The Two-Dimensional Argument Against Materialism

The Two-Dimensional Argument Against Materialism

chalmers at anu dot edu dot au

*[[ An abridged version of this paper is forthcoming in B. McLaughlin (ed.) The Oxford Handbook of the Philosophy of Mind. The full version is forthcoming in my The Character of Consciousness (Oxford University Press). Some material in this paper is drawn from Chalmers 1999, 2002, 2004b, and 2005. ]]

A number of popular arguments for dualism start from a premise about an epistemic gap between physical truths about truths about consciousness, and infer an ontological gap between physical processes and consciousness. Arguments of this sort include the conceivability argument, the knowledge argument, the explanatory-gap argument, and the property dualism argument. Such arguments are often resisted on the grounds that epistemic premises do not entail ontological conclusion.

My view is that one can legitimately infer ontological conclusions from epistemic premises, if one is careful about how one reasons. To do so, the best way is to reason first from epistemic premises to modal conclusions (about necessity and possibility), and from there to ontological conclusions. Here, the crucial issue is the link between the epistemic and modal domains. How can one reason from theses about what is knowable or conceivable to theses about what is necessary or possible?

To bridge the epistemic and modal domains, the framework of two-dimensional semantics can play a central role. I have used this framework in earlier work (Chalmers 1996) to mount an argument against materialism. Here, I want to revisit the argument, laying it out in a more explicit and careful form, and responding to a number of objections. In what follows I will concentrate mostly on the conceivability argument. I think that very similar considerations apply to the other arguments mentioned above, however. In the final section of the paper, I show how this analysis might yield a unified treatment of a number of anti-materialist arguments.

1 The Conceivability Argument

The most straightforward form of the conceivability argument against materialism runs as follows.

(1) P&~Q is conceivable (2) If P&~Q is conceivable, P&~Q is metaphysically possible (3) If P&~Q is metaphysically possible, materialism is false. (4) Materialism is false.

Here P is the conjunction of all microphysical truths about the universe, specifying the fundamental features of every fundamental microphysical entity in the language of microphysics. Q is an arbitrary phenomenal truth: perhaps the truth that someone is phenomenally conscious, or perhaps the truth that a certain individual (that is, an individual satisfying a certain description) instantiates a certain phenomenal property. P&~Q conjoins the former with the denial of the latter.

If Q is the truth that someone is phenomenally conscious, then P&~Q is the statement that everything is microphysically as in our world, but no-one is phenomenally conscious. In this version, P&~Q says that the world is a zombie world. If Q is the truth that a certain individual instantiates a certain phenomenal property, then P&~Q is the statement that everything is microphysically as in our world, but that it is not the case that the individual in question instantiates the relevant phenomenal property. In this case, it will suffice for the truth of P&~Q that the world is a zombie world, or simply that the individual in question is a zombie in a physically identical world. It will also suffice that the individual in question is an invert, who has an experience that differs slightly from the corresponding experience of the corresponding individual in our (physically identical) world.

The first premise of this argument asserts an epistemic thesis, about what can be conceived. The second premise steps from the epistemic thesis to a modal thesis, about what is possible. The third premise steps from the modal thesis to a metaphysical thesis, about the nature of our world.

The third premise is relatively uncontroversial. It is widely accepted that materialism has modal commitments. Some philosophers question whether materialism is equivalent to a modal thesis, but almost all accept that materialism at least entails a modal thesis. Here one can invoke Kripke's metaphor: if it is possible that there is a world physically identical to our world but phenomenally different, then after God fixed the physical facts about our world, he had to do more work to fix the phenomenal facts.

A familiar complication arises from the observation that physicalism about our world is compatible with the possibility of dualism in other worlds, and in particular is compatible with the possibility of a physically identical world that contains extra, nonphysical phenomenology. This means that if Q is a negative truth about our world — say, the truth that no-one instantiates a certain phenomenal property — then materialism about our world is compatible with the possibility of P&~Q. To finesse this point, we can stipulate that in the argument above, Q is a positive truth (one that holds in all worlds that contain a duplicate of our world; see Chalmers 1996, p. 40): if Q is a positive truth, then materialism is incompatible with the possibility of P&~Q. Alternatively, we can conjoin P with a "that's-all" statement T, stating that the world is a minimal world that satisfies P (see Jackson 1998, p. 26). Then even when Q is a negative truth, materialism is not compatible with the possibility of PT&~Q (where PT is the conjunction of P and T).

