Semio-Logics: From Atoms to Anatomy

Dear Colleagues,

The molecular dynamics of biology and medicine, and of life and mind, are nearly incomprehensible. Yet the modern methodologies of molecular medicine describe incredible life-saving therapies constructed from atomistic principles.

(For an oral overview of this concept, see the 2025 MDPI-sponsored IOCPh YouTube video: https://www.youtube.com/watch?v=aPDyNlo0sBs)

Calls for a new mathematics for biology are common. Yet the classical mathematicians continued to assert the computational universality of a mathematics grounded in set theory and promote its “unusual effectiveness” in the sciences, the biomedical facts notwithstanding.

One exceptional voice in these debates was the Fields Medalist, René Thom, who applied his dynamic theories of topological catastrophes and chaos to semio-physics and the semantics of life events; his theories inform a natural generative symbolic nexus linking mathematics to biology and biology to scientific linguistics. Does Thom implicitly presuppose that the existing atomic/(bio)-chemical notation is a precise meta-language for his philosophy of semio-physics?

This Special Issue, titled “Semio-Logics: From Atoms to Anatomy”, seeks to develop the imperative, implicative and impredicative scientific languages of atomicity. Note that, historically, the language of molecular biology emerged as an ad hoc biochemical construct from the simple principle of Bertram Russell: Molecular sentences are formed from atomic sentences and from Whitehead’s principle of organismic “concrescence” operators, generating organic towers of symbolic propositional reasoning. Thom’s dynamic principles of semio-physics are imagined to be derivable from the symbolic logics of the epistemological grammars of Russell and Whitehead.

A different antecedent root of the perplex propositional logic of biomedical signs was proposed by C. S. Peirce (1839-1913). In modern terminology, one can imagine a conscious sequence of computational processes: taxonomical propositional sentences relating and composing scientific signs, semiotics, semes, semiosis, semio-logical consequences, and syntax to generate scientific syntagmatic semantic from syllogisms, and from ascriptions to descriptions.

In this philosophical context, the appellation “semio-logic” refers to the multiplicities of types of related symbolic notations that can be ascribed to any biological system, such as measures of anatomy, physiology, genetics, and awareness grounded in physical metes and the chemical table of elements, i.e., cyber-semiotics.

The types of symbolic metes (measures of hylomorphisms) refer back to the historical concepts explicated and grounded in the objective scientific notations of mathematics, physics, (bio)chemistry and biology. Retroductive catadromic analysis of anatomies are matched with synductive anadromic anabolic syntheses of life.

Semio-logics connects the atomicity of hylomorphisms of scientific methodologies—symbolic as well as structural—to the formal proof systems of these scientific notations. The physics of conservation principles and inverse square laws necessitate the associative and distributive computations of the mete logics of atomic and syndetic molecular numbers. The semantics of the varieties of these logical proof systems intuitively and intrinsically cohere into word-forming elements.

The propositional, generative, synductive idea of “atoms to anatomy” is that computations with atomic numbers emerge spontaneously from the dynamic signs of life which have been recorded as measurements (metes) by reference to the notations of mathematics, physics, chemistry, and genetics. Semio-logics generate cyber-logical topologies, morphisms and propositional terminologies.

The types of metes are defined as physical constructs from the table of elements. Each individual chemical element specifies five metes, five indices, five numbers following Rutherford’s assignment of electrical (atomic) structures: two measures of mass, two measures of electricity and one measure of relative position in the index of atomicity, the atomic number. These numbers are logical constants with natural agency. The nexus necessary to connect two or more pentadic monomial sentences into a syndetic polynomial molecular sentence is a copulative co-predicative grammar that conserves these elemental constants.

