Corrected zombie argument, and where Robin goes wrong:
set H=the set of all physical characteristics of a human,
set Z=The set of all characteristics of a p-zombie
set C = The set of characteristics of conciousness
Definition of a p-zombie:
1. The set Z contains all the members of the set H
2. The set Z does not contain C
Conclusion:
3. H does not include C.
This conclusion logically follows from the definitions.
NB: Assumed definition of a human (set H*):
4. The set H* includes the set Z and the set C (human beings are conscious).
Let’s see what happens when we apply this corrected version of the zombie argument to your prime number example.
1. The set of p-prime numbers contains all the members of the set of prime numbers.
2. The set of p-prime numbers does not contain the number 7
This is just false. You already defined the set p-prime to contain all the prime numbers, and this includes 7. Therefore line 2 contradicts line 1. If you think that is the same as line 1 & 2 in the corrected zombie argument, you are mistaken.
You need to look at the actual logic, and you need to do it without first assuming your conclusion. Let’s have a look at what the argument looks like to a physicalist who has assumed his conclusion and cannot think about the logic without doing so.
RAC: Robin’s Assumed Conclusion: Consciousness is physical.
set H=the set of all physical characteristics of a human. NOTE: set H now implicitly includes set C, due to RAC.
set Z=The set of all characteristics of a p-zombie
set C = The set of characteristics of conciousness
Definition of a p-zombie:
1. The set Z contains all the members of the set H. NOTE: Set Z now also includes set C, due to RAC.
2. The set Z does not contain C. NOTE: We now have a contradiction, because we are claiming set Z does not contain C. But the contradiction is not actually with anything in the zombie argument itself, but with RAC.
Please try again, this time without making assumption RAC.