Jeff, Gary F, Ben, I like Jeff's suggestion very much. It seems to me a a more developed interpretation of the point that Ben had suggested, taking it in the other direction--instead of showing how propositions and arguments can be turned into terms through erasure, we assume instead that propositions and arguments already admit of at least one more blank left to be determined, and they would be like rhemes in this respect.
I don't really have time at the moment to get into the deeper analysis shown in the attachments. I'll say something later if I find the time to dig into it. -- Franklin On Tue, Nov 10, 2015 at 11:48 AM, Jeffrey Brian Downard < [email protected]> wrote: > 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 > ________________________________________ > > >
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