List, Amando from my post of Mon, 07 Aug 2017 11:07:46 -0500
Consider the meaning of the chromaticity (spectra) of 1,2,3… A, B, C,… H, He, Li, Be, B, C, N, O, F, Ne,… A, B, C, D, E, F, G, A, B, C, D, E, F, G, A, B, C,… (musical scales) nad A, nad B, and nad C, etc, (genetic symbols with closure over a set of genetic symbols that represent the potential of inheritance of the genome) Each of these five symbol systems is an accepted social symbol system that is used publicly in everyday communication and by different academic tribes. The factual meaning of the latter three symbol systems are established by factual (reproducible) observations from objects. ------------------- In off-line discussion, Professor Sercovich has requested further discussions of unpublished works. In particular, I submitted a lengthy abstract (which has now been accepted) to the 6 th World Congress. A shortened version will be submitted for publication. The abstract is reproduced below (with typos corrected.) The notion of “emanations” (vibrations) was re-expressed in the modern terminology of “chromaticity”. The term “emanations” plays a critical role in bridging the logical gaps among the symbols of mathematics, physics and chemistry. I suppose that the technical language will be off-putting for many readers. Nevertheless, I decided to post it here because it is may motivate some readers to open new pathways of interpretations of CSP writings on the informational units of logic in relation to the syzygy (compositions) of grammars. Obviously, I welcome comments on this approach to bio-logic. Cheers Jerry Abstract, 6 th World Congress on Universal Logic Is Life Logical? Application of the Peirce-Lesniewski-Tarski Meta-Logics to the Organic Mathematics of the Perplexity of Natural Sorts and Kinds. Jerry LR Chandler, Ph.D., Research Professor, Krasnow Institute for Advanced Study, George Mason University. Fairfax, VA USA Email address: jerry_lr_chand...@mac.com Is life logical? Here, I propose a categorical approach to numeric combinations that unite several formal logics for the purpose of scientific analysis of natural sorts and kinds. In order to represent the novelties of organic objects, this logico-scientific strategy generates novel propositional forms for numbers representing natural sorts and kinds. The collective logics of these novel grammatical sentences are graphically represented within the perplex number system (Chandler, 2009). These novel propositional forms require both copulative and predicative conceptualization of scientific terms in order to inform imperative numerical relations of addition. The logical compositions of the novel sorts and kinds of numbers stand in one to one correspondence (mappings) with the parts of atoms. From this logico-scientific perspective of natural sorts and kinds, meaningful sentences necessary contain both grammatical and numerical elements in order to generate representations of organic mathematics are empirically represented in propositions relating the denotations and connotations of antecedents and consequences. The predicative symbolic terms must inform the denotive predicative symbolic changes and the copulative symbolic terms must inform the connotative copulative changes. The terms in the propositional equations of organic mathematics must be informed by the abstract scientific units of physics, chemistry, biochemistry, genetics, medicine and other associative disciplines. The guiding compositional principle for validating propositions of organic mathematics is simply stated: The union of units unites the unity. The formal logic of the union of scientific units is constrained by the empirical meanings of the scientific symbol systems used to represent natural sorts and kinds. The several notational systems used to represent natural sorts and kinds emerge coherently from the additive logic of the perplex number system (Chandler, 2009, 2015, 2016). Perplex numbers have meaning. From this logico-scientific perspective of information, the compositional logic of scientific forms emerges from the physical attributes of electricity and the atomic numbers. (The traditional geometric forms of mathematical physics can be inferred from organic mathematical terms by merely changing the informational content of the representational metric spaces.) But, the scientific meaning of perplex propositions is only achieved by validation of indicative antecedents to generate an imperative consequent. Within the historical constraints of the scientific symbol systems emerging from empirical scientific observations, a union of the distinctive formal logics of the inorganic sciences inform a set of terms for forming the logical and structural attributes of the organic sorts and kinds. The meaning of perplex numbers is encoded in scientific symbol systems. Within this logico-scientific formalism, the propositional sentences for forming organic entities from inorganic entities representing novel electrical relationships among the electrical parts of the whole. The antecedent parts are represented by symbols for mass and electricity and the consequential whole is also represented by mass and electricity. Organic forms emerge from inorganic forms by creating new species of electrical connections. The scientific necessity for conserving the symbolic meanings of both categories of terms infers combining both copulative and predicative logics for all propositions representing natural sorts and kinds. This novel form of scientific logic was named synduction (Chandler, 2009). The associated philosophy of science is called perplex systems theory. The essential distinction between synduction and other logics is that the grammar of synductive propositions must relate the copulative and predicative terms representative of the semiotics of the natural entity in order to correspond with empirical scientific symbols deduced from its natural emanations. Precursors of the combinatorial structure of the perplex logic of synduction were described by C. S. Peirce (1839-1914), S. Lesniewski (1886-1939) and A. Tarski (1901-1983). A rudimentary relational logic for interpreting the emanations of natural sorts and kinds was formulated by Peirce’s hypothetical method of constructing propositions from emanations (CP 2:230). The formal logic of perplexity aligns the inorganic attributes of the atomic numbers and the forms of mathematical graph theory as is suggested by the relational logic of parts of wholes as suggested by Lesniewski. The necessity of combining symbolic logics is intrinsic to representing multiple symbol systems as is suggested by the conceptual relations between scientific symbol systems and Tarski’s meta-languages. Synductive logic draws on these three conceptual notions of relational logics to create new species of relations in order to organize the parts into wholes (e.g., atoms into molecules). Logical arithmetic operations on the primitive inorganic terms combine predicative terms non-linearly. The