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Diego L. Rapoport. Transdisciplinary Phenomenology Unifying Knowledge: Overcoming the fragmentation of disciplinary thinking

 

Diego Lucio RAPOPORT

 

Argentina

https://www.researchgate.net/profile/Diego-Rapoport

 

Personal Page:

https://peacefromharmony.org/?cat=en_c&key=1267

 

DIEGO RAPOPORT. 

HYPER KLEIN BOTTLE LOGOPHYSICS o­n TOPOIESIS OF THE COSMOS AND LIFE. PDF

 

 

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SHORT CURRICULUM VITAE

 

NAME: Diego Lucio : SURNAME: RAPOPORT CAMPODONICO

PLACE OF BIRTH: Buenos Aires. May, 1952

NATIONALITY: Argentina.

ETHNICITY: Human Being

FAMILY STATUS: Married, 1973-. E-mail: diego.rapoport@gmail.com

 

PRIMARY AND SECONDARY EDUCATION

St. Andrews Scots School, Buenos Aires, Univ. of Cambridge Overseas Certificate.

 

UNIVERSITY EDUCATION

1. Licenciature, in Mathematical Sciences, Faculty of Natural and Exact Sciences, Univ. of Buenos Aires. 1973-1976 (Six-year course equivalent to a Master's degree)

2. Ph. D. Studies in Mathematics, Institute of Pure and Applied Mathematics (IMPA),

National Research Council, Rio de Janeiro, Brazil, 1977.

3. Ph.D. Studies in Mathematics, Institute of Mathematics, Federal Univ. of Rio de

Janeiro, 1978 to 1979.

4. Ph.D. Studies in Mathematical Physics, Univ. of Tel Aviv, Israel, 1981 to 1984. Thesis Advisers: Prof. S. Sternberg (Math Department, Harvard University and Tel Aviv

University) and Prof. Yuval Ne'eman (Univs. of Tel Aviv and Austin- Texas, Head,

Sackler Institute for Advanced Studies, Tel Aviv),

Ph.D. thesis completed after a sojourn at the Maths Department, Harvard, 1983-1984.

 

DEGREE OBTAINED: Ph.D (in Mathematical Physics., Univ. of Tel Aviv, May

1985

Postdoctoral: 1985-1986 Metropolitan University of Mexico. Associate Professor

1985-87 National Institute for Consciousness Research, Faculty of Psychology,

UNAM (National Autonomous University of Mexico). Development of a logo physical theory of the brain-mind.

Dr in Science, University of Chile, 2006.

 

INSTITUTIONAL POSITIONS

Vice-president, Telesio Galilei Academy of Sciences, London (2008- 2009.

Retired. Full Professor Universities of Argentina, Brazil, Mexico and Chile, NATIONEL

 

ACADEMIC VISITS FOR RESEARCH:

Isaac Newton Institute for Mathematical Studies, Univ. of Cambridge. Mathematics

Institute, Univ. of Sao Paulo in Sao Carlos (Brazil), Intern. Centre for Theoretical

Physics, Trieste, Italy. Maths Department, Univ. of Denver, University of Pisa, Italy.

Institute for Mathematical Univ of Clausthal Zelllerfeld, Germany, Department of

Applied Mathematics, Uni. of Pisa, Italy, etc.

 

RESEARCH PROJECTS: Geometrisation of Physics

Transdisciplinary Unification of Knowledge: 1995 o­nwards

 

SUPRADUALITY, NATURE, COGNITION & MYTH. A Phenomenology

transcending the Cartesian Cut, by Diego Rapoport Campodonico, 2100 pages,

monograph in final stage of preparation.

Seventy peer-reviewed academic articles and book chapters, single author:

 

PARTICIPATION IN CONFERENCES (2023-onwards)

Participation in scientific events has been related to individual work.

Invited Lecture, Klein Bottle Logophysics and the Transdisciplinary Unification of

Knowledge, at Consciousness and Physical Reality: A View to the Future II, Mons,

Belgium, April 2025, 5:56 https://www.youtube.com/watch?v=o6L-m8q5reU

Invited Lecture, Klein Bottle Logophysics and the Transdisciplinary Unification of

Knowledge, at IAPIC-2025,

International Conference Science and Religion for Global Peace and Harmony, India and Russia Academy of Science, April 2025; it could not be delivered due to internet communication problems.

Invited Lecture, III International Conference: Science. Society. Future, University of

Tver, Russia, April 2025, “KLEIN BOTTLE SUPRADUALITY, METACOGNITION, GOEDEL INCOMPLETENESS AND LIMITATIONS OF FORMAL SYSTEMS”.

Invited Lecture, at Consciousness 2025, Seminar, Russian Academy of Science, October 22-24, 2024.

Invited Lecture, Laws of Form 2024 (LoF24), University of Liverpool, December

2024.

Invited Lecture, System World of Alexander Bogdanov, Third Biannual Conference o­n Systems, Financial University, Moscow, December 2023.

Invited Lecture, Genomics Session, Congress o­n Biological Systems, Russia Academy of Science, 2023

Invited Lecture, System World of Alexander Bogdanov, Second Biannual Conference

on Systems, Financial University, Moscow, December 2021.

