Frank, Ben, List:
On Nov 11, 2015, at 4:52 PM, Franklin Ransom wrote: > This is all to say that I'm not entirely sure what Jerry want to get at with > talking about "units of measure", and if by that he means something other > than the information conveyed by signs; and in particular, terms. As is often the case, communication between different disciplines often go awry. In this case, my comments reveal a deep split in the concept of units (and union of units). I am referring to systems of logical thought and the symbols that were used by CSP to bridge pragmatism to mathematics. (These symbols are artifacts of thought.) For the philosophical context of the units, I recommend: Aristotelian-Thomistic Philosophy of Measure and the International System of Units (SI): Correlation of International System of Units With the Philosophy of Aristotle and St. Thomas by Peter A. Redpath (Author) The concept of units of measure is of one of the fundamental concepts of the natural sciences and related applied mathematical subjects, such as economics. This topic is of particular concern to CSP philosophy as he spent several years working on measuring gravitational units and their integration into physical unit systems in the 1870 - 1880s. The concept of discrete units is the unstated pre-supposition underlying CSP Graph theory. A unit is a measure of one thing relative to other things. While units have proper names, systems of units relate these proper names in well-defined ways such that the calculations are consistent, complete (hopefully) and generate an exact decision. Very, very often, CSP writes in terms of "units" rather than in terms of mathematical variables or modern set theory. The basic physical system of units are all related to one another. (Think metric system) They are: mass, distance, time, temperature, brightness of light, electricity and mole. Physical calculations are all based on these units or further definitions of relations among these units. see: http://physics.nist.gov/cuu/Units/units.html The basic logical chemical units are the the individual chemical elements. All chemical calculations are based on these units. The related chemical units include molecules, molecular weight, molecular formula, molecular structure and molecular number. (I introduced the logical term "molecular number" for the logical operators linking (connecting) atomic numbers, valence (electricity) and graph theory (mathematics)) The basic biological units are individual species and Linnaeus's hierarchy. In set theory, each element is a unit of a set (except for the empty set ) and a union of units is a set or class. That is, a union unites the elements. (Think Venn diagrams.). The class resulting from the union is a unity. Thus, the assertion: "The union of the units unites the unity" is a statement about forms of symbolic addition. In particular, this assertion applies to arithmetic addition as well as addition of atoms to beget (emergent) molecules. But these few words are remote from the origin of this thread. The question of the grammatical relation between "distinction" and "information" was the motive force that caught my eye. In this regard, the name of the unit confers the objective information content of the unit. In simple terms, the name of an atom conveys the unit of addition for that atom. The union of atoms, each with an atomic number, confers the molecular number by addition of the parts of the whole (mereology). Note the profound distinction between the verbs in these two sentences! In this sense, within the logic of chemistry, "conveys" infers a predicate relation in contrast to "confers" which infers a copulative relation among the atoms. I will address Ben's response separately. Cheers Jerry > Tom, Jerry, Ben, list, > > I don't think Ben observed that fighting someone does not mean the second > party is fighting back; I take Ben to have admitted that the predicate could > be understood in the way I discussed. He merely mentioned that he had been > used to thinking of it as non-commutative due to a particular context in > which he thinks of fighting. My own context of understanding has to do with > years of experience as a wrestler, as someone who fought with his brother on > many occasions (and not usually in a physical way), and as someone who has > made a study of military strategy and read a great deal of military history, > in which diplomatic strategies of persuasion are seen to play a surprisingly > important role as counter-moves against aggressive actions when a struggle > ensues. I understand that Tom doesn't want to think of himself as the kind of > person who gets into fights, but since Tom didn't run away from the fight, > and instead aimed to meet the physical violence with a strategy of his own to > win, Tom did in fact fight, just not with his fists. That's the way I think > of it. > > But really, it's just a question of semantics as to what definition we want > to agree to for what fighting is, and I think one could argue endlessly for > either interpretation. The reason I thought the commutative or symmetrical > aspect of the predicate important is because Jerry sought to juxtapose "Peter > fought Harry" with "Cain kills Abel". Pretty clearly, Abel isn't doing any > killing, so it's one-sided, with Cain acting as agent and Abel as patient. In > "Peter fought Harry", it's not necessarily the case that Peter is agent and > Harry the patient; Harry might well have been the one to instigate the fight. > We simply don't have more information to go on, other than that a fight took > place, and two subjects were involved somehow. If Jerry meant something else > by juxtaposing the two propositions, it would be well if he clarified what he > felt his point was by so juxtaposing them. > > Now the point about chemistry is interesting in itself, and I thank Tom for > pointing out something about the import of Jerry's post that I had missed. > However, I am not sure this affects my response to what Jerry had to say. > Since I have been discussing the logical quantities involved in any term, I > already admit that terms are not simply indeterminate signs that simply act > as placeholders in propositions.