William Lane Craig denies the number zero.

[Neo-Scholastic]

That is beside the point. If you want to say concepts are literally in the brain then you should be able to pull them out of the brain and show them to others...empirically.

All that scientists can do is to show neural correlates. Can you see an electron? Or, weigh one on a scale?

Yes, neural correlates are known and like electrons require highly specialized equipment to "see" since they cannot be directly observed. While no one can set a single electron on a scale in the grocery store their mass can be determined by other means. But these are all non-sequiturs.

People often use figurative language to talk about thought, feelings and ideas. We say things like "it's all in their head" and "my brain tells me..." I object to people using those terms literally in philosophical discussions because they are grossly imprecise and misleading. People experience cobalt blue but there is nothing actually cobalt blue inside anyone's brain. I think that information about thoughts and feelings are somehow encoded in various states of material neurons. I think that specific neural activities are demonstrably part of certain conscious experiences. None of this empirical data proves one way or the other that the concepts/ideas/memories are identical with neural states or that neural processes are identical to any sense or feeling. And there are some good reasons to suppose they aren’t, starting with the observation that mental states have intentionality, a quality generally excluded from physicalist theories. As I have mentioned elsewhere, the mind-body problem is notably absent from the Thomistic tradition. This absence is due having a much different of accepted categories of being.

And that takes us back to the ontological status of concepts like number. Numbers are not independent entities in some Platonic realm of mystical Ideas. Following Aquinas I say that numbers exist as objects of intellect in-formed by things that are numerable because they share objective universal natures. Newton’s laws, for example are descriptive in the sense that the equations (objects of intellect) were invented to organize our observations but they are also descriptive in the sense that they are about a discovered universal nature, mass, an external object, that is part of all physical bodies.

Zero is perhaps kind of a special case. After all, no one can say that non-existence is the property of something, because if it was something then it wouldn’t be zero. It seems self-evident that ‘nothing’ does not exist.