John, List: I finally changed the thread topic, since we long ago departed from discussing R 300.
JFS: In this context, Peirce's statement "every proposition contains a Subject and a Predicate" is about grammar: every English sentence that states a proposition must have a grammatical subject and a grammatical predicate. That sentence is false. Peirce did not say, "Every sentence in English contains a grammatical subject and a grammatical predicate"; he said, "Every proposition contains a Subject and a Predicate." In this context, he was clearly talking about *logic*, not English grammar; i.e., every *proposition*--expressed in *any *Sign System, including EGs--contains a *logical *subject (denoting the Object) and a *logical *predicate (signifying the Interpretant). Even a cursory glance at the textual evidence confirms this. - The title of the manuscript is "Sundry Logical Conceptions," not "Sundry Grammatical Conceptions" (EP 2:267). - The heading for most of its contents, including the quoted paragraph (EP 2:279-281), is "Speculative Grammar," which is the first branch of the Normative Science of logic (EP 2:272); not "English Grammar," or that of any other language, which would fall under the Special Science of linguistics. - In the quoted paragraph itself, Peirce went on to give the familiar example of "Cain kills Abel" and noted (in this particular analysis) that it has *two *subjects, "Cain" and "Abel"; but in English grammar, *only *"Cain" is the subject, while "kills Abel" is the predicate. - Later in the same manuscript, he contrasted the grammar of "the overwhelming majority of languages," including English, with "the way in which the logicians go out of their way to teach that all men think" (EP 2:285). In the standard translation of EGs, each Spot is a *discrete *logical predicate that signifies a Rheme (such as "is a car" or "is red"), while each heavy Dot attached to a Peg of a Spot is an *indefinite *logical subject that denotes "something." The latter can be extended into a Line of Identity that denotes one logical subject to which multiple logical predicates are attributed. However, "A proposition can be separated into a predicate and subjects in more ways than one" (EP 3:885; 1908). This is precisely the *reason *for the ambiguity of the word "subject"--how it is distinguished from the predicate within any given proposition is *arbitrary*, as long as *both* subject and predicate are recognized; neither one can ever be omitted altogether. Nevertheless, "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" (*ibid*). Accordingly, we can treat every one-Peg Spot as a logical subject and its Peg as a *continuous *logical predicate. Such a Spot is either an Abstractive that denotes a character (like "redness"), a Concretive that denotes an individual (like "Cain" or "Abel"), or a Collective that denotes a class (like "car" or "killing"); and its single Peg respectively signifies either "possesses the character of," "is identical to," or "belongs to the class of." A multi-Peg Spot is required only for relations with three or more subjects, one of which denotes the relation *itself*; Peirce suggested "stands" as the label for such a Spot (R 669:17[15]; 1911 May 30). A heavy Dot or Line of Identity still denotes "something." JFS: A grammatical subject by itself is not a syntactically correct English sentence. JFS: The medad Car———, which represents the grammatical subject, may be translated to a different sentence "Something is a car', which states a proposition that is implied by "Some car is red." The first sentence is true, which entails that the second sentence is false. Since a grammatical subject is *not *a complete sentence, it *cannot *be translated into a proposition. The *grammatical *subject of ""Some car is red" is "some car," not "Something is a car"; and its *grammatical *predicate is "is red." The *logical *subjects of "Some car is red" and its corresponding EG (Car———Red) are "something," "car," and "redness"; while its (continuous) *logical *predicate is "_____ belongs to the class of _____ and possesses the character of _____." JFS: You can map every medad to a grammatical sentence in any language you happen to know. Yes, which is why we *cannot *map *any *medad to a grammatical *subject*--as you noted, the latter by itself is *never *a syntactically correct *sentence*. JFS: Before stating the reasons, I'll define a Seme as a Term or a Percept. (Jappy and I prefer the definition "predicate or quasi-predicate", but "Term or Percept" is OK for this example.) It blatantly violates Peirce's ethics of terminology to assign a new definition to a technical word that he invented, rather than maintaining his own. A 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" (CP 4.538; 1906). As such, Terms and Percepts certainly do not exhaust the logical breadth and depth of "Seme." JFS: A Seme is a First, and an Index is a Second. A Second can never be a