John S., List: JFS: By "the proper way", he was talking about transforming an EG into one of Aristotle's sentence patterns. Note that the paragraph begins with EGs.
Peirce did not say anything about Aristotle in his letter to Jourdain, nor in his contemporaneous letter to Welby that discussed "throw[ing] everything into the subject" as carrying the analysis "to its ultimate elements." He indeed mentioned EGs earlier in the paragraph, calling either EGs themselves or his complete theory of logical analysis based on them his "*chef d'oeuvre*," as I have acknowledged all along. However, he went on to give three specific examples of the "proper" analysis that he subsequently described in detail. CSP: ... in existential graphs, every predicate has either a single connexion with one subject (as in "it rains" where the predicate is the present phenomenon and the subject is *rain *or *pluviation*); or secondly, it is a dyadic relative between two subjects and has valency = 2, as Napoleon was mortal, where Napoleon and Mortality are the two subjects, or finally, it connects more than two subjects, as the word *and *does when expressing as is usual *coidentity*, as in 'Napoleon was mortal and mendacious.' (NEM 3:885; 1908) In "it rains," there is one Subject (rain); in "Napoleon was mortal," there are two Subjects (Napoleon and mortality); and in "Napoleon was mortal and mendacious," there are three Subjects (Napoleon, mortality, and mendaciousness). In each case, there is *only one* predicate--the Continuous Predicate--which is represented on an EG with zero, one, and two Lines of Identity, respectively. It turns out that these directly correspond to the three different kinds of Propositions. CSP: Also note that by this system [EGs] every proposition is either hypothetical, categorical, or relative, according to the number of heavy lines necessary to express its form. (R 481:10; no date) I believe that this is precisely why Peirce, although "with great hesitation," ultimately labeled the division "as to the Nature of the Immediate (or Felt?) Interpretant" as Hypothetic/Categorical/Relative (EP 2:489; 1908). As he explained to Jourdain, valency is a property of the Continuous Predicate and directly corresponds to the number of *Subjects *that are "married" by it into a *complete *Proposition. Such an analysis is perfectly compatible with the logic of EGs, especially (as I have noted before) the continuity of the single predicate being represented by continuous Lines of Identity. JFS: The 1902 definition in his Minute Logic is the clearest and most exact statement. It's consistent with everything he wrote later. And there is no evidence for anything else. You keep referencing 1902, but the only time Peirce used "quasi-predicate" was in the "Syllabus" for his Lowell Lectures of 1903; the Collected Papers *incorrectly *date it "c. 1902." "Everything he wrote later" obviously includes the December 1908 letters to Jourdain and Welby, where he presented a *different *analysis of Propositions, even calling it "proper" and "ultimate." That certainly seems to me like *clear *evidence for something else, which he had apparently come to *prefer*. JFS: The fundamental issue about continuity of semiosis involves relating a discrete (countably infinite) set of logical subjects and predicates to a continuum (uncountably infinite) set of possible percepts (AKA quasi-predicates). I see it instead as recognizing that each discrete Instance is an individual embodiment of a continuous Sign, one of its inexhaustible *potential *Instances; and that this is *isomorphic *to the Object of the Sign--each discrete Dynamic Object is an individual embodiment of a continuous General (or Final) Object, one of its inexhaustible *potential *instantiations. JFS: But subjects and quasi-subjects are disjoint from predicates and quasi-predicates. The former denote things, and the latter are true of things. (Note: Those "things" may include events, processes, properties, feelings...) How can subjects be *disjoint *from predicates if they can denote properties? How can predicates by themselves be "true of things" when only a *complete *proposition is capable of being true or false? Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Thu, Feb 7, 2019 at 10:29 PM John F Sowa <[email protected]> wrote: > Jon AS, > > Everything Peirce wrote about semeiotic, from first to last, was > based on his math and logic. Since math and logic are precise, > they can resolve any doubts or questions about the semeiotic. > > > JFS: A seme is a predicate or a quasi-predicate. > > > > This is only true in an analysis of Propositions that throws > > everything it can into the predicate, as modern logic advocates. > > No. It's true for every definition of proposition from Aristotle > to the present. A declarative sentence in any language states a > proposition. But the usual syntax of ordinary language doesn't > fit the patterns of syllogisms. Therefore, Aristotle specified > four "proper" syntax patterns that facilitate the argument. > > In NEM 3:885, Peirce wrote "A proposition can be separated into a > predicate and subjects in more ways than one." By "the proper way", > he was talking about transforming an EG into one of Aristotle's > sentence patterns. Note that the paragraph begins with EGs. And > on p. 886, it states the Aristotelian style of argument: "Major > Premiss, Minor Premiss and Conclusion". > > See the attached NEM3_885.pdf for those two pages. > > > JFS: There is no overlap between a seme and a subject or quasi-subject. > > > > This is clearly false in an analysis of Propositions that throws > > everything it can into the subject, as Peirce eventually advocated. > > No. A syntactic translation of a sentence from one form to another > does not change the proposition. In CP 5.569, Peirce wrote "we speak > of believing in a proposition, having in mind an entire collection of > equivalent propositions with their partial interpretants." > > To define equivalence of propositions, I used CP 5.569 as the > criterion for specifying a meaning-preserving translation (MPT). > See http://jfsowa.com/logic/proposit.pdf > > For any proposition p, there is a denumerable (countably infinite, > but discrete) set of equivalent propositions. Some sentence patterns > are more suitable for Aristotelian arguments, but others are better > for EG rules of inference. During the 20th century, many other proof > procedures have been invented for which various sentence patterns > are preferable. > > > Why should we privilege a terminology and approach that he utilized > > only once ("quasi-predicate" and "quasi-subject") over what he wrote > > more than once ("Seme" and especially "continuous predicate"), later > > in his life, in an analysis that he explicitly called "proper" and > > "ultimate"? > > There's a simple reason. The 1902 definition in his Minute Logic is > the clearest and most exact statement. It's consistent with everything > he wrote later. And there is no evidence for anything else. For the > version in his letter to Jourdain, see the attached NEM3_885.pdf. > > The word "proper" depends on which inference rules are adopted. Peirce > was writing about Aristotelian patterns for over 40 years. In 1866, he > wrote "Memoranda concerning the Aristotelian syllogism" (CP 2.792 ff). > After 1897, he defined different rules for EGs. In 1898, he discussed > syllogisms in Lecture 2 of RLT. Although EGs can be translated to > Aristotelian patterns, the patterns that are "proper" to the EG rules > of inference are quite different from the Aristotelian patterns. > > JAS > > my proposed diagram of Semes/Subjects as continuous lines, > > Phemes/Propositions as continuous planes, Delomes/Arguments > > as continuous spaces, and Instances as discrete points that > > we mark where these all coincide. > > No. Peirce never said or implied anything of the sort. Every > version of language and logic has a finite number of symbols, and > every sentence has a finite length. That implies a denumerable > (infinite, but discrete) set of sentences for defining logical > subjects, predicates, propositions, and arguments. > > The continuity of semiosis is determined by the continuum of the > real world (AKA actual universe). That is why a single name, > such as 'George Washington' can refer to a continuum of stages: > George as a child chopping down a cherry tree during one interval, > apologizing to his father in another interval, becoming a general > in the US army, becoming the first president of the US, and having > his portrait painted and later printed on US one-dollar bills. > > Each discrete sentence determines a predicate that is true during > an interval (a continuum) of stages. During each interval there is > an uncountably infinite of stages of George W. Each stage in that > continuum is a quasi-subjects, which may be perceived as a percept > (quasi-predicate) that is true about George in that stage. > > The fundamental issue about continuity of semiosis involves relating > a discrete (countably infinite) set of logical subjects and predicates > to a continuum (uncountably infinite) set of possible percepts > (AKA quasi-predicates). > > Conclusions: > > 1. The discrete predicates of a language or logic may be true of > everything for which some continuum of quasi-predicates is true. > > 2. The discrete subjects of a language or logic may denote everything > that some continuum of quasi-subjects may denote. > > 3. But subjects and quasi-subjects are disjoint from predicates > and quasi-predicates. The former denote things, and the > latter are true of things. (Note: Those "things" may include > events, processes, properties, feelings...) > > > I believe that this last aspect conveniently reflects the fundamental > > unity of connected Signs; perhaps it is a corollary of Peirce's > > "theorem of the science of semeiotics" that if any Instances are > > connected, no matter how, the resulting system constitutes one Instance. > > I suggest that you revise these comments to relate the world as a > a continuum to the discrete (but countably infinite) sets of possible > sentences for defining logical subjects and predicates. The critical > issues about continuity arise from this mismatch. > > John >
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