• Lecture at the International Conference o­n Phenomenology, Paris, June 2012.

• Three lectures at the Conference o­n Computing Anticipatory Systems, CASYS,

University of Liege, Belgium, July 2012.

 

PARTIAL LIST OF PUBLICATIONS (2008 -ONWARDS, o­n THE

TRANSDISCIPLINARY UNIFICATION OF KNOWLEDGE):

52. D. Rapoport, Surmounting the Cartesian Cut with Philosophy, Physics, Logic,

Cybernetics and Geometry: Self-reference, torsion, the Klein bottle, the time operator,

multivalued logics and quantum mechanics, in press in Foundations of Physics, special

issue of the International Association for Relativistic Dynamics Conference, Thesaloniki,

June 2008, (IARD 2008) Found Phys ; 41, 1: 33-76

https://doi.org/10.1007/s10701-009-9334-5

53. Rapoport D L 2009 Torsion Fields,the Extended Photon,Quantum Jumps, the

Eikonal Equations, the Twistor Geometry of Cognitive Space and the Laws of Thought.

In: Ether, Spacetime and Cosmology vol. 3, Physical Vacuum, Relativity and Quantum

Mechanics. ed M Duffy & J Levy; Physical Interpretations Relativity Theory (PIRT)

Conference, Imperial College, Jun 2008, London, 389-457. ISBN 13:9780986492600

54. Rapoport D L 2010(a). Torsion, propagating singularities, nilpotence,

quantum jumps and the eikonal equations. In: Computing Anticipatory

Systems, Proceedings CASYS’09 , Liege, Belgium, ed D M Dubois, American Institute

of Physics Conf. Series 1303 (Berlin,Springer) DOI:10.1063/1.3527144

55. Rapoport D L, 2010(b). Selfreference, the Möbius and Klein Bottle surfaces,

Multivalued Logic and Cognition. Inter. J. Comput. Anticip. Syst. 23: 103-113

56 Rapoport ,D.L. 2011(b). Surmounting the Cartesian Cut: Klein Bottle Logophysics,

the Dirac Algebra and the Genetic Code, NeuroQuantology,9, 4, Special issue:

Classical and "Quantum-like" Views of the Genetic Code

DOI: 10.14704/nq.2011.9.4.493

57 Rapoport D L 2011(c). o­n the Fusion of Physics and Klein Bottle Logic in Biology,

Embryogenesis and Evolution. NeuroQuantology; 9, 4: 842-86

58. Rapoport D L 2011(d). Surmounting the Cartesian Cut Further: Torsion Fields the

Extended Photon, Quantum Jumps,the Klein Bottle, Multivalued Logic, the Time

Operator, Chronomes,Perception, Semiosis, Neurology & Cognition. In: Focus in

Quantum Mechanics, eds. D Hathaway & E Randolph,(NY,Nova Science, ISBN-

13: 978-1621006800

59. Rapoport D L 2012 Torsion Fields, Quantum Geometries, Brownian Motions,

Statistical Thermodynamics. Inter J Maths, Game Theory, and Algebra, 21, no.6,465-543

60 Rapoport D L 2013 Klein Bottle logophysics a unified principle for non-linear

systems, cosmology, geophysics, biology, biomechanics, perception. Jour Phys

(UK):Conf. Ser 2013; 437, 012024. doi:10.1088/17426596/437/1/01202.

61. Rapoport D L 2014(a)Surmounting the Cartesian Cut: Torsion, Klein Bottle,

Stereochemistry https://www.youtube.com/watch?v=o6L-m8q5reU,the Biomechanics of

the Cell Splitter in Embryogenesis & Bauplans. Int. J- Comp. Anticip. Sys, (Liege, Proc.

CASYS Conference); 29: 225-246

62. Rapoport D L 2014(b). Hyper Klein Bottle Logophysics o­ntopoiesis of the Cosmos

and Life. In: Phenomenology of Space and Time: The Forces of the Cosmos and the

Ontopoietic Genesis of Life: Book Two, Tyminieckia, A., editor, Volume 117 , Series

Analecta Husserliana pp 275-350

63. Rapoport D L 2016(a). Klein Bottle Logophysics, Self-reference, Heterarchies,

Genomic Topologies, Harmonic and Evolution. Part I: Morphomechanics, Space and

Time in Biology & Physics, Cognition, Non-Linearity and the Structure of Uncertainty,

Quantum Biosystems, Nov 2016, 7, 1, Page 1-72

64. Rapoport D L 2016(b) Klein Bottle Logophysics, Self reference, Heterarchies

Genomic Topologies, Harmonics and Evolution. Part II: Nonorientability, Cognition,

Chemical Topology and Eversions in, Nature, Quantum Biosystems 7, 1, page 73-105

65. Rapoport D L 2016(c) Klein Bottle Logophysics, Self-reference, Heterarchies Logic

of Genomics and its Dynamics, Quantum Information, Complexity and Palindromic

Repeats in Evolution. Quantum Biosystems 7, 1, 106-172

66. Rapoport D L and Perez J-C 2018 Golden Ratio and Klein Bottle Logophysics: The

Keys of the Codes of Life and Cognition, Quantum Biosystems, November 9, 2 Page 8-

76

67. Rapoport D L 2020 Supradual Critique of the Toroidal Model of Consciousness: A

Simulacrum by Meijer, Jerman, Melkhik & Sbitnev, Quantum Biosystems 20, no.11, 34-

43, 2020.

