List, Frank, Ben: This discussion has very deep roots into the foundations of CSP's thinking, at least in my opinion. Pragmatically, the situation of the logic of grammatical terms and it relationships to formal logics is an unresolved issue, at least from my perspective. CSP's writings open up several conundrums which deserve inquiry by modern logicians. I explore examples and draw a novel conclusion wrt the role of units in term logic.
Why do I feel this way? Consider the sentence: The verb "fought" establishes a relation BETWEEN Peter and Harry. The nature of this relation depends on the identity of BOTH Peter and Harry. (It differs from the sentence, "Tom fought Bill", these two sentences lack a common TERM.) Consider the following two grammatical issues: Does this sentence, "Peter fought Harry.", contain a predicate? Or, is it an example of what CSP refers to as a "conjunctive copula"? Consider the sentence: Harry fought Peter and contrast it with it's "twin", Peter fought Harry. Does it have the same logical meaning as the first sentence? Does the distinction between the two sentences convey information? If not, why not? If the switch of the order of the terms of this sentence changes the meaning of the sentence, how is it related to grammar? More broadly, one can ask the question, what is the role of the concept of ORDER in grammar in contrast with its roles in logics and mathematics. NB: contrast this sentence with CSP's usage of the sentence "Cain kills Abel". Apparently, CSP is using the term "conjunctive copula" to signify a form of a proposition such that the two grammatical nouns are of equal rank. Is this the case or not? What are other possible meanings for this strange term? In modern logical terminology, these example sentences can be referred to as a "two place predicate". This grammatical usage is analogous to the mathematical usage of n-dimensional spaces such that the distinctive nature of each predicate is ignored and the meaning of each variable TERM is taken as an undefined value. In other words, the material nature of the identity is annihilated in the n-dimensional logic of mathematics. Note the difference between this example and CSP use of blank spaces in a logical proposition of three terms and its extension to a fourth term: "___ sells ___ to ___." "___ sells ___ to ___ for $___." Also, compare this usage with CSP's description of the mapping of an icon to a rhema in which it compares the generative relation of this map to chemical radicals! In my view, a clear and distinct meaning for the relationships among relatives necessarily requires a clear and distinct cognitive stance with respect to the identity of the term. [ergo, a "family tree" of meanings of terms] In this regard, contrast with 3.420-421 wrt relative rhema. (see The Existential Graphs of CSP, D. Roberts, p.21-25 for discussions). The question I would pose to a philosophically-oriented logician is simple: Does the concept of a propositional term infer a unit of measure or not? If the concept of a unit is necessary, then is the meaning of the proposition made distinct by the distinction between the identities of the logical units, ergo, Peter and Harry? I can summarize this line of thought by a general proposition for the logic of terms as units of meaning as in the "Quali-sign-Sin-sign-legi-sign, icon-index-symbol, rheme, dicisign, argument" format for logic by CSP, but now expressed in mereological terms of parts of the whole: "The union of the units unifies the unity." [ergo, a fight, ergo, beta-graphs.] In a metaphysical LOGIC: "The union of the units unifies the unity of the universe." [ergo, existence] Cheers Jerry (BTW, the notion of a logical "term" was introduced rather late in the history of logic, perhaps by Peter of Spain? It was derived from the notion of "terminals" as parts of a sentence.) On Nov 8, 2015, at 3:03 PM, Franklin Ransom wrote: > Ben, Gary F, > > I like Gary's suggestion about "throwing everything" into the predicate or > into the subject. However, not quite everything gets thrown in, right? There > still needs to be some bare minimum subject if everything gets thrown into > the predicate, and some bare minimum predicate if everything gets thrown into > the subject. I'm not sure this works. > > Ben, I thought to myself of that possibility, namely of erasing the subject > and letting the rhema or term remain. But I don't see how propositions and > arguments can really be like terms in this sense, since propositions > certainly require subjects and arguments do because they require premisses in > the form of propositions. > > But, I was looking through Natural Propositions to make sure I understood the > "throwing everything in" idea, and I found a quote from Peirce that Frederik > included in his text that seems pertinent. NP, p.84, quoted from > "Pragmatism", 1907, 5.473: > > The interpretant of a proposition is its predicate; its object is the things > denoted by its subject or subjects (including its grammatical objects, direct > and indirect, etc.). > > So this says that the subject-term represents the object of the proposition, > while the predicate-term represents the interpretant of the proposition. We > should probably imagine that interpretants don't all come down to being cases > of predicate-terms. But if we consider that the conclusion of an argument is > the argument's interpretant, and comes in the form of a proposition, and that > such proposition itself can be interpreted by way of its predicate, then > propositions and arguments can ultimately be interpreted as predicate terms. > A term, in this way, as an interpretant, signifies all the characters of the > propositions and arguments leading to it, while denoting, by way of its > determination from such determining signs, the object(s) of the determining > signs. What do you think? > > Franklin > > > > On Sun, Nov 8, 2015 at 2:14 PM, Benjamin Udell <[email protected]> wrote: > Gary F., Franklin, > Gary, you wrote, > I’m not sure what Peirce meant by saying in 1893 that every proposition and > every argument can be regarded as a term, or what advantage a logician would > gain by regarding them that way. > [End quote] > In "Kaina Stoicheia" III. 4. (EP 2:308), 1904, > http://www.iupui.edu/~arisbe/menu/library/bycsp/stoicheia/stoicheia.htm > Peirce says: > > [....] If we erase from an argument every monstration of its special purpose, > it becomes a proposition; usually a copulate proposition, composed of several > members whose mode of conjunction is of the kind expressed by "and," which > the grammarians call a "copulative conjunction." If from a propositional > symbol we erase one or more of the parts which separately denote its objects, > the remainder is what is called a rhema; but I shall take the liberty of > calling it a term. Thus, from the proposition "Every man is mortal," we erase > "Every man," which is shown to be denotative of an object by the circumstance > that if it be replaced by an indexical symbol, such as "That" or "Socrates," > the symbol is reconverted into a proposition, we get the rhema or term "_____ > is mortal." [....] > [End quote] > > Somewhere Peirce also notes that a proposition is a medadic term. > Best, Ben > > On 11/8/2015 1:48 PM, [email protected] wrote: > >> Franklin, >> >> I’m not sure what Peirce meant by saying in 1893 that every proposition and >> every argument can be regarded as a term, or what advantage a logician would >> gain by regarding them that way. But to me it sounds like a precursor of his >> (much later) observation that one can analyze a proposition by “throwing >> everything” into the predicate or by throwing everything into the subject. >> Maybe his comment in the Regenerated Logic also works in both directions. >> >> In the Kaina Stoicheia passage, when Peirce says that the “totality of the >> predicates of a sign” is “called its logical depth,” and that the “totality >> of the subjects … of a sign is called the logical breadth,” the sign he is >> referring to has to be a proposition, because only propositions include >> subjects and predicates. Each subject and each predicate can be called a >> “term,” but it’s the breadth and depth of the whole sign, the proposition, >> that Peirce is defining here, not the breadth or depth of the terms (which >> is what he defined in ULCE). And, as you say, propositions and arguments >> also have information (which for Peirce is the logical product of breadth >> and depth). >> >> Gary f. >> >> } The birth and death of the leaves are the rapid whirls of the eddy whose >> wider circles move slowly among the stars. [Tagore] { >> >> http://gnusystems.ca/wp/ }{ Turning Signs gateway >> > > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] > . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] > with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at > http://www.cspeirce.com/peirce-l/peirce-l.htm . > > > > > > > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] > . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] > with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at > http://www.cspeirce.com/peirce-l/peirce-l.htm . > > > >
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