The real work in the argument is done by the first and second premises. The second premise is particularly controversial, as there are a number of examples that have led many philosophers to deny that there is an entailment from conceivability to metaphysical possibility. To assess these premises, we need to understand the notion of conceivability.

2 Varieties of Conceivability

Conceivability is to be understood as an epistemic notion, defined in epistemological (and perhaps psychological) terms. To a first approximation, we can say that S is conceivable when S expresses a coherent hypothesis: one that cannot be ruled out a priori. To refine this understanding, it is useful to make some distinctions. (These distinctions are discussed at much greater length in Chalmers 2002.)

We can say that S is prima facie conceivable (for a subject) when that subject is unable to rule out the hypothesis expressed by S by a priori reasoning, on initial consideration. We can say that S is ideally conceivable when the hypothesis expressed by S cannot be ruled out a priori, even on ideal rational reflection. The main difference here is that prima facie conceivability is tied to a subject's contingent cognitive limitations, while ideal conceivability abstracts away from those limitations.

Some examples: (1) '2+2=5' is neither prima facie conceivable nor ideally conceivable; (2) Where S is a highly complex but provable mathematical truth, ~S will be prima facie conceivable for most subjects, but it is not ideally conceivable; (3) Where S is 'There is a flying pig', S is prima facie conceivable, and is almost certainly ideally conceivable.

The notions of conceivability discussed above are versions of negative conceivability which is defined in terms of what a subject can rule out through a priori reasoning. We can say that S is negatively conceivable when S cannot be ruled out through a priori reasoning. The two notions above can then be seen as prima facie negative conceivability and ideal negative conceivability respectively.

It is also possible to define notions of positive conceivability, which is defined in terms of what subjects can form a positive conception of. We can say that S is positively conceivable when one can coherently imagine a situation in which S is the case. Where negative conceivability requires merely entertaining a hypothesis and being unable to rule it out, positive conceivability involves being able to form some sort of clear and distinct conception of a situation in which the hypothesis is true. One can then say that S is prima facie positively conceivable when a subject can imagine a situation that they take to be coherent and that they take to be one in which S is the case. And one can say that S is ideally positively conceivable when its prima facie positive conceivability cannot be defeated on ideal rational reflection (in particular, when arbitrary details can be filled in in the imagined situation without any contradiction revealing itself, and when ideal reflection reveals the imagined situation as one in which S is the case).

Traditional notions of conceivability (Descartes' clear and distinct conceivability, for example) are arguably varieties of positive conceivability rather than negative conceivability. At the same time, the notion of positive conceivability is more complex than that of negative conceivability, and a rigorous characterization of the notion requires saying much more about just what it is to imagine a situation, and so on. I characterize positive conceivability in more depth in Chalmers 2002. In this paper, the roles of positive and negative conceivability will often be interchangable (I will make clear when the difference is relevant), so the informal account above will suffice for present purposes. For much of the discussion one can focus on negative conceivability without much loss, but positive conceivability is available as an alternative if there turn out to be any problems with theses tied to negative conceivability.

Insofar as there is a gap between prima facie conceivability and ideal conceivability, it is ideal conceivability that is a better guide to possibility. This is especially clear in the case of prima facie negative conceivability: we have seen that the negation of a complex mathematical truth may be prima facie negatively conceivable, but it is not ideally conceivable and it is not possible. It is less easy to find cases of prima facie positive conceivability without ideal positive conceivability (see Chalmers 2002 for some potential cases), but insofar as there are such cases, there will be little reason to think that they are possible.

