>It's not difficult. When you think about a tiger, you are not thinking about the brain state associated with said thought. A tiger is different from a brain state. We can safely generalize, and say the content of a thought is different from its associated brain state.

Just because you are not thinking about a brain state when you think about a tiger does not mean that your thought is not a brain state.

Just because the experience of thinking about X doesn't feel like the experience of thinking about Y (or doesn't feel like the physical process Z), it doesn't logically follow that the mental event of thinking about X isn't identical to or constituted by the physical process Z. For example, seeing the color red doesn't feel like processing photons of a specific wavelength with cone cells and neural pathways, but that doesn't mean the latter isn't the physical basis of the former.

>> The correctness of a thought can be judged only by reference to its content, not to its associated state. 2+2=4 is correct, and 2+2=5 is wrong; but we know this through looking at the content of these thoughts, not through looking at the neurological state. This implies that state != content.

Just because our current method of verification focuses on content doesn't logically prove that the content isn't ultimately realized by or identical to a physical state. It only proves that analyzing the state is not our current practical method for judging mathematical correctness.

We judge if a computer program produced the correct output by looking at the output on the screen (content), not usually by analyzing the exact pattern of voltages in the transistors (state). This doesn't mean the output isn't ultimately produced by, and dependent upon, those physical states. Our method of verification doesn't negate the underlying physical reality.

When you evaluate "2+2=4", your brain is undergoing a sequence of states that correspond to accessing the representations of "2", "+", "=", applying the learned rule (also represented physically), and arriving at the representation of "4". The process of evaluation operates on the represented content, but the entire process, including the representation of content and rules, is a physical neural process (a sequence of brain states).

> Just because you are not thinking about a brain state when you think about a tiger does not mean that your thought is not a brain state.

> It doesn't logically follow that the mental event of thinking about X isn't identical to or constituted by the physical process Z.

That's logically sound insofar as it goes. But firstly, the existence of a brain state for a given thought is, obviously, not proof that a thought is a brain state. Secondly, if you say that a thought about a tiger is a brain state, and nothing more than a brain state, then you have the problem of explaining how it is that your thought is about a tiger at all. It is the content of a thought that makes it be about reality; it is the content of a thought about a tiger that makes it be about a tiger. If you declare that a thought is its state, then it can't be about a tiger.

You can't equate content with state, and nor can you make content be reducible to state, without absurdity. The first implies that a tiger is the same as a brain state; the second implies that you're not really thinking about a tiger at all.

Similarly for arithmetic. It is only the content of a thought about arithmetic that makes it be right or wrong. It is our ideas of "2", "+", and so on, that make the sum right or wrong. The brain states have nothing to do with it. If you want to declare that content is state, and nothing more than state, then you have no way of saying the one sum is right, and the other is wrong.