Hi Jon. You wrote:

I would not regard this as an old intuition, merely as a reasonable definition of a mental state. As I have said, I cannot understand what this other concept of a mental state might be. If it is not an experiential state then why not call it a brain state, in which case it ought to have a perfectly normal physical causal description. If the point of functionalism is not to explain what experiences go with what brain processes I cannot think what it is for. Ordinary science does the rest.

As I understand it (I'm studying this at the moment) what functionalism focuses on is neither experience nor physiology but logic. It is based on the concept of the Turing Machine, the output of which is determined by the input in conjunction with, or we might say in the context of, the internal state. The implementation, the physical arrangements, are irrelevant, assuming that they support the logic required. The concept of experience, or consciousness, has no part to play in this, though many believe it amenable to a functionalist explanation. But the main point here, I think, is that the functionalist concept of a mental state does not differ in principle from the internal state of a Turing Machine or, indeed, that of any existing computer. (A general purpose computer is a Universal Turing Machine.)

Here are some references from my course material:

Andy Clark, Mindware: an introduction to Philosophy of Cognitive Science, ch.1&2
Jaegwon Kim, Philosophy of Mind, ch.5
Tim Crane, The mechanical mind: a philosophical introduction to minds, machines and mental representation, ch.3