Hard, Harder, and the Hardest Problem: The Society of Cognitive Selves

Cognitive science, in its quest to elucidate 'how we know', embraces a long list of subjects, while ignoring Mathematics (see Cognitive Science Society website; https://cognitivesciencesociety.org/), which is known for making the unknown to be known (cf. solving for unknowns). There is, within Mathematics, a mathematical account of acquiring mathematical knowledge: F. William Lawvere's Functorial Semantics (PNAS 50: 869-872, 1963). Building on Lawvere's work, 'Functorial Semantics for the Advancement of the Science of Cognition' (Mind and Matter 15: 161-184, 2017) has recently shown how mathematical knowing constitutes an abstraction of ordinary cognition.

In our manuscript 'Hard, Harder, and The Hardest Problem: The Society of Cognitive Selves', our main objective is to develop a scientific theory of the experiential self. Towards this end, we adopt the scientific method of idealization.  We find that the knowing self can be idealized as a mathematical monad, which determines how particulars are generalized.  In light of the representational character of conscious experiences, the mutual relations between mathematical objects, their properties, background, theories, models, and the monad (determining the mathematical representation) constitute a formalization of the relations between physical stimuli, their neural codes, intuition, mental concepts, conscious percepts, and the knowing self.  Furthermore, we argue that the process of relating subjective experiences to the experiencing subject is harder than the hard problem of going from the material world to the realm of conscious experiences; the hardest of all is the problem of accounting for the interactions between the collective consciousness and individual consciousness, i.e. the society of cognitive selves.

The mathematics of acquiring mathematical knowledge, which figures prominently in our conceptualization of 'The Society of Cognitive Selves', is presented in a manner readily accessible to the multidisciplinary audience.  As such, we are confident that our idealization: 'knowing self is a monad' will inspire further investigations of the subjective generalization of objective particulars with respect to a mathematical monad as a model system of the more challenging problem of spelling out the functional dependence of subjective experiences on both objects of experience and the experiencing subject, which is the everyday concern of cognitive scientists and philosophers.