Ben, Jerry, In general, I ditto Ben's interleaved remarks from his post. In particular, I will note a couple of differences:
Jerry wrote: 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? > Ben replied: BU: It has a different meaning. I'm not sure what you mean by "logical > meaning." The word "fought" has the same meaning in both sentences. Taken _ > *separately*_, each sentences has the logical form 'c fought d.' Maybe > that is what you mean by "same logical meaning." But if they're taken > together, (for example as in "Harry fought Peter or Peter fought Harry") > then one letter needs to be assigned to Peter in both sentences and the > other letter needs to be assigned to Harry in both sentences. I would consider "_ fought _" to be commutative, and there is no change in logical meaning, so long as the subjects are the same; in this case, Peter and Harry. With respect to "Cain kills Abel", this would not be commutative. It depends upon the predicate. It should be kept in mind though that logical meaning with ideas like commutative and associative and such typically refer to syncategorematic terms like logical addition, logical multiplication, etc. as we see Peirce describe in his improvement on Boole's Calculus of Logic, or in logical operators like conjunction and disjunction in modern symbolic logic. Another exchange: [JC] 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. > BU: I don't know. I would say, one can ask the question, but in order to answer it, one would have to define one's concept of order. If by order in grammar, you mean syntax, that is pretty clear. And if you said the same for logic, that is pretty clear. And likewise for mathematics. If we're talking about syntax. But in mathematics, at least, order could probably be considered as something other than syntax; there's a lot going on in mathematics. In logic, at least, I know Josiah Royce defined logic as the science of order, and I'm sure one could say a lot about that. Anyhoo, what's the point of all this, Jerry? It's a vague statement you are making. Jerry wrote: 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! Where is this description in CSP's texts? Jerry wrote: 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). I'm not sure what you mean by "the identity of the term", nor do I follow your "ergo." I read 3.420-421, but I don't understand what I'm supposed to contrast it with. I don't happen to have a copy of Roberts's book, so you'll have to help me out here. 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] Jerry, I'm afraid this is all quite over my head. I almost feel as though I'm reading something straight out of Hegel at his most abstruse, and that is saying a lot. Now, setting aside the general confusion I feel from having read your post, it seems to me that you are all along trying to get at the issue of the meaning of terms. I don't understand at all why you felt the need to go to grammar, especially since you don't appear to mean speculative grammar. Or at least, when you reference grammatical nouns, it seems clear. I am somewhat wondering whether you waffle back and forth between the grammar of a natural language and speculative grammar. The discussion of logical quantities, in particular with respect to the meaning of terms, is, I think, a way of getting at the logic of terms. I'm not sure, but my guess is that you want to contrast the idea of a term as a unit of measure (or meaning?) with the idea that terms have logical quantity, or what? Some clarification would be helpful. Btw, at least according to Whately in his Elements of Logic, the Introduction (edition I am reading is from 1853, available through Google books), it was Antisthenes who introduced simple terms, along with propositions and arguments, and the Stoics picked up the distinction from him between simple terms, propositions, and arguments. I would not be surprised to learn that the word "term" itself was not used until Peter of Spain, but the idea or concept of "term" was around longer than that. --Franklin On Mon, Nov 9, 2015 at 1:56 PM, Jerry LR Chandler <jerry_lr_chand...@me.com> wrote: > 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.) >
----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
