> So clearly false if you read the article, or have ever looked at an optical illusion.
"Mind" vs. brain. For example, you will never observe the concept "triangularity" or the number 8 or the color "red" in a brain scan. You will see brain activity correlates between what is most likely someone perceiving an instance of triangularity (e.g., a concrete triangle drawn on the blackboard) or, say, the symbol "8" that's been drawn with a red marker, but those are not concepts, which are general. You cannot imagine "triangularity", only particular triangles. But all physical triangles are concrete and particular. You can't draw or construct an abstract triangle because any such drawing or construction will be a particular triangle that excludes all others (an infinite number of them, actually). Properties like the color red can be thought apart from any particular red thing, but you won't find "red" by itself rolling down the sidewalk.
So you have the following syllogism:
Every physical thing is particular. No abstract thing is particular. Therefore, no abstract thing is physical.
So if we can know things abstractly, then it must follow that such things exist in a nonphysical way in our minds. But there is no physical thing in which abstract things can inhere as abstract things because physical things are always concrete and particular.
Things get worse for reductionists. Current reductive views of physical reality exile properties like color as we commonly understand them to the realm of consciousness or mind or whatever. I.e., color as we commonly think of it is reduced to the experience of the reflectance properties of matter, that is, to a property of the mind, because as we have assumed, it is not a property of matter. But if color is not a property of matter, and the mind is material, then color cannot be a property of the mind. Therefore, the mind must be immaterial. This latter view of reality is essentially Cartesian where the universe is divided into impoverished res extensa and the metaphysical rug of res cogitans under which we can sweep all of those unseemly phenomena that reductive accounts of reality cannot cope with. Of course, you might be able to get away with that as long as you're a Cartesian dualist, but materialism, the metaphysical bastard child of Cartesian dualism, takes Cartesian dualism, jettisons res cogitans and attempts to reduce all of those unseemly phenomena attributed to res cogitans to phenomena proper to res extensa. Of course, materialism is utterly incapable of dealing with this problem by definition. Stubborn, dyed-in-the-wool materialists like the Churchlands or Dennett, instead of rethinking their presuppositions, have resorted to the pathetic tactic of denying the very thing they were supposed to explain. Can't explain color or abstract concepts? Then they must not exist!