Lists, Howard: (This post contains numerous technical arguments that are probably inaccessible to many philosophers of the sort described by Gary F. as "too abstruse for a simple backwoods scholar".)
In answer to your question, I think you are missing the whole point of this endless exchange of philosophical discourse. All graph theory representations are intrinsically triadic in the sense of the propositional logic of terms. That is, two endpoints and the sign of a mathematical connection between the two is a direct representation of three signs on a "sheet of assertion". It boils down to a simple distinction which CSP described in his letter to Lady Welby. This distinction is between the notion of a dyad as an order pair (in the sense of set theory); and, a mapping as a triad in the sense of category theory or topology as mapping of a function between a domain and a range, (three terms, not merely a pair of terms in the sense of set theory). (BTW, this is precisely one of the reasons for my construction of a "perplex number theory" from the theory of units. See the recent API paper by Johanson http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4904611.) These (dyads and triads) are two distinct representations of a logic proposition. (Clearly, Federick struggles with this distinction.) The first notion of an ordered pair, in the set theory sense, is restricted to a conceptualization of a variable. The second notion of a mapping, in the categorical sense, is necessarily a triadic relation because it requires a denotation of which copula is essential to creating (generating, formulating, geometrically distinguishing), the predicate. A COPULA IS NOT necessarily A PREDICATE Sung's thinking also appears to be hopelessly contorted by this distinction between a copula and a predicate. This distinction is essential to describing the "difference that makes a difference" between a mathematical relation and a chemical relation between two signs as representamen of two elements. But Sung appeals to his freedoms of representations as justifications for his strange propositions. CSP grasped this profound logical distinction between the logic of chemistry and the logic of physics but lacked the experimental evidence needed to make a compelling argument in terms of numbers and arithmetic operations. The mathematics of perplex number system resolves this issue. IMHO, your beloved colleague, Robert Rosen, also failed to grasp this logical distinction and was led astray into a mathematical and scientific no-mans-land from which he never emerged back into the community of mathematics. Gary F. hits the nail on the head with his comment of 12/16/ 2014 at 6:01Pm with his comment: "I'm afraid your question is too abstruse for a simple backwoods scholar like me." This is an extremely subtle argument which did not escape CSP but does escape many of his followers, as Gary F. notes. If your wish to think about these concrete propositions more deeply, I suggest you approach these logical terms from the perspective of the mathematical accounting for both qualia and quanta. My personal experience is that CSP language usage attempts to separate qualia from quanta but fails to achieve this scientific objective because compelling factual arguments were yet to be observed. All of this is, of course, merely my opinion. I welcome your alternative propositions. Cheers Jerry Addendum: I just read Jon Awbrey suggestion (12/16/ 2014) that: "In the best mathematical terms, a triadic relation is a cartesian product of three sets together with a specified subset of that cartesian product." This suggestion conflicts with the conservation of charge and the conservation of matter principles of physics relative to the atomic numbers. Just consider the eqn E = mc^2 with respect to the simple equation "Hydrogen + Oxygen" generate Water. (This chemical statement requires both ellipsis and syllepses to interpret the facts of measurements.) Cheers JLRC On Dec 16, 2014, at 7:58 PM, Howard Pattee wrote: > At 02:07 PM 12/16/2014, Gary Fuhrman wrote: >> The reason that "people keep saying you [Edwina] support dyads" is that your >> three "relations" have only two "members" each, to use Peirce's term. A >> triadic relation has three members, not two; and a complexus of three dyadic >> (two-member) relations is not, according to Peirce, "a triadic relation." > > All these claims are unclear to me. Why are these two descriptions > inconsistent? Is there a graph theory representation of a triadic relation > that does not have a dyadic subgraph? > > Howard > > > > > ----------------------------- > 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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