In science, when you theorize that X reduces to Y, you propose a theory that links X and Y in some causal way. Physicists don't just say, "What you experiences as a gas is really a swarm of fast-moving molecules"; instead, they use statistical mechanics to show that with this theory, the kinetic energy of the molecules, taken in aggregate, can explain gas pressure, temperature, and the ability of expanding gas to do work. Similarly, biologists don't just say, "The apparent design of the various capabilities of the various species can be reduced to a long sequence of random mutations"; instead they offer a theory of natural selection to explain why the adaptions seem to have a purpose, to have function.
The computational theory of mind doesn't seem to have this characteristic. Those who make this claim say, "Our mental states can be reduced to a set of physical states/functional states/some other feature of some sort of computation. Now, clearly this sort of theory has the potential to explain at least some aspects of behavior, but I don't see how it explains anything at all regarding the mind.
When I'm thinking, I generally don't experience anything that I would call algorithmic unless I'm consciously executing an algorithm in my mind. What is the connection from mental states comparable to how statistical mechanics connects molecules to the gas laws or how natural selection connects random mutation to apparent design? Where is the theory about the relationship between computational state X causes desire Y or emotion Z or intention W?
Note, it's not enough to show cognitive studies about how certain chemicals are associated with certain emotions, or activity in certain parts of the brain are associated with certain intentions, or evolution can justify certain desires; those observations/theories still leave an explanatory gap between the physical and the mental. Statistical mechanics shows mathematically how the kinetic energy of many molecules is mathematically equivalent to pressure. Where is that equivalence in computational theories of mind? And without that connection, exactly what is the value of those theories?
I've gotten lots of knowledgeable answers, but none of them really address my question (except the one that says that there is no such explanation). Several of the answers point to non-mental things that can be explained by a computational theory of the brain, but I'm not asking about that. Others have pointed out that there is no other explanation for mental states, but that is no reason to think the computational model is correct if it can't explain anything either. Several people have suggested a two-step process where the brain acts like a computing device and causes mental states, but that's just another way to say that one can model the brain as a computing machine; it doesn't explain how mental states just are some aspect of the computation. In fact, it seems to assume a sort of Cartesian dualism, where the brain does something and the mind is an independent sort of substance that just follows along.
So, once again, I'm not asking about computational models of the brain; I'm asking about computational models of the mind. How is anything that happens in the mind reducible to something that happens by computation.