First. Those sentences are false, or at least misleading, and suggest a fundamental misunderstanding of Peirce's Speculative Grammar. His divisions of Signs were ultimately into logical *Universes*, not phaneroscopic *Categories*; a Seme is a *Possible*, and an Index is an *Existent*. Icon/Index/Symbol and Seme/Pheme(Proposition)/Delome(Argument) are two *different *trichotomies, which are related to each other by the "rule of determination." CSP: It is evident that a Possible can determine nothing but a Possible; it is equally so that a Necessitant can be determined by nothing but a Necessitant. (EP 2:481; 1908) Consequently, an Index (Existent) *cannot *be an Argument (Necessitant), but it *can *be either a Proposition (Existent) or a Seme (Possible). Proper names, demonstrative pronouns, and pointing fingers are all examples of Indexical Semes; so are variables in modern predicate logic. Again, it was precisely in order to encompass Indices and Icons--not just Symbols--that "Term" had to be "much widened" in the first place. JFS: Most sentences in ordinary language state propositions without having any word (such as 'is' or 'has') that expresses a continuous predicate. That sentence is true, but irrelevant. As I have pointed out before, the continuous predicate is often embodied in natural language as *syntax*, rather than words. CSP: Take the Proposition "Cain killed Abel." This is identically the same Proposition as "Abel was killed by Cain": It is only the grammatical dress that is different. Other things being equal, everybody will prefer the former. Why? Because it is simpler; but why is it simpler? Because in putting the cause before the effect, it in that respect diagrammatizes the truth. What are the Subjects of this Proposition. Cain, first: that is not only a Subject of the Proposition, but is the principal Subject of the Assertion which a historian would naturally make. But in the Proposition Cain and Abel are, as Subjects, on one footing precisely (or almost precisely, for Cain is preponderant in causality) But besides these, "killed" = committed *murder* upon, is a third Subject, since no study of the words alone, without extraneous experience, would enable the Ad[d]ressee to understand it. What, then, is left to serve as Predicate? Nothing but the *flow of causation*. It is true that we are more acquainted even with that in Experience. When we see a babe in its cradle bending its arms this way and that, while a smile of exultation plays upon its features, it is making acquaintance with the flow of causation. So acquaintance with the flow of causation so early as to make it familiar before speech is so far acquired that an assertion can be syntactically framed, and it is embodied in the syntax of every tongue. (R 664:10-12; 1910 Nov 26-27) In "Cain kills Abel," all three words serve as logical subjects that *denote the Objects* of the proposition, which must already be known to an interpreter from previous Collateral Experience (cf. SS 70; 1908). Consistent with "the flow of causation," the syntax alone serves as the continuous predicate that *signifies the Interpretant* of the proposition, which may be translated as "_____ stands in the relation of _____ to _____." JFS: As Peirce said, no proposition can be built up of non-propositional signs that are somehow "married" to a continuous predicate. What Peirce said--what I *quoted *him as saying--is that "it is not true, *as ordinarily represented*, that a proposition can be built up of non-propositional signs" (CP 4.583; 1906, bold added). A mere collection of Semes is not a Proposition; rather, a Proposition "marries" those Semes (as its subjects) by means of a continuous predicate. The only thing that a Proposition *itself *can convey is this very *relation *among its subjects. Likewise, a mere collection of Propositions is not an Argument; rather, an Argument "marries" those Propositions (as its premisses) by means of a leading principle. The only thing that an Argument *itself *can convey is this very *relation *among its premisses, from which the conclusion follows. JFS: Note that he converted from Unitarian to Episcopalian because the concept of the Holy Trinity, as a triad, supported and was supported by his mathematical philosophy. That sentence is false, or at least highly speculative. Peirce converted from Unitarian to Episcopalian because that was an explicit stipulation of his first wife, Zina, before she would agree to marry him in 1862. