List, John: My thoughts were on a different pattern of syzygy. Comments after your post and after your slide. You will note that I am being very very picky in these comments. This is because CSP logic, which he repeatedly said was based on chemistry failed and the reasons why it failed to represent chemical logic now very clear, at least to me. The root cause of his failure is that the grammatical and scientific representations of chemical relations require both copulated and predicated terms.
In a certain sense, he foresaw the grammatical constraints in his (1860’s) specification of the breadth and depth of information. > On May 22, 2018, at 3:27 PM, John F Sowa <s...@bestweb.net> wrote: > > On 5/22/2018 1:22 PM, Jerry LR Chandler wrote: >> Of particular interest is Venn’s views on the role of “=“ sign. Copula? Or >> predicate? >> Or, in view of symbolization of the modern logic of set theory, should the >> “=“ sign be banned altogether? > > Wittgenstein's answer in the Tractatus is simple: The notation > "x=y" is not a relation between two things. It just says that > 'x' and 'y' are two names for the same thing. > > With his existential graphs, Peirce represented full first-order > logic with equality without having any sign for equality: he just > connected two or more lines of identity. > > With EGs, Peirce resolved the claims by Frege and Russell about > the supposed ambiguity of the word 'is'. See slide 26 below. > > Re banning '=': There is no reason to ban anything. To use > Wittgenstein's (later) terminology, languages, natural or > artificial, can be used to play an open-ended variety of games. > For any pair of language games, there may be some subsets that > can be translated accurately, and other subsets that have no > accurate translation to the other. > > John In my opinion, Wittgenstein was, is, and will be scientifically incoherent. This is a bit of an exaggerate, but perhaps a phrase expresses it better. "Local thoughts only.” Proclamation after proclamation after proclamation… great narratives, but meaningful? This point of view is historically irrelevant. Venn quote from 1880. (Just opinion!) Peirce failed to grasp the notion of identity in chemistry, even in its logic form of 1890-1910. But, indeed, his notion of identity as not a single sign or single thing was ground-breaking and consistent with later developments in physical chemistry. As an aside, How does one grasp the notion of mathematical identities, even in category theory, in light of CSP’s “line of identity”? While I understand the logical motivations of your slide, I do not find the argument to be compelling. See notes below. Cheers Jerry > __________________________________________________________________ > > Slide 26 of http://jfsowa.com/talks/egintro.pdf > > Translating the Word 'is' to Logic > > Three different translations in the algebraic notation: > ● Existence: There is x. iff ∃x > ● Predication: x is a cat. iff Cat(x) > ● Identity: x is y. iff x=y > Strange sentences to me. Three different definitions or intentions of usage? Do you mean “transliterations” rather than translations? > Do these three translations imply that English is ambiguous? > Or is the algebraic notation too complex? > > In EGs, all three uses of the word 'is' map to a line of identity: > ● Existence: There is x. ↔ ▬ > ● Predication: x is a cat. ↔ ▬Cat > ● Identity: x is y. ↔ ▬▬ (a ligature of two lines) > To me, from a notational point of view on the necessity of forming crisp notations for signifying unambiguous meanings, the example clearly shows why CSP notion was not adopted. After all, the concept of identity is one of specification. A line is a line is a line. CSP’s line negates the very concept he is attempting to represent, that is, specification of individuality. For example, the supposed “ligature” of two terms is not shown in the identity component. If identity is merely length, how does it relate to addition, if at all? > As Peirce said, EGs are more iconic than the algebraic notation: > they relate language to logic more clearly and directly. > Well, some may find this conjecture to be persuasive.
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