This article presents a three-part analysis on revealing possible descriptive requirements for a math of intention. Part one, titled Philosophical Reduction, presents reductive reasoning for arriving at three possible problems that ultimately one of which a mathematics of intentionality must satisfy. Part two, titled Scientific Modelling, considers the potential resolution of these problems in light of current scientific theory, allowing the selection of a most probable problem from part one. Part three, titled Computational, Mathematical and Physical Description, considers what descriptions, and the nature of their relations, are required to satisfy the most probable problem. It is proposed in Part 3 that a threefold equivalence of description at a specific level is a necessary requirement to illustrate the formation of intention. In exposing the requirement there emerge two significant consequences for the nature of our current descriptions: a) David Chalmers ‘Hard Problem of Consciousness’ specifically results from the absence of the requirement, and similarly b) Kurt Godel’s incompleteness proofs exist as true only in an operational conception of mathematics that exists post non-inclusion of the requirement. Finally, there is reason to suggest that even if the requirement is revealed and a math of intention realised, a math of consciousness likely cannot follow from it premise – a claim very much counter-intuitive.
Jack Hamilton James