Jon S, List,
I, too, am interested in the way the EGs, as a mathematical tool, might help us clarify the nature of propositions and inferences and the roles that they serve in processes of inquiry. In order to apply such mathematical tools to questions in any part of a semiotic theory (conceived as a normative science), it will help to be clear about the way we are interpreting the various signs in the mathematical system. As such, a close examination of what, in our common experience, is being represented in each part of the formal system will require proper use of a phenomenological theory. Consider the converse direction of the inquiry. As Peirce tries to get clear about the syntax, conventions, precepts and other starting points that have served, up to a given point in his inquiries, as the elements for the formal systems of the EGs, he is progressively trying to formulate clearer postulates from which deductions might proceed. On the one hand, deduction from postulates within a formal system will not be improved by an appeal to a philosophical theory of phenomenology or semiotics. Mathematicians don't need assistance from philosophers in making such deductions. That is their forte. On the other hand, the task of developing and clarifying the postulates for a system that is under development or revision is a task that may very well be benefitted from proper input from philosophy--including theories of phenomenology and semiotics. Having stated these general points, let me formulate the points you are making in different terms. Instead of starting with semes, let's start with rhemes. These are signs of unsaturated predicates that typically are formed by precisive abstraction. And, instead of asking how a seme is represented in the Beta or Gamma system, let's ask how a rheme is represented in the Alpha system. In doing so, we get a much clearer sense that the rheme is represented by an area on the sheet of assertion. Each indeterminate point in that area is a possible object that belongs to the class represented by the rheme. So, if one expresses the rheme "__is red" on the sheet using the index A, then the points in the area of A on the sheet are taken to encompass all white things in the universe of discourse. It is important to keep in mind that, in the EGs, unlike the Euler graphs or system of Venn diagrams, the system is understood to be intensional in character and not extensional. What do I mean by that? The basic way in which areas in the alpha system are related is in terms of the scroll. If A, then B. All assertions, including those are categorical in terms of their surface grammar, are understood on the model of conditionals. Let's suppose that the conditional expresses: "if anything is red, then it is colored." This is a positive assertion, even though it does not represent any actual thing to exist as an individual. The upshot of my suggestion is that, when it comes to clarifying the ideas that are guiding the development of the postulates for the EGs, phenomenology can and should provide considerable guidance as we seek to clarify what each sign in the system means. As such, I recommend considering the role of phenomenological analysis of our experience of engaging in acts of self-controlled reasoning (nicely illustrated in the first Lowell Lecture) in the way Peirce is developing and refining the postulates stated, for instance, in "On the Simplest Branch of Mathematics, Dyadics," MSS 2-3, MSS 511-512, 1903. Note that the first set of postulates for the alpha system provides an account of the precepts governing the assertion of a proposition (e.g., what counts as a well-formed formula in the system). The second set of postulates provides an account of the postulates for transforming any proposition in that system in a way that ensures the validity of the inference. These are the inference rules. How are the guiding principles of deductive inference represented as rules in the alpha system? Look at the postulates. More importantly, look at how those postulates are being formed and what each means. What are the features of common experience--such as the experience of drawing a self-controlled deductive inference that is taken to be valid--that Peirce is trying to represent in each postulate? Let me try to state the upshot of what I'm suggesting again, but in simpler terms. Phenomenology can guide us in two ways when it comes to mathematical systems of logic such as we find in the EGs: 1) In the application of the mathematical tools to philosophical problems--such as those in semiotics. 2) In the development and refinement of the postulates for a system. The second task is particularly difficult. It is one that Peirce seems to excel at. Is your aim in the remarks you are making along the lines of 1 or 2? Either way, the emphasis you are placing on semes, spots and lines of identity may lead to misinterpreting the postulates in the alpha system. As a result, it may lead to a misinterpretation of the other systems built on alpha. --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________ From: Jon Alan Schmidt <[email protected]> Sent: Sunday, April 14, 2019 2:23 PM To: [email protected] Subject: Re: [PEIRCE-L] Re: Logical Analysis of Signs (was Phaneroscopy and logic) Gary F., List: On March 25, I stated the following. JAS: ... I suggest that logical analysis can never decompose a Seme into any other kinds of parts. This is what I take to be the upshot of [Gary F.'s] observation below that a Seme is only a "first" relative to a Proposition or an Argument; i.e., it is the simplest class of Signs according to the relation to the Final Interpretant. When we have carried logical analysis of any Sign to its ultimate elements in that respect, we will find that we have only Semes, continuous predicates that marry those Semes in Propositions, and leading principles that marry those Propositions in Arguments. JAS: Now, consider