Correspondingly, some familiar purported counterexamples to the claim that conceivability entails possibility are really counterexamples to the claim that prima facie conceivability entails possibility. For example, it is sometimes said that both Goldbach's conjecture and its negation are conceivable, while only one of them is possible. Here the relevant notion of conceivability is something like prima facie negative conceivability. There is no reason to believe that both Goldbach's conjecture and its negation are ideally conceivable, so there is no reason to think that this is a counterexample to the claim that ideal conceivability entails possibility. So from here onward, talk of "conceivability" simpliciter should always be understood to be talk of ideal conceivability (either positive or negative).

The other familiar class of purported counterexamples arises from Kripke's analysis of the necessary a posteriori. It is often said that sentences such as 'water is not H 2 O' provide counterexamples to the claim that conceivability entails possibility: it is conceivable that water is not H 2 O, but it is not metaphysically possible.

Here one has to be careful. There is a sense of 'conceivable' in which 'water is not H 2 O' is not conceivable (given that water is H 2 O in the actual world): in this sense, any conceivable situation in which it seems that water is not H 2 O (a Twin Earth world, say) should better be described as a conceivable situation in which water is still H 2 O, but in which there is watery stuff that is not H 2 O. Using the term 'conceivable' this way, one might say that 'water is not H 2 O' seems conceivable (or that it is prima facie conceivable, to one without relevant empirical knowledge), but that it is not really conceivable. We might call this sense of conceivability secondary conceivability (for reasons familiar from a two-dimensional analysis, and discussed in Chalmers 2002). Then the Kripkean cases are compatible with the claim that secondary conceivability entails metaphysical possibility. But at the same time, this claim is not very useful for present purposes, as whether a sentence is secondarily conceivable will typically depend on a variety of empirical factors, and an opponent might deny that zombies are secondarily conceivable, on the grounds that there is an a posteriori identity between phenomenal and physical properties. So a link between secondary conceivability and possibility does not offer an a priori route to conclusions about metaphysical possibility.

Instead, what is relevant here is primary conceivability: the sense in which 'water is not H 2 O' can correctly be said to be conceivable. The notion of negative conceivability defined above is a sort of primary conceivability, as it is defined in terms of what can be ruled out a priori, and 'water is H 2 O' cannot be established a priori. (One might define a distinct notion of negative secondary conceivability, but I will set that aside here.) One can likewise define a notion of positive primary conceivability, so that S is positively primarily conceivable when S can imagine a coherent situation that verifies S, where a situation verifies S when, under the hypothesis that the situation actually obtains, the subject should conclude that S. If the subject imagines a Twin Earth situation with XYZ in the oceans and lakes, and assumes that the situation obtains in their own environment, then the subject should conclude that water is XYZ rather than H 2 O. So 'water is not H 2 O' is positively primarily conceivable, as well as negatively primarily conceivable.

Unlike secondary conceivability, matters of primary conceivability are plausibly in the a priori domain: whether S is primarily conceivable turns on matters of a priori reasoning. But primary conceivability does not entail metaphysical possibility: 'water is not H 2 O' is primarily conceivable, but it is not metaphysically possible.

Still, there remains a link between primary conceivability and metaphysical possibility in these cases. When we conceive that water is not H 2 O, we imagine (for example) a Twin Earth situation in which the watery liquid in the oceans and lakes is XYZ. This situation is metaphysically possible, so there is a sense in which our conceiving involves access to a possible world. Under the usual way of describing possible worlds, this world is not a world in which water is not H 2 O. But the world still stands in a strong relation to the sentence 'water is not H 2 O'. In particular, if we came to accept that our own world had the character of this world (with XYZ in the oceans and lakes), we should then endorse the claim 'water is not H 2 O'.

This can be put in two-dimensional terms by saying that while the Twin Earth does not satisfy 'water is not H 2 O' ('water is not H 2 O' is not true of that world considered as counterfactual), the Twin Earth world verifies 'water is not H 2 O' ('water is not H 2 O' is true of that world considered as actual). Equivalently, we can say that while the secondary intension of 'water is not H 2 O' is false at w, the sentence's primary intension is true there. To a first approximation, a world w verifies S (or S is true at w considered as actual, or the primary intension of S is true at w) when, if we came to accept that our own world is qualitatively like w, we should then endorse S. Strictly speaking, the worlds w that are relevant to primary intensions are centered worlds: worlds that come with a marked "center" consisting of an individual and time. When we consider a centered world w as actual, we consider the hypothesis that we are currently in the situation of the individual at the center. (For much more on these notions, see Chalmers 2004.)

