Cohomological Emergence of Sense in Discourses (As Living Systems Following Ehresmann and Vanbremeersch)

As a significant extension of our previous calculus of logical differentials and moving logic, we propose here a mathematical diagram for specifying the emergence of novelty, through the construction of some “differentials” related to cohomological computations. Later we intend to examine how to use these “differentials” in the analysis of anticipation or evolution schemes. This proposal is given as a consequence of our comments on the Ehresmann–Vanbremeersch’s work on memory evolutive systems (MES), from the two points of view which are characterization of life and use of categorical modeling. It would not be possible to conceive of the “differentials” outside the frame of a MES (and specifically the description of the part played in a MES by the “co-regulators” and their “landscapes” for anticipation and emergence). Furthermore, we hope that this diagram will be useful to exhibit the “emergence of sense” in discourses, and this idea is supported here by a brief examination of how a discourse could be seen as a living system (and then could be studied as a MES).

[1]  S. Alexander.  Space, Time, And Deity , 1920 .

[2]  E. Macbride.  Grundlagen einer Biodynamik Handbuch der Pflanzenanatomie L'Organisation de la matière dans ses rapports avec la vie: études d'anatomie générale et de morphologie expérimentale sur le tissu conjonctif et le nerf , 1923, Nature.

[3]  C. Broad,et al.  The Mind and Its Place in Nature. , 1928 .

[4]  C. L. Morgan,et al.  Life, Mind, and Spirit. , 1926 .

[5]  C. L. Morgan,et al.  The emergence of novelty , 1933 .

[6]  La Naissance de la Vie , 1941 .

[7]  S. Miller.  A production of amino acids under possible primitive earth conditions. , 1953, Science.

[8]  N. Rashevsky.  Topology and life: In search of general mathematical principles in biology and sociology , 1954 .

[9]  Robert Rosen,et al.  A relational theory of biological systems II , 1958 .

[10]  R. Rosen.  THE REPRESENTATION OF BIOLOGICAL SYSTEMS FROM THE STANDPOINT OF THE THEORY OF CATEGORIES , 1958 .

[11]  A. Oparin.  [The origin of life]. , 1938, Nordisk medicin.

[12]  G. Simondon,et al.  L'individu et sa genèse physico-biologique : l'individuation à la lumière des notions de forme et d'information , 1964 .

[13]  N. Rashevsky.  Organismic sets and biological epimorphism. , 1967, The Bulletin of mathematical biophysics.

[14]  Paul C. Kainen,et al.  Weak adjoint functors , 1971 .

[15]  Joseph A. Goguen,et al.  Systems and minimal realization , 1971, IEEE Conference on Decision and Control.

[16]  L'anti-hasard , 1973 .

[17]  J. Nageotte.  L'Organisation de la Matière dans ses Rapports avec la Vie J. Nageotte, Alcan, Paris, 1922 , 1977, Pain.

[18]  G. Chaitin.  Gödel's theorem and information , 1982 .

[19]  L. S. Vygotskiĭ.  Pensée et langage , 1985 .

[20]  M. Minsky.  The Society of Mind , 1986 .

[21]  P. T. Saunders.  Theoretical Biology and Complexity : Robert Rosen, Editor, Academic Press, New York, 1985, 210 pp., $55.00 , 1986 .

[22]  René Guitart.  On the geometry of computations , 1986 .

[23]  A C Ehresmann,et al.  Hierarchical evolutive systems: a mathematical model for complex systems. , 1987, Bulletin of mathematical biology.

[24]  Peter Aczel,et al.  Non-well-founded sets , 1988, CSLI lecture notes series.

[25]  Stuart A. Kauffman,et al.  The origins of order , 1993 .

[26]  N. Costa,et al.  Undecidability and incompleteness in classical mechanics , 1991 .

[27]  G. F. Joyce,et al.  Directed molecular evolution. , 1992, Scientific American.

[28]  David Blitz,et al.  Emergent Evolution: Qualitative Novelty and the Levels of Reality , 1992 .

[29]  Jean-Paul Vanbremeersch,et al.  Semantics and Communication for Memory Evolutive Systems , 1992 .

[30]  A. C. Ehresmann,et al.  Outils mathématiques pour modéliser les systèmes complexes , 1992 .

[31]  A. Pichot.  Histoire de la notion de vie , 1993 .

[32]  C. Sinding.  Les métaphores en biologie: analogies ou outils de pensée? , 1993 .

[33]  G. Simondon,et al.  L'individu et sa genèse physico-biologique , 1995 .

[34]  Yaneer Bar-Yam,et al.  Dynamics Of Complex Systems , 2019 .

[35]  J. Goldstein.  Emergence as a Construct: History and Issues , 1999 .

[36]  Andrée C. Ehresmann,et al.  Memory Evolutive Systems , 1999 .

[37]  Gheorghe Paun,et al.  Computing with Membranes , 2000, J. Comput. Syst. Sci..

[38]  LES ORIGINES DE LA VIE : UN PROBLÈME, DES DISCIPLINES , 2000 .

[39]  Roberto Poli,et al.  The Basic Problem of the Theory of Levels of Reality , 2001 .

[40]  Y. Clot.  Bakhtine, Vygotski et le travail , 2001 .

[41]  Peter A. Corning,et al.  The re-emergence of "emergence": A venerable concept in search of a theory , 2002, Complex..

[42]  Andrée C. Ehresmann,et al.  Emergence Processes up to Consciousness Using the Multiplicity Principle and Quantum Physics , 2002 .

[43]  A. Paul,et al.  Chemical Synthesis of Poliovirus cDNA: Generation of Infectious Virus in the Absence of Natural Template , 2002, Science.

[44]  Jacques Ricard,et al.  What do we mean by biological complexity? , 2003, Comptes rendus biologies.

[45]  J. Bada,et al.  Prebiotic Soup--Revisiting the Miller Experiment , 2003, Science.

[46]  Yaneer Bar-Yam,et al.  A mathematical theory of strong emergence using multiscale variety , 2004, Complex..

[47]  Cristian S. Calude,et al.  Is complexity a source of incompleteness? , 2004, Adv. Appl. Math..

[48]  I. C. Baianu.  Robert Rosen’s Work and Complex Systems Biology , 2006 .

[49]  Andrée C. Ehresmann,et al.  The Memory Evolutive Systems as a Model of Rosen’s Organisms – (Metabolic, Replication) Systems , 2006 .

[50]  I. C. Baianu,et al.  Complex Non-linear Biodynamics in Categories, Higher Dimensional Algebra and Łukasiewicz–Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks , 2006 .

[51]  Eugene M. Izhikevich,et al.  Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting , 2006 .

[52]  Les systèmes complexes , 2006 .

[53]  Alex J. Ryan,et al.  Emergence is coupled to scope, not level , 2006, Complex..

[54]  Ion C. Baianu,et al.  Categorical Ontology of Levels and Emergent Complexity: An Introduction , 2007 .

[55]  Daniel M. Dubois,et al.  Computing anticipatory systems with incursion and hyperincursion , 2008 .

[56]  J. Ricard.  Pourquoi le tout est plus que la somme de ses parties , 2008 .

[57]  Presque tout est indécidable , 2009 .

[58]  On the physical basis of life , 2010 .

[59]  Marcio Lobo Netto,et al.  On building a memory evolutive system for application to learning and cognition modeling. , 2010, Advances in experimental medicine and biology.