John S., List: I changed the subject heading, since we are still not actually discussing EGs and Phaneroscopy.
JFS: But "Bob owns a red car" could be separated in four ways: (1) "Bob / owns a red car." (2) "A red car / is owned by Bob." (3) "A car owned by Bob / is red." (4) "A car / is red and is owned by Bob." You left out a fifth way--"Bob, owning, car, redness / _____ is in the dyadic relation of _____ to a _____ that possesses the character of _____." JFS: Therefore, the set of subjects is disjoint from the set of predicates. My point was that non-continuous predicates, such as "owns/owning" and "red/redness," can be analyzed *either *as predicates *or *as subjects. JFS: The predicate "is a car owned by Bob" can be true or false *of* something only when it is linked to a subject, for example, "That Chevy / is a car owned by Bob." We can also analyze that "predicate" as four Subjects (something, car, owning, Bob) "married" by two Continuous Predicates--"_____ is identical to a _____ that is in the dyadic relation of _____ to _____." JFS: The "proper way" on p. 885 would replace the verb 'breathes' in the sentence "Every mammal breathes oxygen" with the verb 'is' in "Every mammal is an oxygen-breathing animal." No, we have been over this already. The "proper way" is Peircean, not Aristotelian, and analyzes that sentence as "Every mammal is in the dyadic relation of breathing to oxygen." There is no need to insert the word "animal." JFS: Yes, but that is continuity of *pure* predicates, not of predicates that refer to content in the universe of discourse. 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. The only information that a Proposition can *convey*, which therefore belongs to its *Interpretant*, is the logical form of the relation that "marries" all of the referenced Subjects. In order to understand "Bob owns a red car," I need Collateral Experience with not only Bob and cars, but also owning and redness. In order to understand "Every mammal breathes oxygen," I need Collateral Experience with not only mammals and oxygen, but also breathing. JFS: In CP 4.538, Peirce said that the triad rheme/dicisign/argument would have to be widened to cover those image-like things. His earlier definition of quasi-predicate would cover those aspects. Therefore, the widened term 'seme' includes both 'predicate' and 'quasi-predicate'. But no logical subject could ever be a seme. That is *not *what the text says *at all*. The trichotomy that had to be "much widened" was term/proposition/argument; "rheme" and "dicisign" are not mentioned, and as I have pointed out repeatedly, "quasi-predicate" *never *appears in *any *of Peirce's writings, other than its one occurrence in 1903. The definition of "Seme" is "anything which serves for any purpose as a substitute for an object of which it is, in some sense, a representative or Sign," which clearly encompasses *all *logical subjects. 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. But I *did not* put words in his mouth; I said quite plainly that I was taking an additional step. JAS: Bellucci cites another passage where Peirce clearly endorsed... JFS: If he didn't explicitly say something that seems "clear" or "obvious", he probably had some reason for not doing so. But he *did* explicitly say something in this case--three times! 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) I already acknowledged that the EGs reflect his earlier analysis, and that maintaining such an approach makes perfect sense when using EGs to teach first-order predicate logic today. I have a *different *purpose in mind, for which his "proper" and "ultimate" analysis is more suitable. JAS: Perhaps what you mean is that CSP's logic was a logic of Subjects, as I am now employing that (capitalized) term ... JFS: That conclusion is not just imprecise. It's false. Peirce never did and never would say that EGs are "a logic of subjects'. In context, I was directly responding to the assertion that Peirce's logic was a "logic of proper names"; and all I mean by a "logic of Subjects" is what Peirce described to Jourdain as "the proper way in logic." He apparently never discussed how to interpret EGs in accordance with that analysis, which is why I am taking a stab at doing so myself. JFS: It's impossible to have a logic without *both* subjects and predicates. And predicates that refer to content are never "pure". Of course; but again, according to Peirce, "the proper way in logic" is to treat *anything *that refers to content as a Subject, not a predicate. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Wed, Feb 13, 2019 at 9:29 AM John F Sowa <s...