Category theory and consciousness
Matti Pitkänen
Postal address: Department of Physical Sciences, High Energy Physics Division, PL 64, FIN-00014, University of Helsinki, Finland.
Home address: Puutarhurinkatu 9, 10960, Hanko, Finland
E-mail: matpitka @ luukku . com
URL-address: ~http://www.helsinki.fi/~matpitka
Abstract
Category theory has been proposed as a new approach to the deep problems of modern physics, in particular quantization of General Relativity. Category theory might provide the desired systematic approach to fuse together the bundles of general ideas related to the construction of quantum TGD proper. Category theory might also have natural applications in the general theory of consciousness and the theory of cognitive representations.
a) The ontology of quantum TGD and TGD inspired theory of consciousness based on the trinity of geometric, objective and subjective existences could be expressed elegantly using the language of the category theory. Quantum classical correspondence might allow a mathematical formulation in terms of structure respecting functors mapping the categories associated with the three kinds of existences to each other. Basic results are following.
i) Self hierarchy has indeed functorial map to the hierarchy of space-time sheets and also configuration space spinor fields reflect it. Thus the self referentiality of conscious experience has a functorial formulation (it is possible to be conscious about what one was conscious).
ii) The inherent logic for category defined by Heyting algebra must be modified in TGD context. Set theoretic inclusion is replaced with the topological condensation. The resulting logic is two-valued but since same space-time sheet can simultaneously condense at two disjoint space-time sheets the classical counterpart of quantum superposition has a space-time correlate so that also quantum jump should have space-time correlate in many-sheeted space-time.
iii) The category of light cones with inclusion as an arrow defining time ordering appears naturally in the construction of the configuration space geometry and realizes the cosmologies within cosmologies scenario. In particular, the notion of the arrow of psychological time finds a nice formulation unifying earlier two different explanations.
iv) The category of light cones with inclusion as an arrow defining time ordering appears naturally in the construction of the configuration space geometry and realizes the cosmologies within cosmologies scenario. In particular, the notion of the arrow of psychological time finds a nice formulation unifying earlier two different explanations.
b) Cognition is categorizing and category theory suggests itself as a tool for understanding cognition and self hierarchies and the abstraction processes involved with conscious experience. Also the category theoretical formulation for conscious communications is an interesting challenge.
c) Categories possess inherent generalized logic based on set theoretic inclusion which in TGD framework is naturally replaced with topological condensation: the outcome is quantum variants for the notions of sieve, topos, and logic. This suggests the possibility of geometrizing the logic of both geometric, objective and subjective existences and perhaps understand why ordinary consciousness experiences the world through Boolean logic and Zen consciousness experiences universe through three-valued logic. Also the right-wrong logic of moral rules and beautiful-ugly logic of aesthetics seem to be too naive and might be replaced with a more general quantum logic.
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