We can say that when the primary intension of S is true at some centered world (i.e., when some centered world verifies S), S is primarily possible, or 1-possible. When the secondary intension of S is true at some world (i.e., when some world satisfies S), S is secondarily possible, or 2-possible. Then 'water is not H 2 O' is not 2-possible, but it is 1-possible.

The observation that sentences such as 'water is not H 2 O' are conceivable but not possible, in these terms, comes to the claim that these sentences are primarily conceivable (1-conceivable) but are not secondarily possible (2-possible). So there is good reason to believe that 1-conceivability does not entail 2-possibility. However, these cases are entirely compatible with a link between 2-conceivability and 2-possibility, and more importantly for present purposes, they are entirely compatible with a link between 1-conceivability and 1-possibility.

In fact, it is not hard to argue that all of the standard Kripkean a posteriori necessities ('heat is the motion of molecules', 'Hesperus is Phosphorus', and so on) have this structure. For each of these necessities, one might say that it's negation is conceivable but not possible, meaning that it is 1-conceivable but not 2-possible. But in each of these cases, the sentence in question is 1-possible. For example, 'heat is not the motion of molecules' is verified by a world in which something other than molecules causes sensations as of heat. 'Hesperus is not Phosporus' is verified by a world in which the objects visible in the morning and evening skies are entirely distinct. Furthermore, it is plausible that worlds such as these are just what one is conceiving of when one conceives that heat is not the motion of molecules, or that Hesperus is not Phosphorus. So in these cases, there remains a strong link between conceivability and metaphysical possibility.

To summarize, we have seen that the standard counterexamples to a conceivability-possibility link are accommodated by noting that (i) prima facie conceivability is an imperfect guide to possibility, and (ii) primary conceivability is an imperfect guide to secondary possibility. But (i) is entirely consistent with a link between ideal conceivability and possibility, and (ii) is entirely consistent with a link between primary conceivability and primary possibility. Putting the pieces together: all of these counterexamples are compatible with the thesis that ideal primary conceivability entails primary possibility.

There are two versions of this thesis, depending on whether one interprets the relevant sort of conceivability as positive or negative.

(CP+) Ideal primary positive conceivability entails primary possibility (CP-) Ideal primary negative conceivability entails primary possibility.

CP- entails CP+, as ideal primary positive conceivability entails ideal primary negative conceivability. If S can be ruled out a priori, then no coherent imagined situation will verify S. It is not obvious whether or not CP+ entails CP-, as it is not obvious whether ideal primary negative conceivability entails ideal primary positive conceivability. That is, it is not obvious whether or not there is an S that cannot be ruled out a priori, but such that no coherent imagined situation verifies S. (In Chalmers 2002 I argue that there is no such S, so that ideal primary negative conceivability entails ideal primary positive conceivability.) So CP- is at least as strong as CP+ and is possibly somewhat stronger.

Most importantly for present purposes, however, both CP+ and CP- are compatible with all the familiar purported counterexamples to the conceivability-possibility link. Furthermore, it seems that there are no clear counterexamples to either thesis (though later in the paper, I will discuss some potential counterexamples that have been put forward). In particular, both theses are entirely compatible with the existence of Kripkean a posteriori necessities, so while existence of these necessities is often used to case doubt on conceivability-possibility theses, they cannot be used to cast doubt on CP+ or CP-.

So for now, I will take these theses as reasonable conceivability-possibility theses that might be used in mounting a refined conceivability argument against materialism. Later in the paper, I will return to the question of their truth.

