List, Gary: > On Sep 12, 2021, at 10:44 PM, sowa @bestweb.net <s...@bestweb.net> wrote: > > GF: as I said in my post this morning, formal logic produces explicit > formulations (which may include “letters of the alphabet” as symbols of the > variables). But the phaneroscopist’s attention would be distracted from the > basic task of phaneroscopic analysis if he had to pay conscious attention to > such formulations.
I believe that this sentence has unbounded potential to mis-lead the naive reader about the logical interpretations of mathematical terms and chemical terms in CSP’s writings. An assertion about the meaning of a symbols and/or icons lies deep in CSP’s conundrums that address the philosophy of realism in contrast to nominalism. Let me explain. Aristotle (as I understand it) introduced the notion of a letter symbol as a representation for any sin-sign. The modern usage of a letter symbol as a variable lies at the heart of mathematical generalizations and Tarski’s truth functions. For discrete variables, the meaning of a letter symbol is that it can represent any conceivable numerical value. Repeat: ANY. The grounding logic of arithmetic rests on this premise. On the other hand, the formal science of chemistry also uses letter symbols as representations of chemical elements. In sharp and distinctive contrast with the mathematical logic of letter symbols, the chemical letter symbols, such as I, K, O, N, S etc represent one particular species of matter. This species is also represented (equally exactly) with a particular number and with an indefinite range of categorical physical attributes. The grounding logic of chemistry rests on the identity of the species and this species symbol is preserved for all chemical relationships, e.g., molecular formula, molecular structure, molecular handedness, and, most notably, molecular number. Thus, the difference between the mathematical usage of a letter symbol and the chemical usage of a letter symbol is the distinction between the logics of generalities (nominalism, constructivism) and the logics of species (realism, chemical elements, biological species, human individual identities) It is of interest to compare the meaning of the two forms of symbols, for example, “golden" in contrast with “twoness” or “secondness”, iconicity in contrast with quantity without quality. In the “simplest” mathematics, CSP is probably referring to latter usage of the ambiguity of the meaning of a letter symbol as a potential source of iconicity, (creating new images or ideas or thought or patterns or diagrams.... Cheers Jerry BTW, some years ago, in a series of posts, I critiqued John Sowa textbook which sought to relate AI to the trichotomy. At that time, I failed to recognize the origin of the concepts presented above because the logic of chemistry was not yet formally developed.
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