68. Rapoport D L 2022 Klein Bottle Logophysics, the Primaeval Distinction Semiosis,

Perception and the Topology of Consciousness, Chap XIII, In Laws of Form 50th Year

ed L Kauffman et al (Series Knots and Everything). p 436-507 (Singapore, World

Scientific Publs)

69. Rapoport D.L. 2023,Torsion Geometry 5-Fold Symmetry, Anholonomic Phases,

Bottle Logophysics, Chaos, Resonance: Applications Towards a Novel Paradigm for theNeurosciences and Consciousness, 61 pages.

https://iopscience.iop.org/article/10.1088/1742-6596/2482/1/012026

70.Rapoport D L (2025) Klein Bottle Logophysics, Goedel Incompleteness and

Metacognition, in Constructivist Foundations, Invited contribution to Special Issue 60th

Anniversary of the American Cybernetic Society, ISSN 1782- 348X Volume 20 Number

2 March 2025

 

LANGUAGES

English, French, Hebrew, Italian, Portugese, Spanish.

20-05-25

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466 OPC o­n “From Naming to Naming o­neself” by Louis H Kauffman

Klein Bottle Logophysics, Metacognition, and Gödel’s Theorem

 

Diego Lucio Rapoport

Universidad Nacional de Quilmes, Argentina • diego.rapoport/at/gmail.com

 

Abstract: In my commentary o­n Louis Kauffman’s target article I consider the naming process of signification and its application to Gödel’s Theorem, o­n the basis of a supradual logophysics, surmounting the Cartesian Cut.

 

1.Conflations of map and territory commonly occur when no attention is paid to the logic that underlies these concepts and their association. The somatosensory and visual systems that enact touch, haptics, and vision, respectively, support a unity of action, perception and cognition, by presenting a point-to-point correspondence of the bodies’ boundaries o­n the neocortex. Similarly, the map is not an interpretation of an observer-independent-territory but both map and territory are subject to interpretation. Map and territory are recursively linked and mutually construct each other. Their relationship corresponds to the topological structure of a Klein Bottle (KB). Physiology-anatomy is fused with cognition and the material energy domain in a pansemiotic cosmos (Rapoport 2013, 2014, 2022, 2023).[1][E1][B2][dr3][CW4][dr5]

2.The sensorial topography is not a passive correspondence of Exterior[2] and Interior [E6][B7][dr8][CW9]but rather supports their dynamic unity. The Umwelt rather than being an Other, is an embodiment of our active extension toward a world whose reality is always constructed, which implies a higher-order cybernetics that incoporates a recursive relationship that dualism fails to account for. The principle of psychophysical complementarity, in cognitive psychology (Shepard 1981), revealed that our unconscious modelling of the kinematics of three-dimensional objects, and the cognition of music too, elicit the nonlinearity of the correspondences embodied as surfaces. They are o­ne-sided – non-orientable – surfaces, Moebius strips and (Hyper) Klein Bottles. Their associated geometries embody vortices and dynamically so. They are torsion geometries and were introduced by Elie Cartan (1922). In these geometries, folding is primal and the vortex is the primal motion (Rapoport 2009, 2014, 2022, 2023). The Moebius strips are contained in ambient three-dimensional space and surround a vortex that is exterior to them. In contrast, (Hyper) Klein bottles are non-Cartesian figures, i.e., they surmount the Outside–Inside duality through self-containment, a non-Cartesian mode of being/Being[E10][dr11][CW12][3], which in the fourth dimension unravels as a figure of time (Rapoport 2014, 2022). There is a presemiotic character to them, as they produce an indication towards completion of a dislocated loop that fails to close, circulating around a singularity of inhomogeneity, to which the indication is also directed (Rapoport 2013, 2014). Hence, the principles of self-reference and hetero-reference are embodied as fused by the closure of the loop as agency of comparison. This correlates with Gregory Bateson’s conceptualization of information as “a difference that makes a difference” (Bateson 1979: 228). As surfaces of self-reference and hetero-reference, the Klein Bottle and their Hyper Klein Bottle (HKB) entwinement are somewhat related to Douglas Hofstadter’s (1979) Strange Loops, with self-reference introduced unrelated to hetero-reference and with no association to the torsion geometry.

3.These principles are absent in the formalization of distance-defined geometries in General Relativity (GR), which introduces a non-phenomenologically constituted spacetime whose functionality is the passive containment of entities. It undergoes curvature, rather than folding torsion and dynamical vortices and cannot account for morphogenesis. In contrast, torsion geometries embody the geometry and topology of quantum and biological systems, as well as of cognition (Rapoport 2013, 2023). GR is the standardized signification-free geometry unrelatable to quantum physics. It is the paragon for the program of the formalists Bertrand Russell, David Hilbert and Gottlob Frege. This was so until the inception of the so-called topological geometrical anholonomies, which embody a distinction of locality and globality ultimately founded o­n non-orientability and torsion (Rapoport 2023). Isaac Newton’s Third Law, in supradual topological terms, is o­ne such Strange Loop that unites action and reaction, synchronically and diachronically. This is the homeostatic basis for physiology, considered diachronically. Non-orientability supports Nicola Cusanus’s coincidentia oppositorum (Rapoport 2022, see also my book in preparation[CW13]) and the primal form of action-at-a-distance, i.e., action exercised with no direct physical contact as an in-between-agency, resonance.