combined primitive terms create an emergent whole with the concomitant manifestation of new natural emanations. The copulation of the parts of the whole is expressed as a novel grammatical identity of a natural sort or kind. (For examples, the masses of hydrogen and oxygen are combined in the emergent structure of the whole, water, the masses of carbon, hydrogen and oxygen are combined in the emergent structures of carbohydrates and lipids, the masses of carbon, hydrogen, oxygen and nitrogen are combined in the emergent structures of nucleic acid bases and the masses of carbon, hydrogen, oxygen, nitrogen and sulfur are combined in the emergent structures of proteins.) Organic mathematics requires the semantic naming of each unique organic identity in order to be consistent with the species of emanations, the specific patterns of the isomeric copulative unions and the specific emergent physical predicates that are created by copulative unions of parts to become wholes. Consequently, the synductive logic of the natural union of atoms to form molecules differs from B. Russell’s abusive metaphor of combining atomic sentences to form molecular sentences. The concept of the natural association of inorganic electrical particles (e.g., atoms) by copulation (e.g., bonding) into molecular patterns parallels logically the concept of association of terms in propositional sentences. The Tarskian difference that makes a difference between Russell’s logic and synductive logic is the difference between a simple grammatical conjunction (“and”) and a physical combination (“bind to”) expressing the logic of stable electrical forces intrinsic to the relations among atomic numbers. Scientifically, the abductive copulative / predicative statements representing the mapping from atoms to molecules are combined into exact equational forms that are subject to direct empirical verification. Scientifically, a three-fold verification of perplex propositions is required. The first verification denotes the parts of the whole as a composition of atomic numbers such that these specified parts connote the abductive substrates of compositions. The second verification connotes graphically the composition of adjacency relations among the parts of the specific emergent identity. The third verification, which is essential for bio-organic molecules, denotes the three-dimensional electrical arrangements of all the parts of an entity (e.g., the handedness of amino-acids, carbohydrates, nucleic acids, etc.) These empirical validations inform the change of the verbal propositional mood from terms indicative of parts to an imperative term (or terms). Perplex logic links the scientific disciplines by the composition and decomposition of the anatomies of scientific terms (units). The three-fold logical processes of perplexification associate the connotations of the methodical approach to forming symbolic propositions of C. S. Peirce and logical meta-languages of Tarski with the denotive organic mathematics of the atomic numbers concomitantly with propositional terms consistent with Lesniewski concept of denoting part-whole relations. The mathematical concept of partitioning plays a central role in the scientific symbolic representations of assembly and disassembly of natural sorts and kinds. The units of union and disunion are the perplex numbers and networks of relations. Deductive propositions can denote the mapping processes that disassemble the anatomies of larger units into smaller units, such as the atomic numbers. The perplex number line aligns abductively the partitions of all integers with the natural parts of wholes. The perplex number spine associates abductively with each partition a specific set of all possible three-dimensional arrangements of natural sorts and kinds (denoted by electrical particles, atoms, molecules, viruses, cells, organs, organ systems and all higher organisms). The perplex number spine is a line of potential infinite length and a potential infinite number of organic branch points. Each and every organic object associates with an enumerable organization of its electrical parts. Each integer number is associated with a partition of an integer and a perplex mathematical graph that associates the specific electric parts of the whole. The perplex partitions of integers are associated with the labelled bipartite graphs composed exclusively from atomic numbers (Chandler, 2009). A living system can be decomposed by partitioning into anatomical structures, each part connotes a semeiotic identity as a term of natural language. Iterative partitioning of natural sorts and kinds decomposes the whole into simple integer units, the atomic numbers. The equivalency of the relational logic paths of composition and decomposition validate the synductive logic of “proof of structures” for entities arranged along the perplex number spine as structural units and as potential emergent dynamic units, under the constraints of the mass and the electrical laws. The two physical symbolic forms of combinatorial logics of identity (mass and electricity) are used concomitantly to construct deductions from inductive and abductive hypotheses about natural sorts and kinds (scaling). The partitions of anatomical structures of natural sorts and kinds are scaled into collections of forests of the symbolic graphs of perplex numbers. The composition of relations emerges from the electrical relations among the anatomies of the parts. The form of the relations emerges from the electrical forms of the perplex numbers. The number of relations between parts is a function of symbolic language selected to represent the natural sort or kind. In the case of the very simple chemical symbols, the number of relations gained or lost is a simple exact electrical calculation. The interdependencies between the alternative propositional terms for partitions are inferred from semeiotic emanations within the context of the parts of the whole. The propositional terms of different scientific disciplines scale with the identity of the inorganic and organic species, the identity of the ecosystem and the temporal interdependencies among them. The combinatorial relations among parts of the whole generate the electro-dynamics of natural sorts and kinds (oxidation, reductions, transformations, transpositions, translocations, transfers, transactions, and so forth) as well as the quantum electro-dynamics necessary to represent three-dimensional organic forms (handedness). The emergence of relations among the parts of the wholes arranges electrical units of partitions into unities to form anatomies of natural sorts and kinds. In conclusion, the yoga (Sanskrit, union) of the abstract concepts of C. S. Peirce, S. Lesniewski and A. Tarski is the logical ur-root of coherence of multiple scientific symbol systems under the formal numerical constraint: The union of units unite the unity. Little Falls, MN, USA, Submitted Oct 3, 2017
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