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With respect to the role of “existence”, this concept varies widely in different disciplines. As is often the case, I find John Sowa’s views to be troublesome because of the over-generalizations. While the concept of “generalization” is often a necessary presupposition of mathematical practice, it is often deeply constrained in the meaningful sciences that create meaningful proposition that can be tested. > On Apr 28, 2020, at 10:26 AM, John F. Sowa <s...@bestweb.net> wrote: > > The point I'm making is true of every branch of experimental science and > engineering practice. That includes chemistry, which is the first branch > that Peirce studied in detail. The formal logic of chemistry uses symbols for chemical elements as signs for the existence of matter (with specific semiotics predicates.) Since the facts of the chemical table of elements became known in the early 20th Century, each and every sign for a chemical element is a quantification of the predicate, the atomic number. The chemical table of elements enumerates all the known elements. The triad, chemical element, atomic number and a set of physical attributes, is the basis for the formal logic of the chemical sciences. Chemical equivalence relations are expressed in these technical and related terms derived from human sensory experiences. CSP used such chemical terminology frequently in his writings, chemistry was the “bedrock” of his philosophy and was a source of his terminology for graph theory. The concept of a sign, such as the “existence” sign, introduced in the late 19th Century by logicians (Peano?), is NOT used in the formal logic of chemistry. Furthermore, the “existence” sign is NOT essential to any mathematical calculations with numbers and the usual operands and operators of arithmetic. However, if one desires to express non-Peirician notions of continuity, one can extend the language of arithmetic calculations by postulating that equivalence relations are defined by reflexive, symmetric and transitive relations and that these terms are related to both continuity and arithmetic. The mathematical notion of the existence of an equivalence relation is an abstract theory. Because some readers may not appreciate the nature of the distinctions between scientific abstractions and mathematical abstractions, a simpler assertion is as follows: The notation for the chemical sciences expresses human sensory experiences, is pragmatic, realistic and grounded in laboratory experimentation. The notation for mathematics is artificial, the notation is not pragmatic, it may or it may not be realistic. In other words, the triad, Qualisign, Sin-sign and Legi-sign do not logically depend on the mathematical notion of existence. Semiotics is first ground in the sensory experience of the symbol-makers who create these three terms and there meanings. I conjecture that it is necessary (Tarskian) to use three (Whiteheadian) processes, semiosis (Peircian), mereosis (Lesniwskian) and matheosis (my term) to relate the formal logical concept of chemical existence to the formal concept of mathematical existence. (See the paper by John L. Bell, Axiomathes, 2004 for categorical hints about the meaning of this conjecture and its relationship to Peircian notions of identity.) Cheers Jerry
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