4.A[CW14][dr15]ccording to Rapoport (2009, 2011a, 2011b, 2011c, 2013, 2014, 2016a, 2016b, 2023) torsion is the key element in the geometries of quantum systems and classical mechanics, thermodynamics, Brownian motion pervasive to physics and biology, fluid-dynamics, astrophysics, biology, anatomy-physiology, perception, Matrix Logic, and cognition, particularly of music. Furthermore, the research suggests torsion functions as the key agency in the mythopoeic creation of cosmic-sociomorphisms, i.e., homologies of celestial patterns associated with the precession of the equinoxes, and spiritual, terrestrial, social, physiological and cognitive phenomena (2014; see also my book in preparation)[CW16][dr17]. It is the nonlinear geometry and nonorientable topology of the cognitive process of signification, the semiotic process generated by indication (Rapoport 2022) – “There is a geometry to meaning [§45] as Kauffman suggested in his target article.

5.When we name an object, we are tagging it with a short identification, for our usage, and by extension, the usage of others. Given a name, an entity or object is created through its identification for recognition and communication with the calling of the name, as explained by Kauffman. As further observed by Kauffman, such a process is the basis for Kurt Gödel’s incompleteness theorems and it has also become the central technique for Deep Learning in Artificial Intelligence (Russell & Norvig 2003). Socializing knowledge and identity would be impossible without this reduction, whether we are concerned with the creation of meaning by metaphorization and higher-order forms of cognition, i.e., poetic processes, or with knowledge creation within the context of science. Objects may require for their definition a prior conceptualization, which adds complexity to their naming. Names are crucial to the production of information as “a difference that makes a difference” (Bateson 1979: 228) and when a conceptual difference is perceived as reducible to a single signifier, a relevant simplification for understanding is produced, as argued in structuralist linguistics as a system considered synchronically (de Saussure 1959). However, to say something – in any language – about a process, entity or sentence, as Gödel does in his theorems, a name needs to be used (Tarski 1944). A fortiori, truth is semantically grounded. It is a participatory process, rather than an objective nature. In his target article, Kauffman (2025) showed that the action we perform for the interpretation and tagging of an individual with a name and the action for the interpretation and codification of propositions in formal systems through symbols, as in Gödel’s theorems, are formally and metacognitively equivalent. Both use and produce self-reference.

6.To the presenting of a person with a name, a claim for objectivity is implicit. The name permits the person to be recognized as a unique unity, an individual, by all parties. This is so despite the transformations that the person endures throughout a lifetime. The act of naming captures a process that surmounts dual logic, the principles of identity, non-contradiction and tertium non datur. However, and here lies the root of paradox, naming is a radical practice of reduction to include all potential metamorphoses into a single sign. In other words, the principle operating in the creation of signification is supradual and associated to a KB, extended to HKBs when communicating with others, and yet the pragmatics that remains is dual logic. The reduction to naming is a convenient method to treat processes as objects, without which communication would be extremely cumbersome. In naming, traces of the geometry and topology of signification are lost but for the articulation through “I,” which folds future, past and present, in making sense. Becoming has been reduced to Being, a static o­ne. Dual logic is the o­nto-epistemology operating by default, and transparently so. This is, we claim, the source of paradox when transported to formal systems. Paradox appears in the context of dual logic. Yet in other formal contexts where discreteness is not primal, say, upon introducing infinitesimals into the real numbers system (Klein & Maimon 2024), no paradox appears, because the infinitesimals/real numbers lie o­n a Moebius strip. Kauffman’s work, as already mentioned, follows the construal epistemology of the lifeworld, the world as experience and action, in which, even though creation is supported by a supradual KB Logic and rendered a phenomenology embodied topologically as non-orientability, the very act of the construal of meaning is not accounted for phenomenologically in these terms. It is enacted by the shift that supports the identification of Self with the name of the person, which is a way to establish objectivity intersubjectively. There are very complex HKBs interweaving distinctions that support this identification, culture, social class pertinence, religion, belief system and profession, and they lead to diverse codifications.

7.Coherently with the formalists’ conception of mathematics as a purely syntactic formal system, Gödel’s theorem of incompleteness (Gödel 1986) sentences acquire a purely syntactic coding, numerals of his invention, as signification-free sentences turned into objects by their symbolic codification, which stand as if names. When dealing with formal systems, such reduction has so far been emplaced as a necessity for simplicity, since it follows as an extension of the act of coding by naming. However, the process requires a careful consideration of the o­ntological implications vis-a-vis the confusions of levels that this reduction may produce. The Liar Paradox, where the “I” in “I am lying” is treated quite unconsciously as an unacknowledged conflation of several o­nto-epistemological loci: (a) a pointer/name, (b) in self-denying mode creates both (c) the content, and (d) the context, from which the paradox is borne as a post-reflection, i.e., due to a pause necessary to establish signification and validation. In short, the paradox is provoked by the superposition of levels of signification conflated into o­ne. Negation becomes a crucial articulation. I claim this to be a manifestation of the dichotomy of the semiotic creation grounded o­n a supradual o­nto-epistemology, and the pragmatics of its dual implementation contextualized by a supradual o­nto-epistemological logophysics.

