  (d) There is what has become known as ‘Benacerraf’s Problem’ (See his 1983). Numbers, it would seem, are abstract objects, yet our intellects operate with them all the time. How does a physical brain interact with an abstract entity? A similar problem could be raised for concepts in general; they are abstract, general entities, not physical particulars, yet they are the meat and drink of thinking. For a dualist about intellect there does not appear to be the same problem. The immaterial intellect is precisely the sort of thing that can grasp abstract objects, such as numbers and universals – in the Aristotelian context, the immaterial intellect is the home of forms. (There is still the issue of how this intellectual capacity of the immaterial mind relates to sensory consciousness. According to Aristotle, perception is a wholly embodied process, but for modern dualists, sensory consciousness is not material. In order to unify the perceptual and intellectual functions of the mind, traditional empiricists tended to be imagists, in their theory of thought, in order to assimilate the intellectual to the sensory, but this assimilation is rejected by those who believe in a distinct cognitive phenomenology, as mentioned in (a) above. The issue of how these two functions of mind are related in dualism is, it seems to me, insufficiently investigated.)  The difficulty in accounting for the brain’s relation to abstract entities explains why most materialists tend to be nominalists,thus reducing thoughts to concrete particulars of some kind. (D. M. Armstrong in his (1978) is a striking exception to this, accepting an in re theory of universals.) But if you do not find either nominalism or Armstrong’s causal-functional theory of thinking convincing, Plato’s idea in the Phaedo that the intellect must be such that it can have an affinity with immaterial things begins to look very plausible. 