Towards Functorial Calculus of Cognition (original) (raw)

2015

Abstract

How do we conceptualize things? What is the relation between concepts and percepts? These foundational questions of cognitive science have analogs within the mathematical experience of reflecting reality. The relationship between things and their mental representations is analogous to that between mathematical objects and their theories. Based on this comparison, we present a category theoretic account of acquiring mathematical knowledge as a simple analogy model of cognition. We show that the functorial calculus of abstracting concepts and interpreting theories provides a formalization of the interrelationships between physical stimuli and neural sensations, along with mental concepts and conscious percepts constituting cognition. Our investigation of the similarity between mathematics and cognition led us to argue against the contemporary compartmentalization of scientific knowledge and ordinary cognition, and make a case for the understanding of the basic science of knowing in terms of functorial calculus.

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