Abstract

An elementary mathematical proof is offered that mental states cannot be either intensionally or extensionally identical with brain states. the proof consists in taking a subset of mental states, namely, possible thoughts of integers and showing that this set has the cardinal number aleph null; then taking the largest physically possible set of brain states k and the number of subsets of k which is 2 to the power k, and which, no matter how large, is necessarily finite. it follows that these two sets cannot correspond one to one from which it then follows that they cannot have identical elements. i conclude with answers to likely objections and with a denial that my argument supports traditional dualism