List: (This post is rather technical and the contents may be intractably perplex for many readers of this list. One purpose of this post is to crisply separate the fundamental philosophical concept of identity from the mathematical concept of identity. To differentiate CSP view of lines of identity from classical views, see McGinn’s, Logical Properties, 2000, OUP Chapter 1, p.1-14, Identity, for an overview of one philosopher’s notion of “Identity" )
> On Apr 13, 2017, at 8:14 AM, g...@gnusystems.ca wrote: > > But even from the fragment published in CP 1.343-9, one can glean some of > Peirce’s key insights on the subject, given some slight acquaintance with > existential graphs. In graphs such as the one at 1.347, the lines (Peirce > calls them “tails” here) are lines of identity each representing that > something exists. The relation is represented in the graph by the labelled > spot to which they are all attached, and the three “tails” are the relata. In > propositional terms, the graph represents a predicate (the spot) with three > subjects, (i.e. with a “valency” of three). To read the lines in the graph as > relations is to misread the graph. The graph is itself a diagrammatic sign, > but there is no attempt to represent its object(s) or its interpretant on the > sheet of assertion. In fact, I have never seen, anywhere in Peirce’s > writings, an attempt to represent the basic triadic sign relation in a single > diagram. I think the reason is simple: thatkind of triadic relation cannot be > represented that way. But if someone can show me a text where Peirce has done > that, I’ll happily retract that claim. > > This would explain, by the way, why it is that Edwina “can't 'imagize' what > 'one triadic Relation' would look like or how it would function.” If you > represent relations as lines (or “spokes”), you can only represent dyadic > relations. Then Peirce’s graph can only appear to you as a triad of (dyadic) > relations. > I think Gary’s conclusion is problematic because of the the way CSP uses the concept of identity in chemistry as a basis for his concept of identity in logic and / or mathematics. First, a bit of historical context for the emergence of CSP’s view of lines of identity in relation to concrete signs and symbols in applied mathematics and graph theory. CSP's early writings (1860’s, 1870’s) were very accurate representations of the facts of chemistry as they stood in his day. But, following the Karlsruhe Conference of 1861(?), the relationships between chemical symbols and chemical signs underwent rapid development during the remainder of the 19 th Century with three major changes. With the development the electrical structure of atom (1913) and Quantum Chemistry (Schodinger, 1926), and Pauling’s notion of the mechanics of the chemical bond, further profound changes in the logic of chemistry emerged in the 20 th Century. The three major changes following the 1860’s were: 1. Acceptance of the concept of atom identities as separate units conjoined by a chemical bond, forming the relations WITHIN molecules with clear and distinct IDENTITIES different from atoms. 2. Acceptance of the notion of Kekule’s aromatic compounds, benzene, etc. forming cyclic compounds, that is, chemical IDENTITIES with cyclic graphs. The concept of aromatic compounds also modified Dalton’s notion of valence of whole numbers to include fractional valences of ratios of numbers. 3. Pasteur’s separation of molecules with IDENTICAL atomic identities into the optical isomers of D and L tartaric acid with separate physical IDENTITIES. The tetrahedral carbon atoms of tartaric acid must be fitted onto a Procrustean bed in order to maintain a triadic view of chemistry. The fitting process is logically simple. Simply assert that four relations is a combination of three relations. This is his famous reduction hypothesis. It is critical to observed that: the first of these is change in the meaning of chemical signs in relation to chemical symbols; the second of these is a fundamental abstraction about the relationship between atoms and geometry; the third of these is a deep conundrum that DISASSOCIATES the symbol system of chemistry from the symbol system of physics. Thus, these three conceptual scientific break-throughs all extended the notion of chemical identity to aspects of graph theory. Were these concepts the origin of CSP’s views on the supreme importance of identity in the logic of his “chef d’oeuvre"? In Robert’s “The Existential Graphs of Charles S Peirce”, (1973) p. 25, Figures 5 and 6, (3.469 and 4.561) two apodeictic representations of the forms of triadic relations are presented for scrutiny and analysis. The linguistic sentence "John gives John to John” is contrasted with the sentence of a logical graph for ammonia. Is this an adroit usage of the procrustian bedding process to seduce the reader to believe that triadicity has a universal meaning in logic and science? This line of reasoning is further illustrated in the grammar of forming a rheme from icons by invoking the chemical notion of “unsaturated" valences (3.420 and 3.421, Robert’s p. 22). CSP asserts that “Every proposition has one and only one predicate” (4.438) and richly illustrates his view of linguistic theory (Robert’s, p. 114.) Is this another Procrustean bed? In my mind, I am left with an intractable question: Is a Procrustian Bed essential to understanding the role of the identity relation in CSP’s theory of logical graphs of relations? Or, is a semantic explanation possible? Gary F: How do you interpret your views of triadic relations in reference to the citations from Roberts work? Cheers Jerry . These three historical developments forced CSP to attempt to place the facts of chemistry into fabric of mathematics.
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