James Ross's argument from intentional determinacy

James Ross, in his essay “Immaterial Aspects of Thought, presents an argument against a physicalist account of propositional content which I will call the Argument from Determinate Content. He writes:

Some thinking (judgment) is determinate in the way no physical process can be. Consequently, such thinking cannot be a (wholly) physical process. If all thinking, all judgment, is determinate in that way, no physical process can be the (the whole of) any judgment at all. Furthermore, “functions” amng physical states cannot be determinate enough to be such judgments, either. Hence some judgments can be niether wholly physical processes nor wholly functions among physical processes.⁵²

Yet, he maintains, we cannot deny that we perform determinate mental operations. He writes:

I propose now, with some simple cases, to reinforce the perhaps already obvoius point that pure function has to be wholly realized in the single case, and cannot consist in the array of “inputs and outputs” for a certain kind of thinking. Does anyone count that we can actually square numberes? “4 times 4 is sixteen”; a definite form (N x N = N²) is “squaring” for all relevant cases, whether or not we are able to process the digits, or ralk long enough to give the answer. To be squaring, I have to be doing some thing that works for all the cases, something for which any relevant case can be substituted without change in what I am doing, but only in which thing is done.⁵³

I should add that if we don’t literally add, subtract, divide, multiply, square numbers and take their square roots, not to mention perform all the complicated mathematical operations involved in, say, Einstein’s theory of relativity, then physicalism, which not only says that reality is physical but that physics, at least approximately, gets it right, is up the creek without a paddle.

Ross’s argument can be formalized as follows.

1. Some mental states have determinate content. In particular, the states involved in adding, subtracting, multiplying, dividing, in squaring numbers and taking their square roots, are determinate with respect to their intentional content.

2. Physical states are indeterminate with respect to intentional content. Any physical state is logically compatible with the existence of a mulitplicity of propostionally defined intentional states, or even with the absence of propositionally defined intentional states entirely.

3. Therefore, the mental states involed in mathematical operations are not and cannot be identical to physical states.