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Wed, Mar 20, 2019 at 8:34 AM John F Sowa <[email protected]> wrote: > Jon AS and Gary F, > > JAS > > We simply prefer different but equally valid (and equally Peircean) > > analyses of a proposition--you throw everything possible into the > > predicate, leaving only an indicated subject; I throw everything > > possible into the subject, leaving only a continuous predicate. > > I agree that those two methods are logically equivalent. > > But the confusion about the meaning of Semes results from the ambiguity > of the word 'subject'. There is a clear and definitive way to resolve > that ambiguity: In every occurrence in any of Peirce's writings, ask > precisely how the word 'subject' is related to an existential graph. > > > [CSP] every proposition contains a Subject and a Predicate, the former > > representing (or being) an Index of the Primary Object, or Correlate of > > the relation represented, the latter representing (or being) an Icon of > > the Dicisign in some respect" (CP 2.316, EP 2:279; 1903). > > Note the context of that excerpt. The paragraph immediately before it > contains several quoted sentences in English, each of which is called > a proposition. Then look at the end of that paragraph: > > > [CSP] The system of Existential Graphs, which is capable of expressing > > every proposition as analytically as may be desired, expresses an > > assertion by actually attaching an individual replica to the individual > > sheet; and such possible attachment is precisely what the Interpretant > > of a proposition represents before the proposition is asserted. > > In this context, Peirce's statement "every proposition contains a > Subject and a Predicate" is about grammar: every English sentence > that states a proposition must have a grammatical subject and a > grammatical predicate. > > JAS > > This makes it frankly untenable to claim that "the logical subject > > is a predicate" and "a grammatical subject ... is a proposition." > > That sentence is false. The syntax of EGs is defined by lines that > connect monads, dyads, triads... Every EG in which all the pegs > are attached to lines is a medad. Nothing in EG syntax is called > a subject, a predicate, or a proposition. But every medad can be > translated to an English sentence that states a proposition. > > JAS > > by definition a grammatical subject cannot (by itself) be a > > proposition, since it is only one part of a proposition; namely, > > whatever is not the grammatical predicate. > > This is a statement about English syntax. A grammatical subject > by itself is not a syntactically correct English sentence. But > when you translate any sentence to an EG that expresses the same > proposition, that EG will usually have many subgraphs that are > also medads. Every one of them could be translated to a sentence > that states a proposition. > > For example, the sentence "Some car is red" may be translated > to the EG Car———Red. This EG has three subgraphs that are medads: > The medad Car———, which represents the grammatical subject, may > be translated to a different sentence "Something is a car', which > states a proposition that is implied by "Some car is red." > > The second subgraph ———Red is also a medad. It may be translated > to "Something is red", which states another proposition that is > implied by "Some car is red." > > The third subgraph is just a line of identity ——— with nothing > attached at either end. It is also a medad, and it states the > proposition "Something exists." The medad and the sentence are > implied by each of the other three medads and sentences: > "Some car is red", "Something is a car", and "Something is red." > > For more examples of EGs and their mappings to and from English, > see slides 16 to 18 of http://jfsowa.com/talks/egintro.pdf > > After examining those EGs and their translations, note that every > grammatical subject in every English sentence maps to and from > a medad, which can be derived by deleting parts of the larger EG. > Every medad can itself be mapped to a shorter English sentence, > which states a proposition, which is a Dicisign, which is a Pheme. > > And this point is true of *every* language. You can map every > medad to a grammatical sentence in any language you happen to know. > > > Seme," like "term," names a class of Signs; "subject" and "predicate" > > name the two different functions that a Seme (or term) can perform > > within a proposition, depending on how it is analyzed. > > The sentence up to ';' is OK. We agree that the class of signs called > Terms is a subset of the class of signs called Semes. But the part > that follows ':' is false for several reasons: > > 0. Before stating the reasons, I'll define a Seme as a Term or > a Percept. (Jappy and I prefer the definition "predicate or > quasi-predicate", but "Term or Percept" is OK for this example.) > > 1. Semes (terms and percepts) don't perform functions, but they > can be represented by various symbols in various notations. > > 2. In an EG, Semes are represented as monads with one peg that is > not attached to any line of identity. That monad may be a single > node with a label such as Car, Red, or Dormitive-Virtue. Or it > may be an arbitrarily complex EG with one unattached peg. > > 3. In an English sentence, Semes are represented as common nouns > or as nouns with arbitrarily complex modifiers, such