John, list, I think everything you’ve said about EGs here, and how they might represent continuous predicates, is exactly right. What you’ve said about Jon’s MEGs, though, is true only if we read the lines in those diagrams as Lines of Identity; and the main modification Jon made was to read the lines NOT as Lines of Identity but as Lines of Relation. It’s not clear to me how sequences of MEGs could be used to analyze the thought process into the smallest possible steps, which was the purpose for which Peirce invented EGs and made his own modifications to them. The analysis of propositions is only one aspect of EGs as “moving pictures of thought,” and the rules for permissible transformations of graphs are the keys for analyzing the process of thought. I’m doubtful that Jon’s MEGs can improve on Peirce’s EGs in that respect; but then this thread hasn’t done much to explain how EGs fulfill that purpose either.
I started an “EGs and Phaneroscopy” thread because I wanted to explore how EGs might be used to iconize the phenomenological categories (in addition to their main use, which is logical analysis of the thought process). I thought I saw a few clues in Peirce’s writings from 1906, but haven’t come up with an explanation of how they can be used for the analysis of experience into its elements. Nor have I seen anyone else come up with such an explanation. This is not surprising, since (as Atkins shows in his book) Peirce first arrived at his three categories by means of logical analysis, and only began to apply them more broadly in the 1880s, and did not see the need for a separate science of phenomenology until 1902 — and even then he remained primarily a logician, and his phenomenology consisted mostly of applying this three categories heuristically to the analysis of experience/phenomena, working on the hypothesis that the structure of experience itself must be analogous to the mathematical structures revealed by his analysis of the logic of relations. Since I share with Gary R a deep interest in phenomenology/phaneroscopy — and especially the observational part (as opposed to the analytical part) of it — I’ll have to take that to another thread, if I come up with anything to say about it. Propositions appear, they are certainly phenomena, and I suppose they are the essential format of what we call facts (as Peirce said), but there must be more to phaneroscopy than the analysis of propositions; so I’ll leave that to you folks who have contributed to this thread. Gary f. -----Original Message----- From: John F Sowa <[email protected]> Sent: 19-Feb-19 23:34 Edwina, Gary R, and Jon AS, Finally, this thread has reached the dénoument, when the pieces fall into place and the mysterious knots are untied. Every so-called Modified EG (MEG) is false. The file brutus.png shows how to replace MEGs with ordinary EGs that satisfy all of Peirce's criteria. That method, when explained in Peirce's exact words, resolves the outstanding issues about what is proper or ultimate in various contexts. But first, I'll comment on notes by Edwina and Gary R. ET > I see Peirce's work as evolving so that... I don't see Peirce > abandoning much at all. And when he finds himself as having clearly > been in error, he tends to explicitly state that along with his > corrected view... Peirce is constantly experimenting; but, in my > opinion, one needn't take an experiment late in his life as > necessarily "abandoning" those undertaken earlier. I strongly agree. For logic, Peirce began with the 19th c. version of Aristotelian-Scholastic logic when he was 13 and Boolean logic a few years later. During the next 60+ years, major breakthroughs occurred in 1870, 1885, and 1897. After each one, he went through variations and interpretations. But unless he explicitly corrected some error, he didn't reject the earlier versions. The rock-solid stability of classical first-order logic from 1885 makes it the Rosetta Stone for relating Peirce's writings about logic and semeiotic at every period of his life. It's also essential for relating his writings to every version of logic from Aristotle to the present. Peirce explained EGs in several different ways, but the first-order core, the rules of inference, and the translations from one version to another never changed. GR > it seems to me that one remains squarely in the realm of logic as > semeiotic when one is working with EGs because, as now repeatedly > noted: "All that existential graphs can represent is propositions, on > a single sheet, and arguments on a succession of sheets, presented in > temporal succession." CSP I agree. But logic as semeiotic is the foundation. Without it, you get word hash with no criteria for evaluation or correction. GR quoting CSP >> CSP: The system of Existential Graphs (at least, so far as it is at >> present developed) does not represent every kind of Sign. For >> example, a piece of concerted music is a sign; for it is a medium for >> the conveyance of Form. But I know not how to make a graph equivalent >> to it. In CP 2.643, Peirce wrote "the various sounds made by the instruments of an orchestra strike upon the ear, and the result is a peculiar musical emotion, quite distinct from the sounds themselves." As I showed with the graph of a musical score, it's easy to map the notes from a score to any notation for FOL. But the emotions produced by Jascha Heifetz and the kid next door are very different. The musical score can't explain the emotion, but it can be useful as a map for analyzing the performance. Perhaps the note at bar 17, as the kid played it, was grating, and the transition to the next note was abrupt, off tempo, and slightly flat. Yet a professional violinist, in some context, might deliberately play a note that way. Context and purpose are critical for interpreting anything. Music illustrates the distinction between the discrete subjects and predicates in the logic, and the continuous sound, which you or your cat may perceive as streams of quasi-subjects