Better answer with slightly less snow-shoveling fatigue:
Chalmers assumes for the sake of argument that his actions and speech have physical causes. So the quoted claim A, by my argument in the fourth-to-last paragraph of the post, already stipulates the presence of the evidence that we gain from introspection and use to argue for qualia. Thus “would” applies to any logically possible world chosen at random, which may or may not have a “bridging law” to produce qualia. Chalmers doesn’t seem to address the probability of it having such a law given the physical causes or ontology that we find in A. I show this chance exceeds P(that we actually have qualia | the aforementioned evidence for qualia & the assumption that we’ll never prove A logically) -- long derivation at the end of this comment, since previous comments had flaws. Chalmers’ argument against physicalism depends on treating this long conditional proposition as certain enough for his purpose, as its denial would leave us with no reason to think qualia exist and indeed no clear definition of qualia. Without the proposition Chalmers would not have an argument so much as an assertion. I’ll look at what all of this means in a second.
In the grandparent I compare it to the situation in math. Gödel showed that we can’t prove arithmetic will never contradict itself (we can’t prove B logically) and I wanted to express this by saying that in any random logically possible world P(B)<1. Below you express it differently, saying the probability that we live in a logically possible world does not equal 1. According to that way of speaking, then, the chance that at least one logically possible world exists does not equal 1. It equals P(B), since if we could find a contradiction in one world then logic ‘leads to’ a contradiction in all worlds. And yet I argue that we know B, by means of Bayesian reasoning and the neglect of incredibly small probabilities that we have no apparent way to plan for. This would mean we know in the same way that logically possible worlds might tell us something about reality. The form of argument that Chalmers uses therefore takes its justification from Bayesian reasoning (and the neglect of incredibly small probabilities that we have no apparent way to plan for). If we can show that this process offers greater justification for A than for Chalmers’ argument, then we should place more trust in A. This would of course increase the probability of physicalism, which requires A and seems to deny Chalmers’ conclusion.
(In a prior comment I tried connecting the chance of A directly to the chance of B. But that version of the argument failed.)
What follows depends on the claim that our actions and speech have physical causes. If you accept my take on Chalmers’ actual defense, and use C’ to mean the claim that we’ll never find a contradiction in ¬A, while E means the aforementioned evidence for the evidence-finder having qualia (claim Q),
P(A|E&C’)=P(Q|E&C’)
and P(A|E) seems redundant, in which case
P(Q|E&C’)=P(A|E&C’)=P(A|C’)
Now,
P(Q|E)= P(Q|E&C’)P(C’) + P(Q|E&¬C’)P(¬C’)
and since ¬C’ means P(A)=1 within logic, P(Q|E&¬C’) means the chance of Q, given the evidence plus certainty that physical causes duplicating the evidence would produce qualia. So
P(Q|E&¬C’)=1
P(Q|E)= P(Q|E&C’)*P(C’) + P(¬C’)
As for A,
P(A)= P(A|C’)P(C’) + P(A|¬C’)P(¬C’)
and since P(A|¬C’) means the chance of A if ¬A contradicts itself,
P(A)= P(A|C’)*P(C’) + P(¬C’)
by substitution,
P(A)= P(Q|E&C’)*P(C’) + P(¬C’)
P(A)=P(Q|E)
¬C’ would clearly increase the chance of Q|E and C’ would decrease it,
Better answer with slightly less snow-shoveling fatigue:
Chalmers assumes for the sake of argument that his actions and speech have physical causes. So the quoted claim A, by my argument in the fourth-to-last paragraph of the post, already stipulates the presence of the evidence that we gain from introspection and use to argue for qualia. Thus “would” applies to any logically possible world chosen at random, which may or may not have a “bridging law” to produce qualia. Chalmers doesn’t seem to address the probability of it having such a law given the physical causes or ontology that we find in A. I show this chance exceeds P(that we actually have qualia | the aforementioned evidence for qualia & the assumption that we’ll never prove A logically) -- long derivation at the end of this comment, since previous comments had flaws. Chalmers’ argument against physicalism depends on treating this long conditional proposition as certain enough for his purpose, as its denial would leave us with no reason to think qualia exist and indeed no clear definition of qualia. Without the proposition Chalmers would not have an argument so much as an assertion. I’ll look at what all of this means in a second.
In the grandparent I compare it to the situation in math. Gödel showed that we can’t prove arithmetic will never contradict itself (we can’t prove B logically) and I wanted to express this by saying that in any random logically possible world P(B)<1. Below you express it differently, saying the probability that we live in a logically possible world does not equal 1. According to that way of speaking, then, the chance that at least one logically possible world exists does not equal 1. It equals P(B), since if we could find a contradiction in one world then logic ‘leads to’ a contradiction in all worlds. And yet I argue that we know B, by means of Bayesian reasoning and the neglect of incredibly small probabilities that we have no apparent way to plan for. This would mean we know in the same way that logically possible worlds might tell us something about reality. The form of argument that Chalmers uses therefore takes its justification from Bayesian reasoning (and the neglect of incredibly small probabilities that we have no apparent way to plan for). If we can show that this process offers greater justification for A than for Chalmers’ argument, then we should place more trust in A. This would of course increase the probability of physicalism, which requires A and seems to deny Chalmers’ conclusion.
(In a prior comment I tried connecting the chance of A directly to the chance of B. But that version of the argument failed.)
What follows depends on the claim that our actions and speech have physical causes. If you accept my take on Chalmers’ actual defense, and use C’ to mean the claim that we’ll never find a contradiction in ¬A, while E means the aforementioned evidence for the evidence-finder having qualia (claim Q),
P(A|E&C’)=P(Q|E&C’)
and P(A|E) seems redundant, in which case
P(Q|E&C’)=P(A|E&C’)=P(A|C’)
Now, P(Q|E)= P(Q|E&C’)P(C’) + P(Q|E&¬C’)P(¬C’)
and since ¬C’ means P(A)=1 within logic, P(Q|E&¬C’) means the chance of Q, given the evidence plus certainty that physical causes duplicating the evidence would produce qualia. So
P(Q|E&¬C’)=1
P(Q|E)= P(Q|E&C’)*P(C’) + P(¬C’)
As for A,
P(A)= P(A|C’)P(C’) + P(A|¬C’)P(¬C’)
and since P(A|¬C’) means the chance of A if ¬A contradicts itself, P(A)= P(A|C’)*P(C’) + P(¬C’)
by substitution, P(A)= P(Q|E&C’)*P(C’) + P(¬C’)
P(A)=P(Q|E)
¬C’ would clearly increase the chance of Q|E and C’ would decrease it,
so P(A)>P(Q|E&C’)