  Putting his anti-materialist argument outlined above, in section 1, in very general terms, Aristotle’s worry was that a material organ could not have the range and flexibility that are required for human thought. His worries concerned the cramping effect that matter would have on the range of objects that intellect could accommodate. Parallel modern concerns centre on the restriction that matter would impose on the range of rational processes that we could exhibit. Some of these concerns are of a technical kind. Gödel, for example, believed that his famous theorem showed that there are demonstrably rational forms of mathematical thought of which humans are capable which could not be exhibited by a mechanical or formal system of a sort that a physical mind would have to be. Penrose (1990) has argued that Turing’s halting problem has similar consequences.But there are other less technical and easier to appreciate issues. I will mention four ways in which physicalist theories of thought seem vulnerable to attack by the dualist