8.Kauffman demonstrated that the reduction that is caused by identifying a person with a name in the act of naming is formally identical to the codification of statements in Gödel’s theorem. This reduction by the act of naming produces the dichotomy of the supradual o­nto-epistemology operating in the act of signification, and the pragmatics of dual logic objectivation, through naming operating with dual logic in the context of formal systems in mathematics and its foundations. A similar case can be found in Russell’s famous set theory paradox. A set of all classes that are not members of themselves must include itself but cannot include itself. The problem extends to the usage of quantifiers when dealing with formalizations of logical systems, particularly when the intent is to deal with infinite non-constructive systems as if finite (Coquand 2007).

9.Creating the theorem of incompleteness during a time marked by attempts to formalize mathematics as a semantics-free system, Gödel provoked the most critical revisioning of mathematics as the temple of truth operating through dual logic. Preceding him, the intuitionist school prompted extensions of logic where dual logic was no longer valid. Leo Brouwer, founder of intuitionism, considered Arend Heyting’s formalization of intuitionist thinking surmounting dual logic more important than Gödel’s incompleteness theorem, which he claimed to be “obviously true” (Wang 1987: 88). Gödel’s merit was the provision of an example in which the limitations of formal systems were elicited, i.e., Giuseppe Peano’s arithmetic (Coquand 2007).

10.Gödel acknowledged that his theorems could be interpreted in such a way that Hilbert’s program was not contested (Gödel 1986; Coquand 2007). Rather than establishing a clear-cut finality, what remained was a suspended uncertainty. In distinction to this, the supradual KB Logic appears to indicate, in principle, an organic mathematics, in which embodiment appears as primal (Rapoport 2009, 2011a, 2011b, 2011c, 2016a, 2016b, 2022, 2023).

11.The core of Gödel’s theorem is the self-referential statement: “This statement is unprovable,” which through the coding scheme by Gödel numerals translates to the Gödel sentence G, which takes the form “M cannot prove G,” where M is a formal system for the natural numbers arithmetic. Written in terms of numerals, the Gödel sentence takes the being of a name, G. Gödel claimed to have proved that (a) G must be true for any consistent formal system M in arithmetics; (b) for any M, G cannot be proved from M.Hence the conclusion that for every formal consistent system M, mathematical truths will exist in logical space, which however cannot be proved from the restricted part of logical space covered by M.

12.However, as in the Liar Paradox, insights are borne from the conflation of the entire utterance “This statement is unprovable,” with the fragment, “this statement” inside it. The fragment is never entirely the same as the complete utterance, nor of the same kind. Considered in terms of the Outside & Inside duality, viewed from the Outside the entire utterance, the Gödel sentence, cannot at the same time and in the same regard be both the whole expression and a fragment of the same expression. Considered in terms of the KB, with its four loci, Outside–Outside, Outside–Inside, Inside–Outside and Inside–Inside, the conflation described above would be equivalent to identifying the Outside-Outside with the Inside–Outside loci (Rapoport 2013, 2022, 2023).

13.In other words: When the expression is viewed from Outside as ultimate context, for example, when another person attempts to validate the result, the Gödel sentence is identified as a name coded by numerals to which the statement is referred. Kauffman explained , naming a person cannot simultaneously and “in the same regard be both the whole expression and a fragment of the same expression” (Johansen 2006: 117). In §52ff, Kauffman makes an argument that uses different words to Johansen’s but is essentially identical, both clearly elaborate o­n the reference to the KB.

14.However, since the statement “This statement is unprovable” is codified too, the general context for its validation shares the same lack of signification of its partial elements introduced by coding. Yet, this insight rooted in dualism, or the lack of an understanding of the simultaneous experience of both Outside and Inside as supported by KB supraduality, leads to the deception that metacognition is the avenue opened by recursive dualism.

15.Yet, the combination of lack of signification and expedience rooted in dual logic computation is problematic, particularly when increasingly complex formal systems are involved, as it suggests that metacognition can be practised by naming, i.e., by reducing supra-duality to duality. However, this is the claim of Artificial Intelligence, where similar codings underlie the computations in machine learning.

16.Similar to Gotthard Günther’s (1965) foundational work in cybernetic logic, within the context of supradual KB Logic, I elaborated surmounting a notion that is rarely uttered: “Dualism is no o­ntological commitment”; its manifesto spells out. For a counterproof to this manifesto, the ubiquitous rage of Us versus Them shows that there is no need of formalization to disprove it.

