List, John: > On May 24, 2018, at 8:01 AM, John F Sowa <s...@bestweb.net> wrote: > >> JLRC Wrote: >> he foresaw the grammatical constraints in his (1860’s) >> specification of the breadth and depth of information. > JFS responded:
> Without seeing a quotation, I don't know exactly what you're > referring to. But the inverse relation of breadth vs depth > (also called extension vs intention or comprehension) is > as old as Aristotle. And it is usually called a semantic > relations, not a syntactic one. > One relevant passage is W4:381-382 (1886, Elementary Account of Logic of Relations) CSP associates the meaning of breadth and depth with the logic of relations. He does not mention either extension and intention wrt the Logic of Relations. The logic of relation provides for two different modes of extension, addition and multiplication. After noting the unusual arithmetic logic of Boole’s addition and multiplication, he asserts: "Logical addition is aggregation of logical breadth; that is to say whatever propositions that may be signified by x and y , x + y will signify that the proposition which is true if either x or y is true and is false only if x and y are both false.” Should one interpret this assertive sentence to be only a semantic assertion? “Logical multiplication is combination in logical depth; that is to say, xy signifies that proposition which is true only if x and y are both true and false if either is false.” Should one interpret this assertive sentence to be only a semantic assertion? He further distinguishes the notation by addressing the notion of equivalent propositions on p. 382. “that two propositions ought not be considered as equivalent unless every state of things in which either is true would be one in which the other would be true.” and develops an argument wrt to a Biblical /solar example. It is noteworthy that these remarks are different from his earlier position in the 1860s where he discussed breadth and depth from an informational perspective rather than a Boolean perspective. For further discussion of the notions of intention and extension, See M. Malatesta, Primary Logics, 1998? The separation of the concept of logical addition from the concept of logical multiplication is essential for the copulative logic of chemistry (partitions), the predicative logic of abduction, (valence?/chance?), the logic of synduction (choice) and the logic of perplex number system (closure under chance and choice.) This paper is much richer than these few remarks can capture. If time permits I will address more significant issues leaning toward philosophy. Cheers Jerry >> Peirce failed to grasp the notion of identity in chemistry, >> even in its logic form of 1890-1910. > > The first-order subset of his existential graphs have an exact > mapping to and from his 1885 algebraic notation for FOL. > > I'm not aware of his discussions of "identity in chemistry". > Could you quote an example?
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