The 2D Argument Against Non-Materialism

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.


15 thoughts on “The 2D Argument Against Non-Materialism

  1. i can’t see the role for ~p here. if p specifies your physical state, then a mere physical duplicate of you in which ~p v q is true is just one for which q is true. i also take it that a “mere” physical duplicate of you is one in which p&t is true, where t is a that’s-all clause. so i think the premise you want is: pt&q is conceivable.

    • Thanks for following up on this Dave! Thinking through this stuff has been extremely helpful.

      In the original published version of this that is what I did and I think you are right that this is probably the best way to put the premise (I want to write a more up to date version of this stuff, but am now thinking I should keep the formalization as it originally was). I changed it for the talk for a couple of reasons. First, I was trying to avoid the issue of what the ‘that’s all’ clause is doing there. Someone might wonder why we need it, since P is supposed to entail all truths (as you did when I put it this way in the hospitality suite)…I have been thinking about this and might try to write something on it…Second, I was trying to capture the idea that if someone denies that the shombie is conscious (i.e. asserts ~q) then it must be the case that ~p is true (which I take to be the claim that any zombie worlds must differ from ours in terms of basic physics…in general I think it is easy to imagine worlds with physics like ours without consciousness…maybe ones where just Newtonian physics is true, or maybe even quantum mechanics as we understand it now (3,000 years from now this theory may be as quaint as Aristotle’s seems to us, etc, or something like that). This is not the same as the Russellian Monist move, and is what makes zombies seem intuitively to be conceivable even though as described they aren’t).

      But most of all I think I was thinking that that the conclusion of the argument should be [](p –> q). But now that I think about it, I was probably confusing the claim that physicalism is true ([](pt–>q)) with the claim that non-physicalism is false (~[](q–>~pt))…

      But the main issue that I am worried about is the claim that I do not need a modal operator in the first premise so that the second premise is ◊(pt&q) rather than ◊[](pt&q)

      • if you have t you don’t need an explicit modal operator. premise 1 can just be: conceivably (pt&q). on a common understanding of t, pt is in effect the claim that p necessitates all positive truths, so the relevant modal claim is built in here. there may also be nonmodal ways to understand t, e.g. as saying that p includes all fundamental truths.

  2. Note on djc’s two ways of cashing out “t”.

    Assuming that materialism’s truth in our world would imply [](Pt->Q), then, if “t” were cashed out in the first way, [](Pt->Q) would be equivalent to []([](P->A)->Q), where “A” is a statement expressing all and only the positive truths in our world. But on this formulation, we get an unsatisfactory result. For “Q” is possibly false regardless of whether [](P->A), in which case, if [](P->A) then ([](P->A)->~Q), equivalently ~[]([](P->A)->Q), equivalently ~[](Pt->Q). So, it has the absurd result that [](P->A)->~[](Pt->Q).

    The second way of cashing out “t” is preferable and I think best. Accordingly, “t” says that there are no positive basic truths besides those expressed by “P”. Thus “[](Pt->Q)” can be read as saying that Q is true in all the minimal physical duplicates of our world. This way, “[](P->A)->[](Pt->Q)” is trivially true, as it should be.

    • Typo: I meant to say:

      For “Q” is possibly false regardless of whether [](P->A), in which case, if [](P->A) then ([](P->A)&~Q), equivalently ~[]([](P->A)->Q), equivalently ~[](Pt->Q). So, it has the absurd result that [](P->A)->~[](Pt->Q).

      • Haha, the website won’t let a person use corner brackets to make a diamond, just like YouTube. I wish I knew Richard’s way of inserting diamonds! Anyway, to try this one more time, I meant to say:

        For “Q” is possibly false regardless of whether [](P->A), in which case, if [](P->A) then possibly([](P->A)&~Q), equivalently ~[]([](P->A)->Q), equivalently ~[](Pt->Q). So, it has the absurd result that [](P->A)->~[](Pt->Q).

        • on the modal construal of t, pt isn’t [](p->a). it’s p&[](p->a); or better: p & all(r)(r -> [](p->r). i think either of those avoids the problem.

  3. Reply to djc’s last comment:

    Ah, yes. On the first way, [](Pt->Q) would be equivalent to []((P&[](P->A))->Q). Right. That would not trivially imply the absurd result that [](P->A)->~[](P&Pt)->Q). (It would only if “possibly(P&~Q)” were trivially true.) There’s another problem, however, which is that “[]((P&[](P->A))->Q)” is utterly trivial whereas “[](Pt->Q)” shouldn’t be. But there shouldn’t be this difference if they’re equivalent. Perhaps this is why you say the other formulation is better.

    On the “better” formulation, “[](Pt->Q)” is cashed out as “[]((P&all(r)(r->[](P->r))->Q)”. Assuming the intention is to have the “all” of “all(r)” quantify over everything, and have the second two instances of “r” mean “r exists”, then by “all(r)(r->[](P->r))” you mean that, for all r, if r exists then [](P-> r exists). Which worlds would “God” have to check, then, to find out whether [](Pt->Q)? Intuitively God would have to check all the P-worlds such that everything’s existence is entailed by P, to see whether “Q” is also true at those worlds.

    But wouldn’t the P-worlds such that everything’s existence is entailed by P just be the P-worlds where there are no basic positive truths besides those expressed by “P”? If so, we wouldn’t need the nested modality in our formulations.

