On 2/27/2019 12:32 PM, Jon Alan Schmidt wrote:
I focused on representing Propositions, rather than the process of reasoning; and then I decided accordingly to call the resulting diagrams Propositional Graphs, rather than Modified Existential Graphs.
The notation for every version of logic from Aristotle to the present has been designed to facilitate the process of reasoning.
Even so, I still might ultimately adopt your recommendation to stick with EGs
That's a good step in the right direction. Peirce devoted many years to developing a precise notation with the most general and powerful rules of inference ever invented. The best way to preserve that power and precision is to define any proposed notation by a formal mapping to and from his EGs.
You went on to assert that "Seme" cannot possibly apply to a subject, even though Peirce explicitly stated otherwise in an alternate draft of the very same paragraph. CSP: The first member of the triplet, the 'Seme,' embraces the logical Term, the Subject or Object of a sentence, everything of any kind, be it a man or a scribed character, such as h or Pb, which will serve, or is supposed to serve, for some purpose, as a substitute for its Object. It is a Sign which pretends, at least, to intend to be virtually its Object. (R 295:11-12[28-29]; 1906)
No. Before going further, note that my explanation is consistent with the three footnotes by Hartshorne and Weiss to CP 4.538. The first cites CP 2.250f for the triad Rheme, Dicisign, Argument as equivalent to the "triplet... Term, Proposition, Argument." The second says that 'Rmeme' as a synonym for 'Seme'. And the third says that 'Ddicisign' is a synonym for 'Pheme'. I copied CP 2.250-251 at the end of this note. Note that Peirce wrote that a Dicisign is "a proposition or quasi-proposition". He also wrote "A Rheme is a Sign which, for its Interpretant, is a Sign of qualitative Possibility, that is, is understood as representing such and such a kind of possible Object." This point distinguishes logical subject and logical predicate: A subject (which has an attached line of identity) is a sign of some definite object, but a predicate (with its unattached peg) is a sign of some unspecified possible object. In Latin, the word 'quasi', in hypothetical statements, means "as if"; in comparisons, 'quasi' means "as", "like as", "as it were", "almost", "a sort of". CP has 78 occurrences of 'quasi-'. Therefore, the word 'quasi-predicate', which Peirce used at least once, would be suitable for something that played a role similar to a predicate. An alternate word could be 'quasi-rheme'. But if 'Rheme' is a synonym for 'Seme', then Rheme would also include both predicates and quasi-predicates. These points are consistent with the Aristotelian-Scholastic tradition for the terms of syllogisms. Peirce was the author of the article on Syllogism in Baldwin's Dictionary, vol 2, pp. 628-639. It begins
Syllogism consists in stating in one proposition the truth involved in two non-relative propositions after the elimination of a common term as -- All a is b; All c is a; ∴ All c is b.
Note that the common term c occurs in both subject position and object position. As an object, it is just a rheme or monad -- a predicate with one peg that is not attached to a line of identity. But in subject position, it is part of the noun phrase "All c". In an EG, the word 'All' includes a line of identity, which is attached to the unattached peg in the term c. Peirce learned syllogisms in 1852 (age 13), wrote a definitive article about them 50 years later, and continued that interest all his life. For what he wrote in 1911, see http://jfsowa.com/peirce/eg1911.pdf :
But this letter will be long enough without discussing Aristotle and his Greek commentators, a subject on which I should soon tire you, interesting as it is to me. (NEM 3:167-168)
Then he continues on pp. 168-169 with a proof in EGs:
Fig. 11 shows the two premisses "Any M is P" and "Any S is M" ... giving Fig. 17 [Any S is P]
Note that every EG from Fig. 11 to Fig. 17 of eg1911.pdf has two or more terms (S, M, or P). Each subject term is attached to a line of identity that links it to a peg of an object term. This evidence shows that (1) Peirce, Hartshorne, and Weiss agree that a Seme is a Rheme; (2) a term is a monad that may occur in a logical subject or a logical predicate; and (3) as a logical subject, the monad refers to something definite; but as a logical predicate, it refers to some qualitative possibility. Finally, these points enable us to interpret R 295:11-12[28-29]: Since every term is a predicate, a Seme or a Rheme would "embrace" all logical terms, including those which occur in subject position or object position in any sentence. But I admit that the word 'or' in the following list may be puzzling: "the Subject or Object of a sentence, everything of any kind, be it a man or a scribed character, such as h or Pb, which will serve, or is supposed to serve, for some purpose, as a substitute for its Object." Therefore, start with the final sentence: A Seme "is a Sign which pretends, at least, to intend to be virtually its Object." If a Seme is a Rheme, and a Rheme is a sign of "qualitative possibility", this would imply a rather odd conclusion: A qualitative possibility pretends to be a virtual object. This conclusion is a metaphorical way of talking about possibilities such as an indefinite or virtual man, hydrogen atom (H), lead atom (Pb), or anything of any kind. It's consistent with the conclusions above, but a more precise definition would be helpful. That is probably why Peirce did not consider it suitable for the final draft. Conclusion: R 295:11-12[28-29] is consistent with the previous points: (1) a Seme is a Rheme, (2) there is a sharp distinction between logical subjects and logical predicates; and (3) the word 'term' refers to a monad, which represents a definite individual in a logical subject or an indefinite possibility in a logical predicate. John ________________________________________________________________________ CP 2.250 According to the third trichotomy, a Sign may be termed a Rheme, a Dicisign or Dicent Sign (that is, a proposition or quasi-proposition), or an Argument. A Rheme is a Sign which, for its Interpretant, is a Sign of qualitative Possibility, that is, is understood as representing such and such a kind of possible Object. Any Rheme, perhaps, will afford some information; but it is not interpreted as doing so. CP 2.251 A Dicent Sign is a Sign, which for its Interpretant, is a sign of actual existence. It cannot, therefore, be an Icon, which affords no ground for an interpretation of it as referring to actual existence. A Dicisign necessarily involves, as a part of it, a Rheme, to describe the fact which it is interpreted as indicting. But this is a peculiar kind of Rheme; and while it is essential to the Dicisign, it by no means constitutes it.
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