3 A refined conceivability argument

Henceforth, unqualified uses of "conceivability" and "conceivable" should be understood as invoking ideal primary conceivability. I will often be inexplicit about whether positive or negative conceivability is involved. In effect, the argument forms below can be understood as generating two different arguments, depending on whether one understands conceivability as ideal primary positive conceivability or as ideal primary negative conceivability. For many purposes the distinction will not matter. When it does matter, I will be explicit.

Given the discussion above, one might try generating an anti-materialist argument by simply substituting primary possibility for metaphysical possibility in the original argument.

(1) P&~Q is conceivable (2) If P&~Q is conceivable, P&~Q is 1-possible (3) If P&~Q is 1-possible, materialism is false. (4) Materialism is false.

On this reading, (1) and (2) are both plausible theses, but (3) is not obviously plausible. The reason is that materialism requires not the 1-impossibility of P&~Q but the 2-impossibility of P&~Q. That is, materialism requires that it could not have been the case that P were true without Q being true. This is a subjunctive claim about ordinary metaphysical possibility, and so invokes 2-impossibility rather than 1-impossibility.

A materialist might reasonably question (3) by holding that even if there is a world w verifying P&~Q, w might be a world with quite different ingredients from our own. For example, it might be that W does not instantiate true microphysical properties (those instantiated in our world), such as mass and charge, but instead instantiates quite different properties: say, pseudo-mass and pseudo-charge, which stand to mass and charge roughly as XYZ stands to H 2 O. Likewise, it might be that w does not lack true phenomenal properties, but instead lacks quite different properties: say, pseudophenomenal properties. If so, then the possibility of w has no bearing on whether true microphysical properties necessitate true phenomenal properties. And it is the latter that is relevant for materialism.

Still, it may be that the gap between 1-possibility and 2-possibility could be closed. In particular, when a statement S has the same primary intension and secondary intension, then a world will verify S iff it satisfies S, so S will be 1-possible iff it is 2-possible. If P and Q both have primary intensions that coincide with their secondary intensions, then so will P&~Q, and we could run the following argument:

(1) P&~Q is conceivable (2) If P&~Q is conceivable, P&~Q is 1-possible (3) If P&~Q is 1-possible, P&~Q is 2-possible. (4) If P&~Q is 2-possible, materialism is false. (5) Materialism is false.

Here, the truth of (3) requires that both P and Q have primary and secondary intensions that coincide. In the case of Q, this claim is quite plausible. As Kripke noted, there does not seem to be the same strong dissociation between appearance and reality in the case of consciousness as in the cases of water and heat: while it is not the case that anything that looks like water is water, or that anything that feels like heat is heat, it is plausibly the case that anything that feels like consciousness is consciousness. So it is not clear that the notion of "pseudoconsciousness", something that satisfies the primary intension of 'consciousness' without being consciousness, is coherent. Likewise for other more specific phenomenal properties. So there is a strong case that the primary and secondary intensions of phenomenal terms coincide. (For more on this case, see Chalmers 2003b.)

However, in the case of P, this claim is less plausible. A materialist might reasonably hold that microphysical terms (such as 'mass' and 'charge') have primary intensions that differ from their secondary intensions. In particular, it is plausible that the primary intensions of these terms are tied to a certain theoretical role. We might say that the primary intension of 'mass' picks out whatever property plays the mass-role (e.g. resisting acceleration in certain ways, being subject to mutual attraction in a certain way, and so on), and that the primary intension of 'charge' picks out whatever property plays the charge-role (e.g. obeying certain electromagnetic principles, being subject to attraction and repulsion in certain ways, and so on).

By contrast, one might reasonably hold that the secondary intension of microphysical terms is tied to the property that actually plays the role. For example, if property M plays the mass-role in the actual world, then one might hold that in any world in which mass is instantiated, mass is M. It follows that if there are worlds in which some other property M' plays the mass-role, then M' is not mass in that world (at best, it is pseudo-mass). If so, then the primary and secondary intensions of 'mass' will not coincide: the primary intension of 'mass' will pick out whatever plays the mass-role in such a world, but the secondary intension will not.