@bestweb.net> wrote: > Gary F, Jon AS, and Jerry LRC, > > I started to write this note several days ago, but had some other > things on my agenda. The following comments begin with the older > material with just two brief comments about the newer. > > GF > > Given your emphasis on precision, you are apparently referring > > to formal (i.e. mathematical) logic, and not to logic as semeiotic... > > you seem to have skipped over the science which comes between > > mathematics and logic/semeiotic in Peirce’s classification of the > > sciences, namely Phenomenology (or Phaneroscopy) > > In Peirce's classification of the sciences, *formal* logic is a > branch of mathematics. I hadn't seen Atkins' book, but I read the > Google excerpts and ordered it. > > GF > > the new Atkins book on Charles S. Peirce’s Phenomenology, which > > Gary Richmond mentioned a few days ago. Atkins has quite a lot to > > say about the overlaps among logic, semeiotic, EGs and phenomenology, > > From the Google excerpts of Atkins' book: > > p. 5: Peirce... concludes that the categories ought to be found > > first in mathematics, a part of which is formal logic, and then > > traced through phenomenology, normative science (including logic > > as semiotics), and metaphysics. > > > > p. 6: The analysis of the phaneron, moreover, involves both > > logical analysis and inspective analysis. > > As an example, consider the questions about logical subjects and > logical predicates. To show the difference, consider the EG for > "Bob owns a car." That EG can be drawn on a straight line: > > Bob———Owns———Car > > There are two lines of identity, one for Bob and one for the car. > The two monads have one peg each (Bob- and Car- ); and the dyad > has two pegs ( -Owns- ). > > Peirce said that an EG can be "separated" into a logical subject > and predicate "in more than one way". The simplest example is > "Bob" as the subject and "owns a car" as the predicate: > > Bob——— -Owns———Car > > In this case, the line of identity for the subject remains with > Bob, the left peg of Owns is unattached, but the right peg of > Owns remains attached to the line of identity for Car. > > With this short example, there is only one other option: > "A car is owned by Bob": Car——— Bob———Owns- . In this > case, the right peg of Owns is unattached. > > But "Bob owns a red car" could be separated in four ways: > (1) "Bob / owns a red car." (2) "A red car / is owned by Bob." > (3) "A car owned by Bob / is red." (4) "A car / is red and > is owned by Bob." > > In every case, the logical subject has a line of identity with > one end free; and the logical predicate has an unattached peg > where that line had been attached. > > JAS > > How can subjects be disjoint from predicates if they can denote > > properties? > > Consider Bob's red car. There are four possible subjects. > Case (4) "A car" is probably insufficient to determine the referent. > If there is only one Bob in the context, case (1) "Bob" may be > sufficient. Cases (3) or (4) depend on the context and what the > speaker knows about the listener. > > In every logical subject, all the predicates in the subject have lines > of identity attached to every peg. But every logical predicate has at > least one peg that is not attached to any line of identity. > > Therefore, the set of subjects is disjoint from the set of predicates. > > JAS > > How can predicates by themselves be "true of things" when only > > a complete proposition is capable of being true or false? > > Note the difference in syntax. A proposition by itself can be true > or false. But the phrase "true of things" indicates that a predicate > is not true by itself. The predicate "is a car owned by Bob" can > be true or false *of* something only when it is linked to a subject, > for example, "That Chevy / is a car owned by Bob." > > JAS > > JFS: By "the proper way", he was talking about transforming an EG > > into one of Aristotle's sentence patterns... > > > > Peirce did not say anything about Aristotle in his letter to Jourdain > > There was no need to. Every university graduate in the 19th c. was > familiar with Aristotle's syllogisms. For a summary of the patterns > for syllogisms, see slides 15 ff of http://jfsowa.com/talks/aristo.pdf > > Compare the methods in those slides to the attached NEM3_885.pdf. > The "proper way" on p. 885 would replace the verb 'breathes' in > the sentence "Every mammal breathes oxygen" with the verb 'is' > in "Every mammal is an oxygen-breathing animal." > > In that "Aristotelian" transformation, the pure predicate -is- has > two pegs. In the full sentence, each of the two logical subjects > has a line of identity with a free end, which can be attached to > one of the pegs. > > Note that EGs for both logical subjects would contain embedded monads > or dyads for the content: Mammal- Animal- Oxygen- -Breathe- . > > The logical subject for "oxygen-breathing animal" would contain > a teridentity with one line of identity attached to Animal-, one > line of identity attached to the left peg of -Breathe-, and one > line of identity with a free end. That free end could be attached > to the right peg of the pure predicate -is-. > > JAS > > Peirce's further insight in 1906 about this continuity of the Line > > of Identity, as well as that of the blank Sheet of Assertion, was > > what eventually led him to formulate the concept of the Continuous > > Predicate two years later. > > Yes, but that is continuity of *pure* predicates, not of predicates > that refer to content in the universe of discourse. Those pure > predicates are structural elements of EGs -- and of Aristotle's > syllogisms. Both Aristotle and Peirce intuitively recognized the > central role of the copula 'is' long before 1906. > > Bellucci (p. 20) said that after 1908 Peirce never again mentioned > continuous