Axiomathes FUNCTORIAL CALCULUS OF COGNITION (original) (raw)

Abstract

Mathematics is about knowing. Mathematical knowledge is a record of knowing just as sentences, besides being descriptions of the things to which they refer to, exemplify rules of composition. The functorial calculus of acquiring mathematical knowledge resembles cognition, which involves physical stimuli, neural sensations, mental concepts, and conscious experience. Herein we build, on the foundational similarity between cognition and mathematics, a model of cognition. Using category theory we explicated the functorial calculus of going from given particulars to measurements of the given particulars, to conceptualization of the particulars based on their measured properties, to interpretations of the thus formed theories, and resulting in knowledge. This simple model system can be used to systematically address fundamental questions of cognitive science such as 'how do we know?' More immediately, our results argue against the contemporary compartmentalization of scientific kn...

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