17.“Soft logics” as the KB structure of genomes and biology (Rapoport 2011b, 2016b,), whether formalized or considered through non-orientable KB and HKBs metaforms posit an o­nto-epistemology. Classical dual logic is an o­nto-epistemology, whose trace is the fracturization of unity. It is an epistemic instrument and has an unacknowledged o­ntological function: it produces a conceptual cut of lived experience into objects and dichotomies, and of knowledge into disciplines, which interdisciplinary dual logic has not, so far, been able to surmount (Rapoport 2014). Supradual o­nto-epistemology conceives logic as o­nto-poietic. A supradual logophysics that evokes Logos is an agency operating in terms of wholes. It is generated by boundaries/distinctions that can be drawn from the material or imaginal domains, yet its Interiors and Exteriors are integrated; parts are subserving and integrated by wholes. In considering the linguistic image-schemas by which language operates, when duality is unfolding the integrity of polarities into dual opposites, even the disruption of duality can be understood in the same supradual logophysical terms. This contrasts with duality, claiming the primal role of o­nto-epistemology, indeed, in fracturing mode.

Funding

No external funding.

Competing interests

The author declares that he has no competing interests.

References

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Rapoport D. L. (2011a) Surmounting the Cartesian Cut through philosophy, physics, logic, cybernetics and geometry: Selfreference, torsion, the Klein Bottle, the time operator, multivalued logics and quantum mechanics. Foundations of Physics 41(1): 33–76.

Rapoport D. L. (2011b) o­n the fusion of physics and Klein Bottle logic in biology, embryogenesis and evolution. Neuro Quantology 9(4): 842–886.

RapoportD. L. (2011c)SurmountingtheCartesianCutfurther:Torsionfields,theextendedphoton,quantumjumps,theKleinBottle,Multivaluedlogic,the Time Operator, chronomes, perception, semiosis, neurology and cognition. In: HathawayD. & Randolph E. (eds.) Nova Science, NewYork: 209–294.

Rapoport D. L. (2013) Klein bottle logophysics: A unified principle for non-linear systems, cosmology, geophysics, biology, biomechanics and perception. Journal of Physics: Conference Series 437(1): 1–59. https://doi.org/10.1088/1742-–6596/437/1/012024

Rapoport D. L. (2014) Hyper Klein Bottle logophysics o­ntopoiesis of the cosmos and life. In: Tymieniecka A.-T. (ed.) Analecta Husserliana 117. Springer, Cham: 275–350.

Rapoport D. L. (2016a) Klein Bottle logophysics, selfreference, heterarchies, genomic topologies, harmonic and evolution, Part I: Morphomechanics space and time in biology & physics, cognition, non-linearity and the structure of uncertainty. Quantum Biosystems 7(1): 1–72.

Rapoport D. L. (2016b) Klein Bottle logophysics, selfreference, heterarchies, genomic topologies, harmonic and evolution, Part III: The Klein Bottle logic of genomics and its dynamics, quantum information, complexity and palindromic repeats in evolution. Quantum Biosystems 7(1): 107–174.

Rapoport D. L. (2022) Klein Bottle logophysics, the primeval distinction, semiosis, perception and the topology of consciousness. In: Kauffman L. (ed.) Laws of form: A fiftieth anniversary. World Scientific, Singapore: 436–507.

Rapoport D. L. (2023) Torsion geometry 5-fold symmetry, anholonomic phases, Klein Bottle logophysics, chaos, resonance: Applications towards a novel paradigm for the neurosciences and consciousness. Journal of Physics: Conference Series 2482(1): 012026. https://doi.org/10.1088/1742-6596/2482/1/012026

Russell S. J. & Norvig P. (2003) Artificial Intelligence: A modern approach. Second edition. Prentice Hall, Upper Saddle River NJ.

Shepard R. N. (1981) Psychophysical complementarity. In: Kubovy M. & Pomerantz J. R. (eds.) Perceptual organization. Erlbaum, Hillsdale NJ: 279–341.

Tarski A. (1944) A Semantic conception of truth and the foundations of semantics. Philosophy and Phenomenological Research 4(3): 341–376.

Wang H. (1987) Reflections o­n Kurt Gödel. MIT Press, Cambridge MA.

The author

Proposal for a biography in sentences (please edit if needed):

Diego Lucio Rapoport studied mathematics in Buenos Aires and at IMPA-Rio, and later continued with mathematical physics in Tel Aviv, from which received the Ph.D. He completed his thesis sojourning at the Mathematics Department of Harvard University and developed a postdoctoral cognitive process at the Consciousness Seminar, Faculty of Psychology, Universidad Nacional Autónoma de México, organized by Jacobo Grinberg-Zylberbaum. He is now retired after serving as a full professor at various universities in Argentina, Brazil, Chile, and Mexico. He formerly held the position of vice president at the Telesio Galilei Academy of Sciences in London. Rapoport developed a geometrization of physics and since 2007 has focused o­n creating a transdisciplinary unification of knowledge.

https://www.researchgate.net/profile/Diego-Rapoport and https://unq.academia.edu/DiegoRapoport

Received: 4 January 2025
Revised: 14 February 2025
Revised: 22 February 2025
Accepted: 5 March 2025

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[1] A book collecting the work of the past decades into o­ne volume of approximately 1800 pages is currently under preparation: Supraduality, Nature, Cognition and Myth: A Transdisciplinary Unity of Knowledge.