and quasi-predicates. (A cat that likes music: <http://minervaclassics.com/harpcat1.jpg> http://minervaclassics.com/harpcat1.jpg ) JAS > In Peirce's "proper" or "ultimate" analysis of Propositions, "pure" > predicates are the only predicates. Anything that refers to content > in the universe of discourse--i.e., anything that can only be > understood by an interpreting Quasi-mind that has had previous > Collateral Experience with it--is a Subject; it belongs to the Object > of the Proposition. No. That claim is false for many reasons. First of all, The words 'proper' and 'ultimate' are both relative terms that depend on context. And the contexts for those two words have nothing in common. CP has 124 occurrences of 'proper'. Some of them narrow the meaning of a word, such as 'proper name' or 'history proper'. The others occur with words like 'for' or 'with' that refer to some context. For example, consider the chair you're sitting on. Sitting is its *proper* use. But you could also use it for many other purposes. You might stand on it to change a light bulb, or you might use it to hold some books you're putting on a shelf. The "ultimate" analysis of the chair depends on whether you're talking with a carpenter, a chemist, or a nuclear physicist. The first two might give you useful advice for some purposes, but not for sitting. If the physicist starts talking about quarks and leptons, that might be ultimate, but it's not proper for any use of a chair. As for the quotation, "when we have carried analysis so far as to leave only a continuous predicate, we have carried it to its ultimate elements" -- that kind of "ultimate" is rarely proper for any useful application. To illustrate that point, let's turn to the MEGs. Each one has a teridentity or a ligature of multiple teridentities, which falsely state that some wildly different things are identical. For example, the MEG for "Brutus kills Caesar" has a teridentity, which states that there is a single entity in the universe of discourse, which happens to be identical to Brutus, Caesar, and the act of killing. That proposition is false. The attached brutus.png shows how to generate correct EGs by following Peirce's directions. At the top is the simplest way to translate "Brutus kills Caesar" to the EG, Brutus———Kills———Caesar . This EG has a dyad -kills- with two unattached pegs, and two logical subjects, each with its own line of identity: Brutus——— and Caesar——— . The second EG in brutus.jpg has one more logical subject, which is the gerund 'killing' (a nominalization) with a line of identity that is also attached to a triad named Rel. I'm using the name Rel for the pure predicate that Peirce defined in NEM 3:886, 3rd line from the top. As Peirce said, Rel is a pure predicate. With Rel, the second EG states "Brutus stands in the relation 'killing' to Caesar." All four EGs state the same proposition. But the roles of Brutus and Caesar in the first and second are shown only by their position on the left or the right. To show the roles explicitly, linguists often use "case relations" or "thematic roles", such as Agent and Patient in EG #3. In that EG, the monad Killing- is attached to a teridentity, which is attached to two dyads, -Agent- and -Patient-. Those dyads are linguistically primitive, but they are not logically "pure". To "purify" the EG, they can be converted to the monads Agency- and Patiency- by nominalization (hypostatic abstraction). Then those monads would be connected to the pure predicate Rel in the fourth EG at the bottom of brutus.png. In summary, all four EGs in brutus.png state exactly the same proposition as the English "Brutus kills Caesar." the first EG has two logical subjects, and one impure predicate (which represents content in the UoD). The second has three logical subjects and one pure predicate named Rel. The third has three logical subjects and two predicates that express linguistic content: -Agent- and -Patient-. The fourth has five logical subjects and two pure predicates. Re ultimate analyses: The second and fourth EGs are ultimate in the logical sense of having only pure predicates. The third is ultimate in the linguistic sense of showing the case roles. The fourth is ultimate in both the logical sense and the linguistic sense. Re proper analyses: That depends entirely on context. Note the word 'proper' in NEM 3:885: "the proper way in logic is to take as the subject whatever there is if which sufficient knowledge cannot be conveyed in the proposition itself, but collateral experience on the part of its interpreter is requisite." That quotation mentions the experience of the interpreter. That would be content in the Universe of Discourse, which is never expressed in pure predicates. And the purpose of that conversion is relevant only in the context of communication with some interpreter. Conclusions: 1. Although all four analyses state the same proposition, they would be "proper" for different purposes. The first EG is probably the most useful for ordinary communication and reasoning. The second EG would be useful when it's necessary to refer to the act of killing: "Some senators thought that the killing was justified." But the third and fourth would be "proper" only for a theoretical study in logic or linguistics. 2. All the examples in this note and in my previous note show the clear distinction between logical subjects and predicates: subjects always have a line of identity with a free end that had previously been attached to some peg of a predicate; and predicates always have one or more unattached pegs. 3. The Modified EGs are false, but most of them could be converted to correct EGs by using the pure predicate Rel. But 'to' and 'from' are not pure predicates because they refer to something in the UoD. The preposition 'to' could be nominalized as Direction-toward, and 'from' could be Direction-away. 4. As Peirce experimented with new ways of stating his ideas, his newer terminology remains consistent with the older versions, unless he explicitly corrected them. But sometimes the newer terms are more general than the older ones. It's essential to check the examples and definitions to determine how the old and new terms are related. 