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Abstract, International System Science Society, Mini-symposium, May 25, 2024
A Hylomorphic Philosophy for the Perplexity / Complexity of the Medical Sciences
A simplified skeleton of a formal philosophy of scientific systems of thought will be briefly sketched. My motivations for this work emerged from methodological gaps that separate inorganic from organic reasoning such as the vast logical voids between representations of physical, biochemical, clinical, and epidemiologic data as exhibited by dose-response relationships. This hylomorphic analysis and synthesis cognitizes the semiotic, semic and semantic differences between the axiomatic formal grammars of mathematics / physics and the axiological grammars of chemical / biological / medical languages used to communicate the facts of life. The axiological grammars of scientific numbers, theories, concepts, observations, and theses can be formalized within the category of atomicity. The atomistic perplexity of semic, ontological and epistemological patterns of thought are constructed from logical particles (the table of elements), rather than geometric axioms. The semantic correspondence between the identity of concrete molecular formula (as perplex permutation groups) and the mathematical identity of axiomatic space groups inverts these two formal representations of material objects.
Advances in mathematical representation theory during the twentieth century, such as group and graph theory, can create a precise correspondence between the logical particles of atomicity and perplex number theory. The order of number symbols generated by Peano’s axioms are in one-to-one correspondence with the axiological order of the (perplex) atomic numbers. The relationships between inorganic and organic reasoning are generated by the cybernetical ordination of atomic numbers as arithmetic electrical units (perplex number compositions of organic structures).
A critical difference between the symbolic logics of quantitative grammars of axiomatic and axiological sentences is the meaning of logical connectives. Classical predicate logic lacks the symbolic agency necessary to compose the primitive (atomic) parts of systems into emergent copulated sentences (of the form “subject-verb-predicate”, in the sense of Leibnizian reasoning with diagrams) that are intrinsic to the representations of material processes.
S. Feferman (2014) proposed formally separating pre-logical and pre-mathematical terms from the grammar of mathematical logic. I propose that the perplex disciplinary languages of chemistry and molecular biology can serve as pre-logical and pre-mathematical objects for the formal composition of the constituencies of the medical sciences (as well as related sciences). My earlier work on the mathematical philosophy of the table of elements as a grounding for molecular and clinical data fits this form of reasoning as well as other formal axiological reasoning justified by semic theories of hylomorphisms. My earlier works include the following references.
1. J.L.R. Chandler, “Algebraic biology” Axiomathes, vol. 19(3), 2009, pp. 297–320.
2. J.L.R. Chandler, “An introduction to the perplex number system”, Discrete Applied Mathematics, vol. 157, 2009, pp. 2296–2309.
3. J.L.R. Chandler, “Is Life Logical? Application of the Peirce-Lesniewski-Tarski Meta-Logics to the Organic Mathematics of the Perplexity of Natural Sorts and Kinds, 6th World Congress and School on Universal Logic, 2018, pp. 496-500.