    • (i) yes, that’s part of the reason why the second formulation is better. (ii) “all” quantifies over propositions (actually all positive propositions). (iii) yes, these two classes of worlds would plausibly coincide. which is better depends on whether one is more comfortable with talk of modality or fundamentality (there are plenty who are comfortable with the former but not the latter).

      • Nice. Thanks for your help!

        I am also going to do a quick test for future reference. I understand that if one writes “&loz” followed by a semi-colon followed by a space, it will insert a diamond. Let’s see if I can get this right: ◊ (I can do it). But I don’t know whether the space is necessary, so I’ll try without it as well: ◊(I can do it). [Fingers crossed.]

  4. Thanks James and Dave, I am finding this discussion very helpful.

    So, Dave, which way were you thinking of ‘t’ when you appeal to the conceivability of Pt & ~Q as a way to show that if one can conceive of zombies then it doesn’t matter if the PI and SI of consciousness coincide?

  5. What is the difference between a materialism that holds □(p→q) and an idealism that holds □(~q→~p)?

    I suspect that it comes down to restrictions on the meaning of p. The p that the physicalist is talking about in □(p→q) must be an assertion about a situation in which ◊(p→q), and this is also the meaning of p in the Chalmers 2D argument. Under the physicalist model there are presumably other possible sets of physical facts that would not result in qualia. So it seems that the physicalist assertion here is “those particular physical facts which sometimes imply qualia necessarily imply qualia”, or (◊(p→q)→□(p→q)).

    That seems to motivate the idea of considering the duplicate with identical p, so that p is asserting physical facts about which ◊(p→q) is accepted as true.

    The idea of a duplicate is troublesome to me (if all of the physical facts are really the same, we are talking about the same physical world rather than a duplicate), but we could also look at a sentient human being at some point in time (e.g. 8am yesterday). All of the physical facts about that moment in time continue to be true about that time, since p is invariant with respect to our perspective on the reality that contains those asserted physical facts. This invariance with respect to perspective is part of the definition of a physical fact–any physical fact can be put into a form that is independent of the knower’s perspective. The question then is whether the actual experience of 8am yesterday (the q) persist as a necessary implication of the persistent truth of the assertion p.

    This is a temporal equivalent to the question “If X fells a tree in the forest, and you don’t hear it, does X hear it?” I think the physicalist argument here is that if X is identical to you in all the relevant physical aspects (e.g. X isn’t just a lightning bolt), then the answer is yes, even if X is displaced from you in space or time.

    At 8am yesterday it was (if our memories are reliable about this) the case that (p&q), and the facts asserted by p continue to be true about the reality of that time–that p-world.

    So if I stub my toe, it seems that this physicalism says that the pain is somehow eternal in the persistent, real anguish of some me that is frozen in time, because if those qualia ever were real implications of the physical facts, then they must persist as real implications of those same physical facts in the p-world of that time.

    To the dualist, this physical four-space manifold exists, but awareness tours it, moving through time, and this gives rise to the possibility of (p&~q). Thus the p-world of 8am yesterday is possibly now a zombie world, the awareness having moved on.

    To the idealist, the four-space manifold is but a model of the rules by which different aspects of qualia relate to each other, so there is no meaning to any physical reality in the absence of qualia. The p world only meaningfully exists as a model of aspects of such qualia as currently exist. The abstract world of the objective facts asserted by p is concrete only to the extent those facts have referents in q.

    But I don’t think that dualism actually asserts (p&~q), after all, the dualist spirit that tours the space-time continuum could be pervasive enough that it happens to be the case that ~(p&~q). Dualism asserts that (p&~q) is metaphysically possible, a stance that is denied in both in physicalism and idealism.

    It seems to me that the physicalist argument here is based on the assertion that ((p&q)v(~p&~q)) implies a metaphysical identity between p and q. But that argues as much for idealism as for physicalism, it doesn’t rule out all non-materialism, only dualism.

    I really don’t understand how the physicalist can possibly know whether this material p-world of 8am yesterday is now a zombie world or exists with all its qualia. Since the physicalist cannot know this, I don’t understand how the physicalist finds (p&~q) inconceivable nor how the physicalist asserts knowledge that a person at 8am yesterday contemplating a duplicate of the p-world could know that duplicate exists with all its qualia.

    If the material existence of the p-world irreducibly depends on the perspective of the observer, then “material existence” is, by definition, not a fact within p.

  6. First, it seems like just because something is conceivable doesn’t make it possible. I can conceive of myself being able to breath and talk and live and thrive in the vacuum of space. That doesn’t mean it’s possible.

    I don’t see much consideration for time. That is, at any one time nothing is exactly as it was at any other time, so there could never be an exact duplicate, because even one’s own self is never the same as itself from moment to moment.

  7. Hi Shack Toms, yeah this is something I have thought about before. I tend to think that Physicalism as I understand it is compatible with both Idealism and Materialism on certain understandings of those claims. Though I guess I am open to being wrong about this…

    Sam, there are different senses of ‘possible’. The sense of possibility here is the one in which you could live and breathe and thrive in space. It is not physically possible given the way the word is now, but with some slight modifications we could make it happen…as to the time thing, the idea is that you duplicate some initial state and the laws which govern the state transitions and then the systems unfolds in time in exactly the same way that it would in the actual world.

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