There are other views of the semantics and metaphysics of microphysical terms that may reject this argument for the distinctness of the primary and secondary intensions of 'mass'. In particular, the argument will not go through on views according to which it is necessary that mass is the property that plays the mass-role. (These include views on which 'mass' is a nonrigid designator whose secondary intension picks out different properties that play the role in some worlds, and views on which it is necessary that M is the property that plays the mass-role, where M is the property rigidly designated by 'mass'.) Still, the view sketched above is a quite reasonable view — more plausible than the alternatives, in my opinion — and it is the view that best grounds resistance to an inference from the 1-possibility of P&~Q to its 2-possibility. So we can suppose that the view is correct in order to see what follows.

On this view, a world may verify P without satisfying P. The secondary intension of P requires that certain specific properties such as mass, spin, and charge are distributed in a certain specific way across space-time, with appropriate causal and nomic relations among them. The primary intension of P requires only that whatever properties plays the mass-role, the spin-role, and charge-role are distributed in this way. If w is a world where these roles are played by properties other than mass, spin, and charge (we might say that they are played by "schmass", "schmin", and "schmarge"), which are otherwise distributed in the right way over space-time and have appropriate causal and nomic relations among them, then w will verify P, but it will not satisfy P. Here, we might say that the physics of W has the same structural profile as physics in the actual world, but that it has a different intrinsic profile, in that it differs in the intrinsic properties that fill this structure. To verify P, a world must have the right structural profile, while to satisfy P, a world must have the right structural and intrinsic profile.

It follows that premise 3 is not guaranteed to be true. Because a world can verify P without satisfying P, it may be that P&~Q is 1-possible but not 2-possible. However, this requires that P and Q be related in a certain specific way. In particular, it requires that some worlds that verify P also verify ~Q, while no worlds that satisfy P also satisfy ~Q. This requires in turn that some worlds that have the same structural profile as the actual world verify ~Q, while no worlds that have the same structural and intrinsic profiles as the actual world satisfy ~Q. We can assume for the moment that the primary and secondary intensions of Q coincide. Then we can put all this by saying that the falsity of (3) requires that the structural profile of physics in the actual world does not necessitate Q, but that the combined structural and intrinsic profiles of physics the actual world do necessitate Q.

This idea — that the structural properties of physics in the actual world do not necessitate the existence and/or nature of consciousness, but that the intrinsic properties of physics combined with the structural properties do — corresponds to a familiar view in the metaphysics of consciousness. This is the view that I have elsewhere called Russellian monism (or type-F monism, or panprotopsychism). On this view, consciousness is closely tied to the intrinsic properties that serve as the categorical bases of microphysical dispositions. Russell and others held that the nature of these properties is not revealed to us by perception (which reveals only their effects) or by science (which reveals only their relations). But it is coherent to suppose that these properties have a special nature that is tied to consciousness. They might themselves be phenomenal properties, or they might be protophenomenal properties: properties that collectively constitute phenomenal properties when organized in the appropriate way.

Russellian monism is an important view on the mind-body problem. I think that it is certainly not ruled out by the conceivability argument and by related arguments. If Russellian monism is true, then when we conceive of zombies, we hold fixed the structural properties of physical systems in the actual world, but not their intrinsic properties (which are protophenomenal properties). If we consider these intrinsic protophenomenal properties to be physical properties, then Russellian monism will qualify as a form of physicalism. But because it relies on speculation about the special nature of the fundamental properties in microphysics, it is a highly distinctive form of physicalism that has much in common with property dualism, and that many physicalists will want to reject.[*]

*[[ A related position arises from views on which laws of nature are necessary (e.g. Shoemaker 19xx), and on which there is a lawful connection between physical properties and phenomenal properties in our world. Such a view may hold that it is essential to physical properties that they have this nomic profile, so that there is no world satisfying P&~Q. Some versions of this view will deny (2), and are discussed later in the paper. But other versions may accept (2), holding that there is a world verifying P&~Q, but will hold that it involves distinct "schmysical" properties that lack this nomic profile. The resulting view resembles Russellian monism in some respects, but differs from the usual form in taking the connection between physical and phenomenal properties to be nomic in the first instance. Because it turns on this nomic connection, this view does not provide any loophole for materialism: at best, it yields a version of property dualism on which the laws of nature connecting physical and phenomenal properties are necessary. See objection 12 in section XX for more on related issues. ]]

In any case, we can now close the loophole in the previous argument as follows:

(1) P&~Q is conceivable (2) If P&~Q is conceivable, then P&~Q is 1-possible (3) If P&~Q is 1-possible, then P&~Q is 2-possible or Russellian monism is true. (4) If P&~Q is 2-possible, materialism is false. (5) Materialism is false or Russellian monism is true.

