There is a long history of philosophical intuition that the human mind must be more than physical or mechanical. I argue that this intuition arises from the perfect “transparency” of physical and mechanical states, in the sense that such states have no obscure or occult elements, but are fully intelligible in (usually) mathematical terms. In the paper, I derive a contradiction from the claim that such a physical system has genuine intentionality, comparable with an intelligent human. The contradiction arises from the fact that, according to physicalism, the physical properties of a brain state determine the narrow propositional content of any conscious thought occurring in that state. This fact allows a physical property of brain states to be defined using Cantor’s diagonal construction, and then a contradiction results if a physical system is assumed to form thoughts involving that property.

1. This claim needs to be understood carefully, since Laplace’s demon may not possess (for example) the concepts “water” and “lake”, and so may not be able to infer the sentence: “lakes (on earth) are filled with water”. Nevertheless, once these terms are defined, in the language of physics, Laplace’s demon can infer that the sentence is true. In a similar way, even though the axioms of second-order Peano arithmetic are categorical, and hence logically entail all of the truths of arithmetic, to infer a true sentence about prime numbers one first needs a definition of “prime number”.

2. I do not assume that a human being such as Mary could perform these inferences, since they may be too complex.

3. If it turns out (contrary to my view) that such narrow content does not exist, then the mind-reading thesis can be defined as the claim that Laplace’s demon could infer a person’s conscious intentional content from their physical brain state, together with all relevant parts of their environment. This alternative definition does not affect the argument.

4. In other words, every property in the class is the image underf of at least one of the objects.

5. Or, if narrow content does not exist, then Laplace’s demon also needs a physical description of some features of M’s environment. This point applies every time I refer to the “possible states” of M.

6. I am not sure if anyone endorses ultra-idealism, but the “Mathematical Universe Hypothesis” of Tegmark (2008), according to which, “Our external physical reality is a mathematical structure”, is at least a very similar claim, and it also seems to be refuted by the argument in this paper.

7. Russellian monists do of course appeal to alleged non-mathematical aspects of the human brain to explain consciousness and other mental phenomena. On the definition of ‘physicalism’ used here, however, Russellian monism is not a physicalist view since it denies the conceptual transparency of the world.

8. To be precise, physicalism entails that some concrete entity, whose state at some timet is perfectly represented by a mathematical structure, has conscious intentionality.

9. See Chalmers (2003) for definitions of Type-A and Type-C materialism.

Authors and Affiliations

1. Langara College, 100 W. 49th Ave, Vancouver, BC, V5Y 2Z6, Canada

   Richard Johns

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Correspondence toRichard Johns.

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