified version of the more complex relations that must obtain when we consider all the different types of signs and sign relations that are needed for the process of interpretation to be possible. This way of diagramming sign relations is different from the way these relations have been represented by other interpreters of the texts (e.g., Nadin, Merkle, Johansen and Lizka). As far as I can see, this set of diagrams more faithfully represents the kinds of relations Peirce is describing in "The Logic of Mathematics, an attempt to develop my categories from within," the essays on the nomenclature and division of dyadic and triad relations, the discussion of dichotomic and trichotomic relations in "The Simplest Mathematics," The Logic of Relations (CP 3.456), The Reader is Introduced to Relatives in The Critic of Arguments (CP 3.415), etc. --Jeff Jeff Downard Associate Professor Department of Philosophy NAU (o) 523-8354 ________________________________________ From: [email protected] [[email protected]] Sent: Tuesday, November 10, 2015 8:10 AM To: [email protected] Subject: RE: [PEIRCE-L] Vol. 2 of Collected Papers, on Induction Ben, Franklin et al., If this is what Peirce had in mind when he wrote (10 years earlier) that “every proposition and every argument can be regarded as a term”, then he was saying that a proposition can be regarded as a term if you erase from it the very components that make it a proposition. And the same for reducing an argument to a proposition. Possible, I guess, but it seems oddly uninformative to me. } We may come, touch and go, from atoms and ifs but we're presurely destined to be odd's without ends. [Finnegans Wake 455] { http://gnusystems.ca/wp/ }{ Turning Signs gateway From: Benjamin Udell [mailto:[email protected]] Sent: 8-Nov-15 14:14 To: [email protected] Subject: Re: [PEIRCE-L] Vol. 2 of Collected Papers, on Induction Gary F., Franklin, Gary, you wrote, I’m not sure what Peirce meant by saying in 1893 that every proposition and every argument can be regarded as a term, or what advantage a logician would gain by regarding them that way. [End quote] In "Kaina Stoicheia" III. 4. (EP 2:308), 1904, http://www.iupui.edu/~arisbe/menu/library/bycsp/stoicheia/stoicheia.htm Peirce says: [....] If we erase from an argument every monstration of its special purpose, it becomes a proposition; usually a copulate proposition, composed of several members whose mode of conjunction is of the kind expressed by "and," which the grammarians call a "copulative conjunction." If from a propositional symbol we erase one or more of the parts which separately denote its objects, the remainder is what is called a rhema; but I shall take the liberty of calling it a term. Thus, from the proposition "Every man is mortal," we erase "Every man," which is shown to be denotative of an object by the circumstance that if it be replaced by an indexical symbol, such as "That" or "Socrates," the symbol is reconverted into a proposition, we get the rhema or term "_____ is mortal." [....] [End quote] Somewhere Peirce also notes that a proposition is a medadic term. Best, Ben On 11/8/2015 1:48 PM, [email protected]<mailto:[email protected]> wrote: Franklin, I’m not sure what Peirce meant by saying in 1893 that every proposition and every argument can be regarded as a term, or what advantage a logician would gain by regarding them that way. But to me it sounds like a precursor of his (much later) observation that one can analyze a proposition by “throwing everything” into the predicate or by throwing everything into the subject. Maybe his comment in the Regenerated Logic also works in both directions. In the Kaina Stoicheia passage, when Peirce says that the “totality of the predicates of a sign” is “called its logical depth,” and that the “totality of the subjects … of a sign is called the logical breadth,” the sign he is referring to has to be a proposition, because only propositions include subjects and predicates. Each subject and each predicate can be called a “term,” but it’s the breadth and depth of the whole sign, the proposition, that Peirce is defining here, not the breadth or depth of the terms (which is what he defined in ULCE). And, as you say, propositions and arguments also have information (which for Peirce is the logical product of breadth and depth). Gary f.
66-fold classification of sign relations with labels.pdf
Description: 66-fold classification of sign relations with labels.pdf
Nested sign relations.pdf
Description: Nested sign relations.pdf
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