No, a mathematical model of consciousness is not possible. First we must distinguish between the natural consciousness of Dasein studied according to Heidegger's analytic (in which there are indeed certain proto-topological notions present) and the awakened insight-imbued ego-absolving consciousness. In both cases the idea of a mathematical model of consciousness is a serious mistake because all mathematics assumes that the fundamental problems regarding circularity in the a priori and analytic we discussed have been solved (i.e. by modelling consciousness via mathematics we are already making assumptions about consciousness necessary to justify the use of mathematics). This is analogous to the error of trying to give a philosophical account of language via meaning-as-use theories. As we wrote in the conclusion of our paper on Analyticity, Computability and the A Priori:
How can we shed greater light on the questions and problems discussed in this note? What methods should be employed to go beyond the seemingly unbreakable circularity between logic, computation, arithmetic and combinatorial intuition? A possible answer lies in adopting a rigorous phenomenological approach or the combination of such an approach with something along the lines of Piaget's genetic epistemology. We need to investigate thoroughly what it means for us to learn something (like counting, calculating), to know how to do something, to understand rules, to know how to play a game and to understand a game. All of this is at present unclear and difficult. It is naive and dogmatic to take these topics that demand extensive investigation and elucidation as some kind of philosophical explanation as done for instance in meaning-as-use theories. The elucidation in question needs to proceed not by formal abstract reification (which leads to the same circularity) but by investigation of the matter itself in its concrete lived experience, both personal and interpersonal.
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