5. Points #2 and #4 imply that the earlier words 'quasi-predicate' and 'quasi-subject' apply to the nonsymbolic icons or images when they are used as predicates or subjects. Although Peirce did not discuss them in connection with EGs, he used the word 'index' in a way that is similar to the use of an EG line of identity. A quasi-predicate would have something like an unattached peg; a quasi-subject would have something like an index that can point to a peg. 6. Point #5 implies that the "widening" of the word 'rheme' to 'seme' in seme/pheme/delome would include both quasi-predicates and logical predicates. It's also likely that pheme would also be widened to include propositions stated by images combined with something that served as an index. 7. The sharp distinction between subjects and predicates implies that a seme could never refer to a logical subject or a quasi-subject. Since Peirce had frequently used the word 'subject', it's unlikely that he forgot to mention it as the "widening" of the word 'seme'. But it's quite likely that he forgot the word 'quasi-predicate', which he had only used in one MS, several years earlier. Some implications of these conclusions: JAS > The "proper way" is Peircean, not Aristotelian, The method of replacing an arbitrary verb that connects the subject and predicate with the copula -is- was specified by Aristotle, and it was taught in every textbook in the 19th c. CP has over 300 occurrences of "Aristot" from every period of Peirce's writings. Peirce certainly added new revisions and extensions. But Peirce and all his readers had studied Aristotle. According to his ethics of terminology, he always used Aristotle's terminology in the same way it had been translated to Latin and then to English. JAS > The trichotomy that had to be "much widened" was > term/proposition/argument; Note the first sentence of CP 4.538: "A familiar logical triplet is Term, Proposition, Argument." Familiar for his readers always meant Aristotelian logic as taught in every 19th c. textbook. That sentence also had a footnote, presumably by Hartshorne & Weiss, which added the synonyms rheme and dicisign. Since the editors understood Peirce's frequent references to Aristotle, I trust their judgment in writing that footnote. The English word 'term' is derived from the Latin 'terminus', which refers to both "ends" of an Aristotelian proposition: the subject and the predicate. >From slide 15 of <http://jfsowa.com/talks/aristo.pdf> >http://jfsowa.com/talks/aristo.pdf : > The four sentence patterns: > > Universal affirmative: Every S is P. > Particular affirmative: Some S is P. > Universal negative: No S is P. > Particular negative: Some S is not P. In syllogisms, the letter S represents the subject term; P, the predicate term; and M, the middle term. All three letters represent exactly the same words or phrases. But -- and this is a huge **BUT** -- the subject term is always preceded by the word 'every', 'some', 'no' (or something equivalent), and the predicate never has those words. When translated to an EG, every subject term has a line of identity, and every predicate term has the equivalent of an unattached peg. If you want to understand Peirce precisely, you must study the sources that he studied *and* the sources he assumed that his audience or readers had studied. It also helps to study modern logic, since many logicians from the 20th and 21st c. have also had good ideas that help clarify some of the issues. > JAS: The additional step that I am taking is to recognize... > JFS: If Peirce did not explicitly take that step, don't put words in > his mouth. > JAS: But I did not put words in his mouth; I said quite plainly that > I was taking an additional step. The phrase 'the additional step' is a claim that it's implied by or justified by something Peirce wrote. If that step seems to be clear or obvious, there may be some reason why Peirce never took it. There are two possibilities: (1) he didn't find that step useful or relevant, or (2) you may have missed some relevant obstacle. Peirce never wrote the triad subject/proposition/argument, and it contradicts both the Aristotelian term/proposition/argument and his own rheme/dicisign/argument. By repeating it, you're claiming to know what Peirce would have or might have said. That puts words in Peirce's mouth that he would have spit out in disgust. At the end of this note are three quotations, which I have analyzed in whole or in part above. I'm including them here just to emphasize that they are totally irrelevant to the claims about the words 'proper' and 'ultimate' and to the claims about subjects and predicates. John ______________________________________________________________________ CSP: I regard everything to which the assertion relates and to which reference can be removed from the predicate, although what is referred to be a quality, relation, state of things, etc. as a Subject. (R 611) CSP: But the proper way in logic is to take as the subject whatever there is of which sufficient knowledge cannot be conveyed in the proposition itself, but collateral experience on the part of its interpreter is requisite ... The result is that everything in a proposition that possibly can should be thrown into the subjects, leaving the pure predicate a mere form of connection ... (NEM 3:885) CSP: When we have analyzed a proposition so as to throw into the subject everything that can be removed from the predicate, all that it remains for the predicate to represent is the form of connection between the different subjects as expressed in the propositional form ... when we have carried analysis so far as to leave only a continuous predicate, we have carried it to its ultimate elements. (SS 71-72)
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