In fact, there are quite a lot of concepts that are imaginable but not logically possible. Any time a mathematician uses a proof by contradiction, they’re using such a concept.
We can state very clearly what it would mean to have an algorithm that solves the halting problem. It is only because we can conceive of such an algorithm, and reason from its properties to a contradiction, that we can prove it is impossible.
Or, put another way, yes, we can conceive of halting solvers (or zombies), but it does not follow that our concepts are self-consistent.
Yeah, that’s probably right. I’m not sure what “logically possible” means to philosophers, so I tried to give a reductio ad absurdum of the argument as a whole, which should work for any meaning of “logically possible”.
Logically possible just means that “it works in theory”—that there is no logical contradiction. It is possible to have an idea that is logically possible but not physically possible, e.g., a physicist might come up with a internally consistent theory of a universe that hold that the speed of light in a vacuum is 3mph.
These are in contrast to logically impossible worlds, the classic example being a world that contains both an unstoppable force and an unmovable object; these elements contradict each other, so cannot both occur in the same universe.
Is a world with Newtonian gravity and non-elliptical orbits logically possible?
Is a world where PA proves ¬Con(PA) logically possible?
Is a world with p-zombies logically possible?
Too often, people confuse “I couldn’t find a contradiction in 5 minutes” with “there’s provably no contradiction, no matter how long you look”. The former is what philosophers seem to use routinely, while the latter is a very high standard. For example, our familiar axioms about the natural numbers provably cannot meet that standard, due to the incompleteness theorems. I’d be very surprised if Chalmers had an argument that showed p-zombies are logically possible in the latter sense.
“Chalmers argues that since such zombies are conceivable to us, they must therefore be logically possible. Since they are logically possible, then qualia and sentience are not fully explained by physical properties alone.”
This is shorthand for “in the two decades that Chalmers has been working on this problem, he has been defending the argument that...” You might look at his arguments and find them lacking, but he has spent much longer than five minutes on the problem.
I get the impression Chalmers is using something like Conceivable1 for the “zombies are conceivable” part of the arguments then sneakily switching to something more like Conceivable3 for the “conceivable, therefore logically possible” part.
I suspect you already know this, but just in case, in philosophy, a zombie is an object that can pass the Turing test but does not have internal experiences or self-awareness. Traditionally, zombies are also physically indistinguishable from humans.
I used the first meaning. Doesn’t Chalmers use it as well?
Things that are imaginable are not therefore logically possible. I find it an unreasonable and untrue leap of reasoning.
Does that make sense?
In fact, there are quite a lot of concepts that are imaginable but not logically possible. Any time a mathematician uses a proof by contradiction, they’re using such a concept.
We can state very clearly what it would mean to have an algorithm that solves the halting problem. It is only because we can conceive of such an algorithm, and reason from its properties to a contradiction, that we can prove it is impossible.
Or, put another way, yes, we can conceive of halting solvers (or zombies), but it does not follow that our concepts are self-consistent.
Yeah, that’s probably right. I’m not sure what “logically possible” means to philosophers, so I tried to give a reductio ad absurdum of the argument as a whole, which should work for any meaning of “logically possible”.
Logically possible just means that “it works in theory”—that there is no logical contradiction. It is possible to have an idea that is logically possible but not physically possible, e.g., a physicist might come up with a internally consistent theory of a universe that hold that the speed of light in a vacuum is 3mph.
These are in contrast to logically impossible worlds, the classic example being a world that contains both an unstoppable force and an unmovable object; these elements contradict each other, so cannot both occur in the same universe.
OK.
Is a world with Newtonian gravity and non-elliptical orbits logically possible?
Is a world where PA proves ¬Con(PA) logically possible?
Is a world with p-zombies logically possible?
Too often, people confuse “I couldn’t find a contradiction in 5 minutes” with “there’s provably no contradiction, no matter how long you look”. The former is what philosophers seem to use routinely, while the latter is a very high standard. For example, our familiar axioms about the natural numbers provably cannot meet that standard, due to the incompleteness theorems. I’d be very surprised if Chalmers had an argument that showed p-zombies are logically possible in the latter sense.
This is shorthand for “in the two decades that Chalmers has been working on this problem, he has been defending the argument that...” You might look at his arguments and find them lacking, but he has spent much longer than five minutes on the problem.
I get the impression Chalmers is using something like Conceivable1 for the “zombies are conceivable” part of the arguments then sneakily switching to something more like Conceivable3 for the “conceivable, therefore logically possible” part.
I suspect you already know this, but just in case, in philosophy, a zombie is an object that can pass the Turing test but does not have internal experiences or self-awareness. Traditionally, zombies are also physically indistinguishable from humans.