This argument is valid. I discussed the case for premises (1), (2), and (4) earlier, and I have just now argued for premise (3). I think that (5) is the proper conclusion of the conceivability argument. For the reasons given above, such arguments (and also related arguments such as the knowledge argument and the property dualism argument) cannot exclude Russellian monism, and Russellian monism is arguably a form of physicalism, if a distinctive and radical kind. So the possibility of Russellian monism needs to be explicitly acknowledged as an option in the conclusion.

A couple of minor notes on the argument. First, to be fully explicit, the argument might take the truth of Q as a premise. If Q were false, the ground for accepting (4) would collapse. In the less explicit version of the argument above, we can consider the truth of Q part of the case for accepting premise (4). In fact, for reasons given earlier, the case for (4) requires that Q is a positive truth about consciousness. Alternatively, one can remain silent on whether Q is a positive or negative truth, and handle this matter by conjoining P with a "that's-all" clause asserting that the world is a minimal world in which P (or equivalently, by building such a that's-all clause into P).

Second, it is worth noting that (contrary to a common supposition), the assumption that Q has the same primary and secondary intensions is not necessary for the argument for (5) to go through. To see this, we can consider the version of the argument where we adjoin a "that's-all" clause to P. From (1) and (2), we can derive the conclusion that there is a minimal world verifying P in which the primary intension of Q is false. If P has the same primary and secondary intensions, then this world will be a minimal P-world in which the primary intension of Q is false. This world must differ from our world, because the primary intension of Q is true in our world. (There is a small loophole here arising from the possibility that this world differs merely in the location of the center of the relevant centered world. I discuss this loophole in section 5.) It follows that there is a minimal P-world that is not a duplicate of our world, so that physicalism is false of our world. It could be that strictly speaking physicalism will be true of consciousness, because P necessitates Q, but physicalism will be false of properties closely associated with consciousness, namely those associated with the primary intension of Q. We might think of this sort of view as one on which phenomenal properties are physical properties that have non-physical properties as modes of presentation.

Alternatively, if P has different primary and secondary intensions, then by the reasoning given in the earlier discussion of premise (3), one can conclude that either there is a minimal world satisfying P in which the primary intension of Q is false (which again entails the falsity of physicalism), or that the primary intension of Q is necessitated by the structural and intrinsic profiles of physics in our world, but not by the intrinsic profiles alone. This view can be considered another form of Russellian monism, in that the intrinsic properties of physics in our world are crucial for constituting the properties associated with the modes of presentation of consciousness. So if Q has a distinct primary and secondary intensions, then one will have to formalize premises (3) and (4) somewhat differently, but the argument for (5) will still work just as well.

This completes the exposition of the two-dimensional argument against materialism. In what follows I will address some objections to the argument that arise from the recent literature. I have already said what needs to be said about premises (3) and (4), and I do not anticipate significant objections to them (with one exception that I will discuss). I will discuss some objections to premise (1) and some hard-to-classify objections relatively briefly, and then I will focus on objections to the crucial premise (2).

4 Objections to Premise (1)

Premise (1) says that P&~Q is conceivable: that is, that we can conceive a world physically identical to ours containing zombies and/or inverts. It is worth noting that such a world need not be an entire zombie world. One might worry that there are complications associated with imagining oneself to be zombie, at the center of a centered world. For the purpose of the argument, it usually suffices to conceive of a physically identical world in which some other being, corresponding to a conscious being in this world, is a zombie or an invert.