( Moreover, since the idea of logical > quantity has been around for millenia, developments in chemistry clearly are > not responsible for their introduction into logical theory.) Rather the > import of a proposition depends upon the import of the terms. But as is > famously known, there are certain relations that can be studied in logic > regardless of the terms involved, so not everything depends upon what the > terms are, only that there are terms. Now, If we wanted to discuss the > 'logic' of the oxygen atom, I would take it that first of all we would have > some information about the characters that are ascribed to oxygen and about > all the real things that oxygen applies to. Then we might want to consider > oxygen's relations with other kinds of atoms in the form of propositions and > arguments, and we know propositions and arguments have their own information. > This is all to say that I'm not entirely sure what Jerry want to get at with > talking about "units of measure", and if by that he means something other > than the information conveyed by signs; and in particular, terms. > > -- Franklin > > On Wed, Nov 11, 2015 at 12:23 PM, Ozzie <[email protected]> wrote: > Franklin, Jerry, Ben ~ > >> 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? > > > This issue is more straightforward if instead of 'fought' one compares "Harry > punched Peter" and "Peter punched Harry." There's clearly a big difference > between those two statements. > > As Ben observed, 'fighting' someone (or something) does not mean the second > party is fighting back, or even aware the first party is fighting. The one > Harry is fighting may be indifferent, far away, already dead, not yet born, > or mythical. In "Harry fought X," the fight was Harry's to define. Harry > acted, so Harry decided, so the logic is that of Harry. > > A semantic shortcut doesn't resolve the matter. Saying that a verb between > the names of two people ("A fought B") is 'commutative' carries its own > logical burden. Most verbs are not used that way, after all. The > commutative interpretation of 'fought' requires observers and listeners to > assume, without explanation, that Harry and Peter exhibit > symmetrical/complementary behavior. Making this assumption explicit permits > its accuracy to be tested, and its other implications to be deduced. The > commutative verb conceals any difference between Harry's logic and that of > Peter -- as though no relevant difference could exist between two people. > > (I offer empirical evidence against the commutative verb: Long ago in high > school, a fellow named Jack decided to fight me. He threw two punches, while > I threw none. Instead, I talked to him (in a persuasive manner). Jack > fought Tom, but Tom did not fight Jack.) > > Now, if both Peter and Harry are fighting, when the observer uses 'fought' > after one name instead of the other ("Harry fought Peter"), that phrasing may > indicate (or hint) to a listener that Harry initiated the fight. It may also > reflect an affiliation between Harry and the observer, the outcome of the > fight, or the observer's belief about the loyalties of the listener. > > If the battle is mutually engaged in by Harry and Peter, and if the observer > is informed and impartial, then neither "Harry fought Peter" nor "Peter > fought Harry" would be incorrect, but neither would provide a faithful, > unambiguous account of the 'transaction' between Harry and Peter. "Harry and > Peter fought each other" is a neutral description. > > A recent comment by Jerry about the evolution of Peirce's thinking is > pertinent to this discussion. As Jerry noted, early in Peirce's career, the > will (logic) of the chemist dominated each compounding 'transaction' that > occurred in lab: "I add two parts of hydrogen to two parts of oxygen to make > water." The only Pragmatic logic was that of the (purposeful) chemist, while > atoms were perceived and manipulated within a semiotic context: A+2B = 2B+A > = C. > > Later, as Jerry noted, the new analysis and notation meant that each atom was > modeled as obeying its own logic. Then, chemical reactions were described as > optimizing (Pragmatic) responses by the various atoms to a change in their > environments. The logic of the principal actors -- atoms -- became > paramount; the logic of the chemist-observer moved to the sidelines. "In > close proximity their valence electrons synchronize, causing one hydrogen > atom to combine with two oxygen atoms, and they become water." > > If "Harry fought Peter," then only Harry is known (from the statement) to > behave purposely. Peter is present, but not animated by any known logic. > That is the old, non-Pragmatic chemistry. > > Regards, > Tom Wyrick > > > > On Nov 9, 2015, at 7:46 PM, Franklin Ransom <[email protected]> > wrote: > >> 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 <[email protected]> >> 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 >> [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] > . 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