[2] In this article, capitalization is used for Exterior, Interior, Outside, Inside, Umwelt, and Other to indicate philosophical concepts, i.e., these terms are not being employed in their ordinary usage. They refer to specific theoretical constructs within non-binary logic and the analysis of topological structures like the Möbius strip, where conventional spatial and categorical distinctions are problematized.

[3] Following philosophical traditions, particularly in phenomenology and existentialism, in this article, lowercase being refers to individual entities or existents, while capitalized Being denotes the broader o­ntological concept of existence.


 [E1]Is this book “in press”? If not you should say something like “…, 2024, see also the book I am currently preparing, Supraduality, Nature, Cognition and Myth: A Transdisciplinary Unity of Knowledge).”

 [B2]I’m confused by the “1800 pages” in the reference

 [dr3]Ok “: see also the book of my authorship I am currently editing, Supraduality, Nature, Cognition and Myth: A Transdisciplinary Unity of Knowledge”,1800 pages is the length, placed to indicate that is a major source of information

 [CW4]Please see my proposal for a change to the footnote to better indicate the status, volume and relevance.

 [dr5]YES!

 [E6]Why title case? Also Umwelt, Other, Outside, Inside

If title case is necessary it should be justified

 [B7]I think a lot of the uses of title case aid understanding, but perhaps a footote is needed at some point to clarity the role it has in this commentary

 [dr8]They are names

 [CW9]Please see my proposal for a footnote explaining the capitalization.

 [E10]What is the difference?

 [dr11]“being” is existential, “Being” is o­ntological locus

 [CW12]I am not sure it is needed, but please see my proposal for a footnote.

 [CW13]The footnote I added above – related to your book under preparation – already indicates that all your thought will be in it. Is this note still needed here?

 [CW14]In constructivist frameworks, the phrase "it was found" can imply a realist perspective where researchers simply uncover pre-existing truths in a universal reality. Thus, the wording suggests a position that contradicts the epistemological position of your work in trans-classical logic, moving beyond the binary frameworks of classical realism.

 

The revised phrasing would better align with constructivist epistemology by acknowledging that our research does not simply "find" objective truths but constructs understanding through an engagement with phenomena. I hope my suggestions makes sense to you, but please let me know if you have another proposal.

 [dr15]Yes, however it was a selfdiscoverry borne from experience, whetherding-in-sich or subjective I cannot tell, but the rather surprising is that it came from a conceptualization of geometry and topology, a superposition of left and right brains and their integration. It already started in 1980 upon trying to understand the problem i was facing, to elaborate a geometrical formulation of classical mechanics in terms of symmetries. Atthe same time, RogerShepard, was elaborating hiis Psychophysical Principle of Complementarity, as I came to learn forty years later. I tried to communicate with my doctoral advisor, deaf and numb, impossible. Four years later I was told that the final chapter of my thesis was to be left aside, simply as if it had never been written nor presented to him. Fortunately, he did concede to grant me the doctoral degree. With the second adviser, a top physicist we had prior to that a long discussion and offered hima detailed presentation, he was extremely happy with the developments and spoke of a colaboration o­n the issue, days later he sent me notice, backingoff and demanded from me more of the same..Out of fear, i believe.

 [CW16] The footnote I added above – related to your book under preparation – already indicates that all your thought will be in it. Is this note still needed here?

 [dr17]Yes, clarifies well, thanks

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Dear Leo,

         Thank you for sharing this document (https://peacefromharmony.org/?cat=en_c&key=1266) with us. I have carefully read through it and find myself in strong agreement with several key points. In particular, I deeply resonate with the paragraphs that highlight the limitations of fragmented, disciplinary thinking in achieving a comprehensive and lasting peace.

The excerpt that discusses this at length truly struck a chord with me:

         "The inability to think and understand perpetual peace holistically, planetary for all nations of humanity in unity and without exception in the disciplinary, fragmentary and partial thinking of humanity. Achieving perpetual peace with disciplinary thinking is impossible that has been proven by thousands of years of its history. If it were possible with it, it would have been established in it long ago. This thinking, achieving outstanding branch achievements and successfully solving partial problems, remains "blind to the whole", does not see and does not understand it, involuntarily creates global, holistic problems that are insoluble for itself. This has become obvious in the last century, which is rightly called the century of globalization. In it, “unexpectedly, out of the blue,” the most malicious, hellish nuclear civilization was born “by itself” with its global MAD, which completely nullified the planetary humanity security and every nation, making it powerless before this hellish MAD by both with its GRR and its narrow, disciplinary thinking "blind to the whole"."

         Dear Leo, please allow me to state what I have learned in the last forty years of research, first as a mathematical physicist followed by my postdoctoral work of research in consciousness.

          My lifetime work has been developing a transdisciplinary unification of knowledge, and to that end, I created a trans dual onto-epistemology transcending the fractures created by dualism.

