Stimpy:
I agree that our brains have no access, in particular, to information about set B. Nevertheless, I still think that we can reason about the properties that any possible set B must necessarily have. This is independent of any particular properties set B might have.
I don't think so, because the properties of set A, while independent of any properties of set B, could still be dependent on the properties of the Ur-set.
It would depend on the content of the theories.
Let's consider two mutually exclusive possible Ur-set theories, in the extreme, one of which makes prediction X about the state of (sub)set A, the other making prediction Y. At the same time, theory X predicts the existence of phenomenally realized information, giving a certain property X* for it; theory Y doesn't.
We confirm prediction X. Now we have reason to believe theory X, and with it the property X*.
Causally closed with respect to set B.
The problem with the argument from parsimony here, as I see it, is that materialism requires the rejection of the existence of phenomenal consciousness. Property dualism accepts the existence of phenomenal consciousness, and gives the best possible explanation under the assumption that phenomenal consciousness exists. Parsimony can't be invoked because property dualism explains something that materialism must deny the existence of.
Because it's necessary in this case to take the existence of phenomenal consciousness into account.
Yes, in the ways I set out above.
I think I can accept this formulation.
But I don't think I can accept this one, because I don't accept the implication.
But we don't have access to any information about set B. Keep in mind that when I say that, I mean that our brains, which ultimately are going to have to do all of the work of figuring this stuff out, do not have access to any information about set B.
I agree that our brains have no access, in particular, to information about set B. Nevertheless, I still think that we can reason about the properties that any possible set B must necessarily have. This is independent of any particular properties set B might have.
Doesn't this violate the premise that set A is causally closed?
I don't think so, because the properties of set A, while independent of any properties of set B, could still be dependent on the properties of the Ur-set.
In other words, let's imagine that we did have two competing theories about the Ur-set. Could they possibly make different predictions about observations made in set A? If set A is causally closed, then nothing that is not a part of set A can have any affect on it. By claiming that set A is causally closed, you are saying that set A could be exactly the way it is without there being anything else at all. In fact, this is exactly what you are saying when you say that p-zombies are logically possible.
It would depend on the content of the theories.
Let's consider two mutually exclusive possible Ur-set theories, in the extreme, one of which makes prediction X about the state of (sub)set A, the other making prediction Y. At the same time, theory X predicts the existence of phenomenally realized information, giving a certain property X* for it; theory Y doesn't.
We confirm prediction X. Now we have reason to believe theory X, and with it the property X*.
If set A is causally closed, then by definition, no observation made within set A could possibly reveal whether or not there is anything besides set A, or any information about it. This means that as long as you accept that it is possible that materialism is correct, property dualism is, at best, a competing theory which makes no additional testable claims. It must therefore be rejected in favor of the more parsimonious theory, materialism.
Causally closed with respect to set B.
The problem with the argument from parsimony here, as I see it, is that materialism requires the rejection of the existence of phenomenal consciousness. Property dualism accepts the existence of phenomenal consciousness, and gives the best possible explanation under the assumption that phenomenal consciousness exists. Parsimony can't be invoked because property dualism explains something that materialism must deny the existence of.
After all, you could postulate an infinite number of such additional layers of reality, with an unlimited degree of complexity of relationships. Why bother?
Because it's necessary in this case to take the existence of phenomenal consciousness into account.
OK. A more pertinent question would be, do you think it is possible, at least in principle, to find out?
Yes, in the ways I set out above.
Fair enough. This raises another subtlety about the Mary problem, though. If there is no storage of this "phenomenal information", then I would assert that Mary "gains something new" everytime she experiences red, regardless of whether she has experienced it before or not, and then immediately loses it again.
I think I can accept this formulation.
In other words, I do not think that you can meaningfully say that Mary "learns" any new phenomenal facts when she sees red for the first time, because "learning" implies that the information is stored in some way.
But I don't think I can accept this one, because I don't accept the implication.