Comment 23 by Steve Zara :

No, because we are talking about extra ingredients to physics, not new discoveries about how things behave.

I'm not sure it is possible to make a clear distinction between these ideas. However if we look at modern physics as it is applied in cosmology, we use a curious mixture of relativity theory and quantum theory, without having actually reconciled them. Then the second law of thermodynamics is added in to the mix as it cannot be derived from either as they are both time symmetrical. Incidentally, I quite like Bolzmann's suggestion that the second law is an illusion caused by us experiencing time in the direction of increasing entropy. Speaking of experiencing time, there does not seem to be any reason why we should experience it as flowing rather than, say, experiencing out whole life at once. Maybe we don't need any new physics to deal with this but, if so, it is not obviously so.

No it isn't, and causal closure is precise. It means that every physical event has a physical cause.

Putting it like that is problematical since it assumes that for every event something else which is the cause of it can be identified. That's why I prefer to formulate it Humean terms in terms of descriptions of events falling under universal laws.

It certainly doesn't work with substance dualism because the extra substance would have to interact with conventional substance, and that breaks closure.

Not if like David Chalmers you say the interaction went only one way, from physical substance to mental substance.

It doesn't work with property dualism because property dualism is a load of pig poo. If there are mental properties that co-incide with physical properties, there is no way we could know of them unless they interact with physical properties, and yet the definition of property dualism is that they don't interact.

Well there are several versions of property dualism the most well known being anomalous monism according to which there are no strict psycho-physical laws.

One motivation is to make sense of statements involving reasons instead of causes. Thus on this view "He ate the toast because he felt hungry" is not even a candidate for a causal statement because there is no strict law relating feeling hungry to eating toast. However it can function as an explanation. For causes you have to look to the physics.

Another is the so-called realization problem. Pain may turn out to be realized in a certain way in humans however other animals, aliens or machines may not possess the same structures and yet, under appropriate circumstances, we might still feel justified in saying they are in pain.

It's not a non-sequitur. This isn't about description, but about new physics, about extra ingredients. We have the ingredients of nature sorted out up to the TeV energy scale. We don't look for new particles at the scale of torch battery energies (which is way above that of the processes in the brain), we slam together beams which have the energies of aircraft carriers.

You are mistaking the energy needed for the probe for the energies involved in the processes being investigated. See for instance this quote - it's from Wikipedia but I believe it to be correct:

It is widely believed that any theory of quantum gravity would require extremely high energies to probe directly, higher by orders of magnitude than those that current experiments such as the Large Hadron Collider can attain. This is because strings themselves are expected to be only slightly larger than the Planck length, which is twenty orders of magnitude smaller than the radius of a proton, and high energies are required to probe small length scales. Generally speaking, quantum gravity is difficult to test because the gravity is much weaker than the other forces, and because quantum effects are controlled by Planck's constant h, a very small quantity. As a result, the effects of quantum gravity are extremely weak.

It's pretty simple. If we express ideas because of physical processes (talking, nerve cell firings), then those ideas must be in our brain cells because something has influenced our brain cells.

"2+2=4" is an idea but it isn't anywhere. It may be represented in your brain cells but it does not have to be for you to use it competently. Did you know, for instance, that alligators do not naturally run wild in Norfolk? Is it represented somewhere in your brain cells? Maybe it is now but was it before you read the statement? So did you know it then? The point about knowledge and other ideas is that they are not primarily about representation but about competence. But, although the knowledge is not represented anywhere you would still be able to use it competently. Thus if you came across an alligator while walking your dog you would still be surprised and register this event as something special. Alternatively if someone said he/she saw one you would still display an appropriate degree of skepticism.

..Talking about ideas isn't an abstract process, it's a physical process.

Obviously!

... Therefore any new physics must necessarily influence brain cells, ...

If some new physics is needed to account for the brain then obviously it will involve the brain, but so what?

... and that hits the problem of causal closure, of the Dirac equation.

This last statement just seems like a non-sequitur. Why can't I equally well argue that any new physics "hits the problem of causal closure, of the Dirac equation?" What's so special about brain cells that this problem arises with respect to them but not anywhere else?