each of these elements from the standpoint of valency. A Seme can be a monad, but a continuous predicate is at least a dyad joining two Semes as subjects in a Proposition, and a leading principle is at least a triad joining three Propositions as premisses and conclusion in an Argument. Consistent with Peirce's classification of the sciences, logical analysis (logica utens) thus confirms that this aspect of Speculative Grammar--the first branch of the Normative Science of logic (logica docens)--fully conforms to the principles provided by Phaneroscopy. On March 27, I added the following. JAS: ... a Seme can be a monad (one-Peg Subject Spot) and a continuous predicate is at least a dyad (Line of Connection); but does it reveal anything about the valency of a leading principle? In EGs, the latter corresponds to a transformation rule, which brings to mind part of what Gary F. quoted in the "Phaneroscopy and logic" thread earlier today. CSP: Suppose then a Triad to be in the Phaneron. It connects three objects, A, B, C, however indefinite A, B, and C may be. There must, then, be one of the three, at least, say C, which establishes a relation between the other two, A and B. (EP 2:364; 1905) JAS: Can we say that A is the initial Graph, B is the subsequent Graph, and C is the convention that permits the change from A to B? If so, does this confirm that a leading principle is at least a triad? I recently came across this manuscript passage, which seem to confirm that logical leading principles and the corresponding transformation rules for EGs are indeed triadic. CSP: ... Reasoning, to which appeal is usually made in an endeavor for self-control, is manifestly a triadic phenomenon, as I shall show you. Meanwhile let it suffice to note that a syllogism is a relation between two premisses and a conclusion. The simplest form of syllogism is the modus ponens by which from a consequence and its antecedent we infer its consequent. It can do no harm to show how such an inference is performed by Existential Graphs ... Thus the inference is analyzed into three distinct steps, of which the first is plainly triadic, requiring two distinct conditions, namely that a graph-instance should be in an area, and that a second instance of the same graph should be outside that area not enclosed in any cut not enclosing the other, whereupon we are permitted to erase an oddly enclosed graph-instance. The modus tollens, by which from a consequence and the falsity of its consequent we infer the falsity of its antecedent appears in Existential Graphs as involving precisely the same triadic step and otherwise as being even simpler than the modus ponens. (R 650:35-37[34-36]; 1910 July 28) In accordance with principles provided by Mathematics and Phaneroscopy, Semeiotic--specifically, Speculative Grammar--recognizes the indecomposable elements of all Signs as Semes, continuous predicates, and leading principles. Continuous predicates are the only mode of connection between Semes, marrying them into Propositions; and leading principles are the only mode of connection between Propositions, marrying them into Arguments. From these postulates, as I outlined on March 29, Peirce's theorem of the science of semeiotics follows--"if any signs are connected, no matter how, the resulting system constitutes one sign" (R 1476:36[5-1/2]; 1904). Since the entire Universe is a system of connected Signs (CP 5.448n1p5, EP 2:394; 1906)--facts as true Propositions (EP 2:304; 1904) married by the logic of events as leading principles (CP 6.218; 1898)--it constitutes one Sign, "a perfect sign" (EP 2:545n25; 1906); specifically, an Argument and therefore a Symbol, but involving "Indices of Reactions" and "Icons of Qualities" (CP 5.119, EP 2:193-194; 1903). Like all Symbols, it is indeterminate to some degree (EP 2:322; 1904); but like all Signs, it is determined by an Object other than itself (CP 8.177, EP 2:492; 1909), constantly being made more determinate--the ongoing aspect of Creation (CP 1.615, EP 2:255; 1903). This is reflected in EGs by how they represent the continuous relations of (ter)identity and (ter)coexistence. Any individual subject (Line of Identity) that exists in any logical Universe (Sheet of Assertion) is capable of further determination by attaching more predicates (Spots), and any logical Universe is itself capable of further determination by attaching more individual subjects and their predicates. CSP: The mode of being of the composition of thought, which is always of the nature of the attribution of a predicate to a subject, is the living intelligence which is the creator of all intelligible reality, as well as of the knowledge of such reality. It is the entelechy, or perfection of being. (CP 6.341; 1908) 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 Sun, Apr 14, 2019 at 6:25 AM <[email protected]<mailto:[email protected]>> wrote: Jon, thanks for this — it not only answers my question, but also clarifies (for me anyway) the usefulness of Existential Graphs for directing attention to features of experience. I’ll probably never study this semiotic system in as much detail as you are doing, but maybe I’m starting to get Peirce’s pragmaticistic point about what can (and can’t) be done with language as a means of exploring meaning spaces (as I called them in my book). One thing I can’t do with language is explain why such exploration is worthwhile … it’s like trying to explain why evolution is worthwhile. Message ends. Gary f. From: Jon Alan Schmidt <[email protected]<mailto:[email protected]>> Sent: 13-Apr-19 21:11 To: [email protected]<mailto:[email protected]> Subject: Re: [PEIRCE-L] Re: Logical Analysis of Signs (was Phaneroscopy and logic) Gary F., List: I agree that the color assignments are arbitrary, as evidenced by Peirce's own inconsistency, and thus strictly conventional rather than iconic. As he himself recognized, that shortcoming pertains to