predicates: "continuous predicates are by no means > abandoned. Instead, they are incorporated within the system > of Existential Graphs." > > Note that predicates that refer to content may refer to discrete > content or continuous content. But continuity in the content is > independent of the two pure predicates in the the EG structure. > > Furthermore, these issues about pure predicates are unrelated to semes. > As Peirce said, semes are wider than predicates because they refer to > content such as images and percepts of images. That is why the letter > to Jourdain is irrelevant to any questions about semes. > > JAS > > Subject, Proposition, and Argument obviously correspond to rheme, > > dicent, and argument in this text and to Seme, Pheme, and Delome > > in the later division > > No. A rheme is never a subject. See the examples above. For > a second opinion, note what Bellucci (2013, p. 38) said: "It thus > appears that “rhema” and “predicate” are used interchangeably, but > that a rhema is better called a predicate when considered in the > context of a proposition." > > The same criteria distinguish quasi-subjects and quasi-predicates, > which are images or percepts of images. When an image is used as > a quasi-predicate some places on the image could serve as quasi-pegs. > When an image is used as a quasi-subject, an index of some sort > could serve as a quasi-line of identity. > > The terms 'quasi-peg" and 'quasi-line' are mine. I'm using them > only to emphasize the parallels between a symbolic notation for > logic and the kind of semiosis that occurs during perception. > > In CP 4.538, Peirce said that the triad rheme/dicisign/argument > would have to be widened to cover those image-like things. His > earlier definition of quasi-predicate would cover those aspects. > Therefore, the widened term 'seme' includes both 'predicate' and > 'quasi-predicate'. But no logical subject could ever be a seme. > > JAS > > The additional step that I am taking is to recognize... > > Bellucci cites another passage where Peirce clearly endorsed... > > No. If Peirce did not explicitly take that step, don't put words > in his mouth. If he didn't explicitly say something that seems > "clear" or "obvious", he probably had some reason for not doing so. > > Bellucci's article, which I strongly endorse, is a detailed analysis > of the limited amount of evidence -- just five short comments that > Peirce wrote between 2006 and 2008. Bellucci suggests a good reason > why Peirce never mentioned continuous predicates after 1908: > > Bellucci, p. 4 > > Peirce does not abandon continuous predicates after 1908; quite the > > contrary, they just merge with the continuous graphs within the > > diagrammatic system of Existential Graphs that he is then developing > > and perfecting. > > In short, three pure predicates form the structural foundation of EGs: > the line of identity, the blank Sheet of Assertion, and the triad for > teridentity. After recognizing their fundamental nature in EGs, > Peirce found no further need to discuss them separately from EGs. > > JAS > > I am not a logician, so please forgive my imprecision. Peirce > > was quite clear about the scope of "everything" in his own > > statements, and also provided helpful examples. > > > > CSP: ... I regard everything to which the assertion relates and > > to which reference can be removed from the predicate, > > > > Perhaps what you mean is that CSP's logic was a logic of Subjects, > > as I am now employing that (capitalized) term; > > That conclusion is not just imprecise. It's false. Peirce never > did and never would say that EGs are "a logic of subjects'. It's > impossible to have a logic without *both* subjects and predicates. > And predicates that refer to content are never "pure". See the > examples above. > > For a clearly written tutorial about EGs in MS 514 (1909), which Peirce > regarded so highly that he sent a clean copy to Mr. Kehler in 1911, see > http://jfsowa.com/peirce/ms514.htm > > In ms514.htm, Peirce's words are in black, and my commentary is in red. > For more examples, see http://jfsowa.com/talks/egintro.pdf > > JLRC > > Jean-Yves Beziau, 13 QUESTIONS ABOUT UNIVERSAL LOGIC > > http://www.jyb-logic.org/Universallogic13-bsl-sept.pdf > > This short and terse essay is a good starting point for comparing > > CSP’s views with modern logics. > > I agree. But I don't believe it's possible to have a single unified > logic. However, I believe that Peirce's EGs would be an excellent > common core with other logics as extensions or variations of the core. > > Following are the slides for two lectures I presented in 2015: > > At a Peirce session of the APA in Vancouver in April 2015, I presented > "Peirce, Polya, and Euclid: Integrating Logic, Heuristics, and Geometry" > For the slides, see http://jfsowa.com/talks/ppe.pdf > > At a Smart Data conference in San Jose in August 2015, I presented > a 3-hour tutorial on natural logic, which included some of the slides > in ppe.pdf: http://jfsowa.com/talks/natlog.pdf > > Starting with the natlog.pdf slides is good for an intro and overview. > See the last slide of each lecture for references and URLs. > > John >
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