On wednesday I gave my talk out here in Tucson. You can see a rehearsal of it below. The discussion was very interesting and I thought I would quickly jot down a few notes on what happened.

Right at about 1:00 minute into the talk Dave Chalmers spontaneously objected to the way that I had formalized the shombie argument, which I reproduce here for ease of reference.

1. (~p v q) is conceivable
2. If it is conceivable then it is possible
3. if it is possible then non-materialism is false

In short his objection was that (~p v q) isn’t the right way to formalize the first premise of the argument. He had two related points to make. The first contention was that I needed a modal operator to capture the tension between the physicalist and the non-materialist. So, I would need something like [](~p v q) (which is equivalent to ~<>(p & ~ q)). But of course I do not want to do this at all! That would make premise one totally inconceivable. I really do not think I am able to conceive of the entire space of possible worlds and see that this is true in each of them. In fact Dave makes much the same point in his 2D argument against Materialism paper against a similar move made by Yablo. All that is needed in premise one is that it is conceivable that consciousness is physical at one possible world, not all of them!

This brings up his second objection, which was that (~p v q) is conceivable but in a way that doesn’t license the inference in premise three. So, one can easily conceive of someone being conscious, and so conceive of that person being conscious or our physics being false. But this misses the point of premise one. It is not merely that (~p v q) is conceivable. Rather the claim is that I can conceive of this being true of my physical duplicate. Since we know that ~p is false at this world (we are considering a physical duplicate of me in a world that duplicates our completed physics so p must be true) it has to be the case that q is true. That is just to say that this physical duplicate of me has consciousness in just the way that I do. What is key here is that this world merely duplicates our completed physics. So, it is no good to object that this would be true in a world where there are Cartesian spirits plus our physics (as David Pitt did). That world has more in it than our physics but the shombie world, and hence my shombie twin, has just our physics.

Given all of this premise one should perhaps be re-worded as 1′.

1′. A mere physical duplicate of me, of which (~p v q) is true, is conceivable

But of course I do agree that physicalism is the thesis which holds [](p –> q). The only point I have been making above is that I do not need to include the modal operator in the first premise, which is a premise about what is conceivable. I do not need to conceive of a necessary truth in order to conceive of a shombie: that is the crucial point. The necessity comes from an independent argument that identities, if true, are necessarily true. This is the role that Kripke’s argument is playing. It is that argument which should convince us that it is necessary that the physical facts entail the qualitative facts. Given this I should probably state the third premise as 3′.

3′. If shombies are possible then, if identities are necessary then non-materialism is false.

So, summing up, we can state the more explicit 2D argument against non-materialism as follows.

1′. A mere physical duplicate of me, of which (~p v q) is true, is conceivable
2. If it is conceivable then it is possible
3′ If it is possible then, if identities are necessary then non-materialism is false.
4. identities, if true, are necessarily true
5. Non-Materialism is false

There is more that I want to say (and more interesting questions and issues raised in the discussion) but I will have to come back to it later.