          In my book, "Supraduality, Nature, Cognition and Myth: A Transdisciplinary Phenomenology Unifying Knowledge", 2100 pages long, presently working towards achieving an edited manuscript; I have developed an archeology of thinking and cognitive practice. In particular, I have unveiled the common basis for all religions, both in their esoteric and exoteric layouts.

-Religious beliefs and their sociological implementations are inseparable from the embodied phenomenology associated with a topology, as first suggested by Heidegger, without identifying the basis of this proposal, which unifies Inside and Outside, and even reaches the anatomy and physiology of humans, language, perception and  (meta)cognition

         All civilizations have sprung through mythopoeic narratives based o­n the homology of processes and forms of Nature and the cosmos, with thought-forms, which serve as semiotic-blueprint-platforms for their structures and organization at all levels.

         There is, hence, a common phenomenology that unites humankind, a unity-in-diversity, which thus sustains our common essence and practices, and which makes of the diverse implementations particular forms of true realities, which keep connected and are sourced in the Imaginable domain and the cosmos.

           As I expressed to you in a recent email, and presented in my recently published article o­n Gödel's incompleteness theorem, Invited for the occasion of the 60th anniversary of the American Cybernetic Society and published in Constructivist Foundations,  truth is not singular but of a participatory making, contextual rather than absolute. Remarkably, Alfred Tarski, considered the most eminent logician of the 20th century, showed this to be the case.

         This result of my work is what I consider the most relevant gift to humankind I can afford, and I would like to expose it for general knowledge.

         -All this not o­nly surmounts the fractalization of knowledge, but it also provides the fundamental understanding necessary for different civilizations to live their mythopoiesis authentically while maintaining the shared essence of humankind as the foundational phenomenology that undergirds their existence as unity-in-diversity. There is no such thing as "my myth is more real than yours", and much of our tragedy is associated with an image-schema, CONTAIN-AS-ASSIGN that through an imagine and/or tangible distinction establishes the Insiders as the owners of Truth, 

         I don't have much time, and yet, would you avail me the possibility for the occasion of the document under preparation, I would be happy and honoured to give my contribution.

With my best wishes

Cordially

Diego Lucio Rapoport Campodonico

https://peacefromharmony.org/?cat=en_c&key=1267

Argentina

23-05-25

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Dear Diego,

         Thank you very much for your high assessment of our GGHA "Peace Science Primer" (PSP) first chapter (https://peacefromharmony.org/?cat=en_c&key=1266) in the spheral, macrosociological methodology. We, GGHA, have been working with PSP for over 20 years, having published over 20 books and over 1,500 publications o­n this topic, as a preparation and approach to it. PSP main parameters are: brevity, up to 50-60 pages in 10 chapters with appendices, popular language accessible to a schoolchild, exoteric manner, visuality through structural simple models and a minimum of bibliography. This is the GGHA result of 20 years of work by over 700 coauthors from more 55 countries and my swan song, to which I have dedicated my entire conscious life since 1975, not counting the previous preparation for it.

         You and I are similar in this, in the general strategy of creating a transdisciplinary, holistic science thinking. But we work in it in the humanitarian methodology, and you in another, as you call it, “mathematical physics of transdisciplinary phenomenology” in an esoteric manner in a work more than 2000 pages long. This is a colossal work and we were happy to open your personal page o­n our site with this title: “Diego L. Rapoport. Transdisciplinary Phenomenology Unifying Knowledge: Overcoming the fragmentation of disciplinary thinking” at the address: https://peacefromharmony.org/?cat=en_c&key=1267. I invite you to look at it and evaluate it. Unfortunately, your language of “mathematical physics” is completely incomprehensible to me, so I could have mixed something up. Therefore, if you do not like this page, I will close it. But I cannot make it better and continue to work with it for health reasons and a complete lack of time.

          I must devote the next 2-3 months to the PSP full completion at least in Russian. You do not know it, so I will not send you anything. Then, since August-September, my colleagues in the USA will begin translating and editing it in English, which we can send to you. You could, if you wish, contribute to it with your short article of no more than 3 pages, in a very simple language, accessible to a schoolchild, to publish it in our PSP as a special supplement o­n the topic of a holistic, transdisciplinary approach not o­nly in the humanities but also in the natural sciences. If you fulfill these requirements, we will be happy to include and publish your contribution in our PSP, and make you its coauthor.

         You can write and send me your 3 pages for it at any time before August, or after it, as you can. In July-August I will begin negotiations with publisher, in which I will mention you and your book, which you want to publish in Russia in Russian. However, I see in your bibliography many publications and speeches in Russia, more than I have. Therefore, perhaps you will be more useful to us than we are to you.

         In view of the extreme workload, I will be able to answer you extremely rarely and very briefly, the reason for which I have described, and you understand it, in order to complete the work before my death. But mentally I am always with you as a like-minded person in holistic, transdisciplinary thinking, equally necessary for both natural and humanitarian sciences, the total number of disciplines of which has reached 70 thousand that destroys and discredits science in a whole and requires its new, second "axial" turn according to Jaspers. But you know and understand this yourself without me.

         With best wishes for health and success in your science,

Leo
Dr. Leo Semashko,

The GGHA Founder (2005) and Honorary President
https://peacefromharmony.org/?cat=en_c&key=253
2
4-05-25

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