Constructive Mathematics, Quantum mechanics, Free Will and Consciousness

The objective of this paper is to show that non-constructive mathematics is incapable as a framework for research on consciousness. Indeed, we shall discuss how non-constructive mathematics is inconsistent with the physics of consciousness which deals with quantumness. This inconsistency implies the incapability of non-constructive mathematics to represent the free will of a conscious agent. Furthermore, we shall suggest Constructive mathematics (and topos theory which is one of its models) as an alternative framework to study consciousness. The pivotal role of the excluded middle law in our discussion will be addressed in detail.