List, All: Peirce's system of Existential Graphs (EG) has two main parts, Alpha for propositional logic and Beta for first-order predicate logic. He explores a Gamma part for aspects of modal logic, but later assigns that name instead to Beta with shading rather than cuts for distinguishing a universe of possibility from the universe of actuality (CP 4.576-581, 1906). This means that he must "add a *Delta* part in order to deal with modals" (RL 376, R 500:3, 1911 Dec 6), but he apparently never takes any further steps in that direction.
The sheet represents existence in EG and the entire continuum of reality in my proposed system of Synechistic Graphs (SG). Alpha graphs, typically scribed as single capital letters, therefore signify states of things that are individual in EG and general in SG. On the other hand, the constituent parts of Beta graphs in *both* EG and SG stand for that which is general, at least to some degree, in accordance with one of Peirce's early logical insights. CSP: The absolute individual can not only not be realized in sense or thought, but cannot exist, properly speaking. ... All, therefore, that we perceive or think, or that exists, is general. ... That which exists is the object of a true conception. This conception may be made more determinate than any assignable conception; and therefore it is never so determinate that it is capable of no further determination. (CP 3.93n, 1870) This applies even to proper names like "the second Philip of Macedon" (CP 3.93). Surprisingly, Peirce nevertheless claims decades later to be having trouble figuring out how to include general objects in EG. CSP: The operation of hypostatic abstraction consists in substituting for any predication that of possessing a quality, or that of standing in a relation. ... The hypostatically abstract quality or relation is necessarily general, that is, is not subject to the principle of excluded middle. The universe of characters is thereby quite outside the universe of existents. ... A hypostatical abstract is an object whose being consists in the possibility of a predicate and which stands in a peculiar relation, that of being possessed by, to whatever there may be of what that predicate is true. I have not yet discovered a suitable mode of representing such objects in existential graphs. (RS 145(s):23&26-27, LF 1:513-514, 1905) On the contrary, it seems clear to me that in Beta graph-instances, the written names *symbolically* represent general concepts and thus "afford the means of thinking about thoughts in ways in which we could not otherwise think of them. They enable us, for example, to create Abstractions" (CP 4.531, 1906). Evidently Peirce did not interpret EG that way, at least not before recognizing the role of "continuous relations" (R 611:8-10[13-15], 1908 Oct 28) or "pure predicates" (NEM 3:885-886, 1908 Dec 5) or "continuous predicates" (SS 70-72, 1908 Dec 14), which are signified by the syntax alone. They correspond to each attachment of a name to a heavily drawn line of identity, which denotes an object in the universe of discourse. CSP: What I mean is that the sign "A is red" can be decomposed so as to separate "is red" into a Copulative and a Descriptive, thus: "A possesses the character of redness." But if we attempt to analyze "possesses the character" in like manner, we get "A possesses the character of the possession of the character of Redness"; and so on *ad infinitum*. (CP 8.352, EP 2:485, 1908 Dec 25) In this approach, every name or line is a different *subject* of the proposition, "that with which some collateral acquaintance is requisite to the interpretation" (SS 70). For example, although the sentence "Cain kills Abel" consists of only three words, it is diagrammed as having five logical subjects--the names "Cain," "killing," and "Abel" for three concepts, plus the lines between them for two indefinite objects such that the complete translation is "something possessing the character of Cain stands in the relation of killing to something possessing the character of Abel." Peirce calls this "the proper way in logic" (NEM 3:885) because "when we have carried analysis so far as to leave only a continuous predicate, we have carried it to its ultimate elements" (SS 72). In any case, that is how I interpret Beta graphs in SG. In accordance with Peirce's contemporaneous taxonomy of sign classes, the names are descriptive abstractives, the lines are designative concretives, and the "continuants" relating them to each other--including the sheet itself for conjunction, along with any scrolls for disjunction and implication--are copulative collectives (CP 8.349-375, EP 2:484-490, 1908 Dec 25). Moreover, although each line *indexically* denotes an object, it also *iconically* signifies that it is general--not just continuous, but also capable of further determination since there is always room to add another branch for attaching another name. Peirce himself recognizes this aspect. CSP: Since no perfectly determinate proposition is possible, there is one more reform that needs to be made in the system of existential graphs. Namely, the line of identity must be totally abolished, or rather must be understood quite differently. We must hereafter understand it to be *potentially* the graph of *teridentity* by which means there always will virtually be at least one loose end in every graph. In fact, it will not be truly a graph of *teridentity* but a graph of indefinitely multiple identity. (CP 4.583, 1906) The upshot is that SG, like EG from which it is adapted, "enables us to carry the logical analysis of terms, propositions, and arguments to the furthest point possible in the nature of things" (R 296:7-8, 1908). What remains to be discussed is the *meaning* of a general concept as represented by a name, which is what Peirce's pragmatism--i.e., pragmaticism--purports to establish. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
_ _ _ _ _ _ _ _ _ _ ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to [email protected] with no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