Rutherford’s assignment of agency to material identities suffices to construct an atomic representational topology for permutation groups of semio-logical systems:

1. A bipolar number line of Coulombic indexes that separates positive nuclei from negative electrons for any permutation group of elements, e.g., any vinculated multiset of atomic numbers (i.e., a molecular number).
2. A planar bipartite graph of the adjacent Coulombic attractors and repellers constructed from the semiotic taxonomy of the permutation group.
3. An identity space group organized from the Rutherfordian metes of a permutation group.
4. A conscriptive word (a polynomial, via onomatopoeia from the names of chemical elements) that assigns precisely the connectives between the permutation group and syntagmatic syllables, which constructs the linguistic terminology of organic chemistry from the names of the atomic constituents.
5. A dynamic numerical (Coulombic) grammar for hylomorphisms that arranges the planar bipartite graphs into conformations that correspond with the metes of the scientific notations ascribed, prescribed, described, conscribed, and circumscribed to both the predicated and re-predicated permutation groups.

The philosophical abstractions of this perplex topology enable the ab initio computations of organic terminology from the atomic numbers. For example, the perplex co-operative, co-distributive, co-predicative and synductive reasoning of atomicity can associate and distribute the attractors and repellers of Thom’s semio-physical theory of representation. The quantum orientation of both right- and left-handed organic molecules, essential to biological dynamics, are derivable. The co-predicative grammar of organic catalysis becomes computable.

It is astounding that a metrical topology can be constructed from collections of bipolar particles; how are such constructed semio-logical objects related to Thom’s formalization of mathematical attractors and repellers?

It is surprising that the addition of electrical terms of atomic numbers generates molecular biological polynomials; what are the matrical and logical implicatures for the electrical field theories of atomic conjunctures and the dynamics of biological emergence, development and homeostasis?

The hylic topological tablatures from the table of elements and semio-logic propositional grammar include both nominal identity matrices and polynomial adjacency matrices; what are the implicatures of these matrices for the three classical forms thermodynamic reasoning, from the ideal gas laws, from classical chemical dynamics and from the electro-chemical (Nerst) equation? For the ab initio computation of “artificial life”?

The copulative connectivity necessary for semio-logical transactions on permutations groups of atomic numbers (as physical identities) generates combinatorial explosions of chemical terms (polynomials); what are the explicative consequences of putative transactive transformations for theories of biological emergence? For theories of dynamic neural network? For artificial intelligence?

This call for papers seeks imaginative proposals that explore the philosophical analyses of modern atomicity in its current perplex self-referential forms. Current biomedical computations preserve the ab initio computations from atomic numbers and molecular formulae. A meaningful synectic grammar is needed to connect the logical terms emerging from interlinguistic methodologies of measurement and communication. A meaningful syndetic algebra is needed to express the perplex taxonomic topologies used in the biomedical sciences, e.g., genetics, pharmacology, toxicology and disease etiologies.

The propositional conjecture of a co-operative, co-distributive and co-predicative synective grammar corresponding precisely with a perplex syndetic algebra opens the potential for semio-logic systems of dynamic governance. This call for papers spans such analytic and synthetic philosophies of natural reasoning.

References:

MDPI  IOCPh (2025) https://www.youtube.com/watch?v=aPDyNlo0sBs

An introduction to the perplex number system. Discrete Applied Mathematics 157 (2009) 2296–2309

Semiotics of Complex Systems: A Hierarchical Notation for the Mathematical Structure of a Single Cell. Information Processes in Cells and Tissues (1998). Springer pp 185–195

Third Order Cybernetics: Biosemiosis and the Logical Contrasts between Electro-Chemical and Electro-Mechanical Cybernetics. IFRS Conference, Linz, 2012

An Introduction to the Foundations of Chemical Information Theory. Tarski–Lesniewski Logical Structures and the Organization of Natural Sorts and Kinds. Information 2017, 8, 15; doi:10.3390/info8010015

Prof. Dr. Jerry LR Chandler
Guest Editor

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• symbolic logics
• scientific taxonomies
• medicine
• emergence
• semiotics
• computational theory
• structuralism
• molecular biology