Jon: > On Feb 10, 2021, at 7:44 PM, Jon Alan Schmidt <jonalanschm...@gmail.com> > wrote: > > JFS: In mathematics and logic, equivalence means freely interchangeable in > all contexts without any change in meaning. > > No, it means freely interchangeable within a particular formal system. In the > context of classical logic, which treats the universe of discourse as > individual, a scroll is indeed equivalent to and interchangeable with nested > cuts/ovals. Nevertheless, as I demonstrated with Shafiei's example of ex > falso quodlibet > (https://list.iupui.edu/sympa/arc/peirce-l/2021-02/msg00019.html > <https://list.iupui.edu/sympa/arc/peirce-l/2021-02/msg00019.html>), the same > classical EG with nested cuts/ovals can have multiple natural-language > translations, which is not the case when scrolls are employed instead. After > all, does someone really mean exactly the same thing when saying "if A then > B" as when saying "not both A and not-B"? Peirce certainly does not think so. > >
While I agree with your assertion, Jon, in realism, the situation is more highly constrained than this paragraph alludes too. CSP may have used the bedrock logic of chemical radicals to construct the logical distinctions among natural nominative objects (plural individuals) in order to construct the perplex predicates of meaningful abstract sentences. This is necessary to copulate the individual abstract symbols from the many to the one; that is, from atoms to a molecule, or, another words, from n individual distinctive atoms to a single polyatomic molecule. Within the possible patterns of “n” individual terms of a composite sentence, the natural logic may need to make specify a specific unique pattern for all n terms. That is, “a" is here and not at any of the other n-1 locations, “b” is there and not at any of the other n-2 locations, “c” is over there and not at any of the other n-3 locations, “d” is opposite of “c” and not at any of the other n-4 locations. And so forth to any arbitrary large n. These logical assertions were well known to CSP under the guise of the handedness of molecules such as described by Pastuer and by van't Hoff and LaBel. Thus, such assertions are necessary but not sufficient to copulate the nominative forms of the numerical information as antecedent to the pragmatic consequences predicated by the indices of “n”. In the chemical sciences, these locative logics are organized into a scientific logic of valence and handedness and are components of the standard scientific methodology of today. >From the perspective of CSP logical trichotomies, these forms of negations are >essential. And necessary to relate and to copulate the indices of the sin-sign >to the legi-sign via the dicisign. Copulation makes chemistry attractive, fun and creates natural sorts and kinds. Under thoughtful planning of contexts, repetition is habit forming and reproducible. Cheers Jerry
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