tinctured surfaces just as much as colored Spots and/or Lines. The main utility that I see for the latter comes when we analyze a discrete predicate into a hypostatically abstracted subject and a continuous predicate. The color reflects the Universe to which the Dynamic Object denoted by the Spot belongs, as well as the corresponding continuous predicate that the Line attached to it signifies. However, I am starting to question this approach myself, in part because of another passage that I recently encountered, which also addresses your last point below. CSP: We remark among Existential Graphs two that are continuous; that is, they may be regarded as consisting of parts; but all parts of them are perfectly homogeneous with the whole. Continuity is not an Existential character; it only belongs to the Object of the nature of Laws. Consequently, the Continuous Graphs do not express Existential Predicates but only Logical Predicates. The two continuous Graphs are the Blank, which expresses Coëxistence and the Line of Identity, which expresses Numerical (i.e. individual) “Sameness.” The peculiarities of these two Graphs are partly Essential, and belong to the Phaneron, and are partly Accidental. This connection through the blank depends on the Creative power of the mind by which it makes entia rationis. The triad of combination is associative. All this should be said at this point. And point out that it supposes a triad. That ordinary Graphs are connected with the Blank is a totally different manner from their connection with one another is to be regarded as an accident of the particular mode of diagrammatization employed. In employing Graphs to study the properties of the Phaneron, two different ways of conceiving the relations of ordinary Graphs to the Blank, or Graph of Coëxistence, present themselves. One is to consider the latter Graph as a Graph of Inexhaustible, because Infinite, Valency; the other is that every Graph should be conceived as having an additional Peg by which it is joined to the Blank, or Graph of Coëxistence or Cobeing. And now the part of the Blank to which any Graph is joined should be regarded as a triad, so that the valency is not diminished by the junction. I mean that if p represents a Peg of the general Graph of Coëxistence, and the Graph g is joined to that Graph, it should be conceived as joined to a special portion of the Blank which is triadic, so that the junction still leaves a Peg free. For the representation of identity, on the other hand, the mode of diagrammatization of the System is entirely satisfactory, the special Graph of Teridentity being introduced when it is needed. (R 499s; 1906) I take "Existential Predicates" to be what I have been calling "discrete predicates," and "Logical Predicates" to be what Peirce elsewhere called "continuous predicates." This then seems to warrant my claim that the continuous relations of coexistence and identity can also be characterized as continuous predicates. The noteworthy difference between these and other continuous predicates, besides their being symmetrical (cf. R 284:88[83]; 1905), is that although they are generally treated as dyadic, they are really degenerate forms of triadic relations--tercoexistence and teridentity--in the sense that there is always room for another attachment. CSP: It follows in the first place that every line of identity ought to be considered as bristling with microscopic points of teridentity ... In the second place it follows that using “coexistence” in such a sense that it is mere otherness, then since if anything is not coexistent with itself the same is equally true of anything else ... it follows that a very appropriate symbol for ter-coexistence ... is simply any blank point of the sheet ... (SS 199; 1906 March 9) This explains what I noted in my post yesterday--the continuity of (ter)coexistence and (ter)identity is expressed with an infinite series of indefinite intermediate subjects, while that of "possessing a character" or "standing in a relation" is not. The former have "Inexhaustible, because Infinite, Valency"; while the latter have finite valency, but are still indecomposable once everything requiring Collateral Experience/Observation has been thrown into the subject. Put another way, we can add any number of Graphs to the Sheet of Assertion, and any number of branches to a Line of Identity at Spots of Teridentity; but a Line for "possessing the character of" (or "belongs to the class/collection of") could only be attached to exactly two Spots. Moreover, another convention would be needed for which Spot belongs at each end of the latter, since the signified relation is asymmetric. Perhaps I should adopt one of Peirce's proposed solutions after all--use red for a Concretive Spot ("Solomon"), blue for an Abstractive Spot ("wisdom"), and purple for the Line between them ("possesses"); or simply revert to traditional black Lines of Identity and use a two-Peg Predicate Spot for "possesses" (the character of) attached to a red Concretive Spot on the left Peg and a blue Abstractive Spot on the right Peg. The latter is consistent with using a Predicate Spot for "stands" (in the relation of) that has three or more Pegs, but would be very cumbersome for any sentence with multiple adjectives. Maybe I will just go back to one of my earlier ideas--color only each Subject Spot (if anything), and consider its single Peg to represent the corresponding continuous predicate. 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, Apr 13, 2019 at 6:42 AM <[email protected]<mailto:[email protected]>> wrote: … I don’t see “continuous predicate” and “continuous relation” as interchangeable, and I don’t see the line of identity (or coexistence) as a predicate, because I don’t see it as signifying anything. Do you? And if so, what advantage do you see in looking at it this way? Gary f.
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