as > a string of adjectives that precede the noun and/or relative > clauses or prepositional phrases that follow the noun. They > may occur in any position in an English sentence where a common > noun may occur. > > 4. But Semes cannot be used as grammatical subjects unless they > are part of a complete noun phrase. That requires them to be > preceded by an indexical word, such as 'a', 'the', 'some'. > 'every', 'this', 'that'... > > > JFS: But a conjunction of Semes does not become a Pheme until, by some > > judgment, it is asserted about something determined by some index. > > > > Yes--in your analysis, which treats all Semes except variables > > as predicates. > > A variable is an Index. A Seme is a First, and an Index is a Second. > A Second can never be a First. But the two parts Seme + Index can > be combined to state a proposition, Dicisign, or Pheme. > > > In mine, a conjunction of Semes does not become a Proposition (Pheme) > > unless and until they are "married" as subjects by a continuous > > predicate, which is usually embodied as syntax; that is why "it is > > not true, as ordinarily represented, that a proposition can be built up > > of non-propositional signs" (CP 4.583; 1906). > > That statement is false for several reasons: > > 1. Most sentences in ordinary language state propositions without > having any word (such as 'is' or 'has') that expresses a > continuous predicate. > > 2. As Peirce said, no proposition can be built up of non-propositional > signs that are somehow "married" to a continuous predicate. > > 3. But an index by itself maps to a line of identity, which is a medad > that states the proposition "Something exists". That proposition > can be built up by attaching monads at either end: Car———Red. > > 4. A Seme, by itself, describes a possibility (1ns). An index, by > itself, indicates some existent (2ns). An index combined with > one or more Semes adds more description about that existent. > > For more about percepts, images, and indexicals, please read or > reread Jappy's article: > > https://www.ocula.it/files/OCULA-15-JAPPY-Peirce-rhetoric-and-the-still-image.pdf > > JAS > > a single quotation from a single manuscript does not demonstrate > > that Peirce was always thinking in terms of EGs > > In reply, I'll start with Gary's comment about your notes: > > GF > > I think it would be better to go directly to Peirce if you want to > > get a grip on how one does phaneroscopy … and I mean to a continuous > > text, not a collection of quotes plucked from various contexts. > > Yes. And my comment about the centrality of Peirce's logic is based > on the totality of everything he wrote from the 1860s to the end. > He declared himself a logician at the age of 13, and logic inspired > or explained every aspect of his philosophy. > > For some continuous text that demonstrates how his math and logic > are always present behind his non-mathematical discussions, I > recommend Peirce's late letters to William James (around 1909). > As an example, see the attached copy of NEM 3:851. > > This page, as in other letters to James, is preceded by several pages > of heavy math and followed by a two pages of EGs. Peirce apologized > to James for all the math, and he explained that he included it for > the benefit of other readers who may see it in the future. > > Note the passage that begins "Argument 3rd: I have long urged that, > in itself considered, any one concept is just as simple as any other." > After that, he mentions the very mathematical "barycentric calculus", > which he presented in the previous pages. He used that complexity > to explain simplicity. But James would have to take his word for it. > > As an example, consider a screen door. Even a child can recognize it, > use it, and understand its purpose. The percept/Seme would be simple. > But the predicate/Term/Seme would have to be rather complex to describe > the wire mesh and other parts of the door. > > Lower on that page, Peirce wrote "the system of Existential Graphs is > the only system that does to perfection that which all logical algebras > have aimed to do..." Then the next two pages discuss EGs. > > This page illustrates several points: (1) Semes, as percepts or > concepts, can be simple, even though the predicates that describe > them may be rather complex. (2) Peirce was thinking in terms of > math/logic, even when he was writing for readers like James who did > not understand the math. (3) But it's important to remember and > use the Bedrock of logic to analyze and explain the details of the > passages that don't seem to be mathematical. > > Even when he wrote on "big picture" themes such as God, his math and > logic influenced what he wrote and did. Note that he converted from > Unitarian to Episcopalian because the concept of the Holy Trinity, as > a triad, supported and was supported by his mathematical philosophy. > > John >
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