The premise can be understood as invoking ideal primary negative conceivability or ideal primary positive conceivability. The first version makes a somewhat weaker claim (positive conceivability entails negative conceivability, but the reverse is not obviously the case), and is slightly more straightforward. In this version, the premise simply says that P&~Q cannot be ruled out a priori: that a priori reasoning cannot rule out the hypothesis that P obtains and that someone else is a zombie, for example. The second version makes the somewhat stronger claim that we can (in principle) clearly and distinctly imagine a situation in which P holds and in which someone is a zombie or an invert, where the hypothesis that this situation obtains cannot be ruled out by a priori reasoning. Of course, any difference in strength here will be balanced by an inverse difference in strength for the corresponding versions of premise (2).

I discussed the strong prima facie case for these claims in Chalmers (1996), and will not try to recapitulate it here. The zombie hypothesis is at least prima facie coherent and imaginable. To reject the premise, one needs to find something that undermines the prima facie coherence and imaginability, such as some sort of a priori incoherence, contradiction, or unimaginability in the hypothesis that emerges on reflection. A detailed defense of the premise involves arguing that no candidate for this sort of undermining can succeed. Here I will consider various suggestions.

(1) Analytic functionalism. One way to reject the conceivability premise would be to accept an analytic functionalist view of consciousness, on which what it means to say that someone is conscious is that they have a state that functions in an appropriate way in their cognitive system and their behavior. If consciousness were defined in this way, then any functionally identical being would be conscious by definition, so zombies would be ruled out. Analytic functionalism about consciousness is widely rejected, however, and I have argued against it at length elsewhere (see e.g. the discussion of type-A materialism in Chalmers 2003a), so I will not argue against it further here.

(2) Prima facie but not ideal conceivability. It is natural to suggest that zombies may be prima facie but not ideally conceivable (see van Gulick 2000 and Worley 2003 for suggestions along these lines). This corresponds to the position that I call type-C materialism in Chalmers (2003a), according to which there is a prima facie epistemic gap between physical and phenomenal truths that may be closed on ideal reflection, perhaps because of new discoveries about physical processes, or perhaps because of novel reasoning. To very briefly summarize the argument there: to render zombies incoherent even on ideal reflection requires some sort of conceptual link between physical and phenomenal concepts. Given that physics and physical concepts are all structural-dynamical in character (and new scientific developments are unlikely to change this, although see option (3)), phenomenal concepts must have a character that is linked to structural-dynamic concepts in an appropriate way. Upon examination, the only candidate that is remotely tenable is the hypothesis that phenomenal concepts are functional concepts. But we have already seen that there is good reason to reject that view.

A related objection (e.g. Bailey forthcoming) holds that arguments from ideal conceivability are toothless, as non-ideal creatures such as ourselves cannot know whether or not a given statement is ideally conceivable. I think that there is no reason to accept this claim. Although we are non-ideal, we can know that it is not ideally conceivable that 0=1, and that it is ideally conceivable that someone exists. We know that certain things about the world (say, all philosophers are philosophers) are knowable a priori, and that certain things about the world (say, that there is a table in this room) are not so knowable, even by an ideal reasoner. Likewise, reasoning of the sort above gives us very good reason to think that there is no a priori entailment from physical to phenomenal truths and that zombie hypotheses are conceivable, even for an ideal reasoner.

(3) Expanding the conception of the physical. Stoljar (2001) argues that whether zombies are conceivable depend on how we understand physical properties. When we conceive of zombies, we hold fixed t-physical properties, or properties as characterized in physical theory. But we may not hold fixed o-physical properties, or the underlying properties of physical objects, including the intrinsic properties that play the roles characterized in physical theory. So the position is left open that o-physical zombie duplicates are both inconceivable and impossible: if we adequately conceived of the o-physical properties, we would see that any o-physical duplicate of a conscious being is conscious. And if we expanded P to include hypothetical o-physical concepts of these intrinsic properties (characterizing their intrinsic nature), then P&~Q would be inconceivable. I think that this is an important position, but it is clearly a version of Russellian monism, so I take it to be compatible with the overall argument given above.

(4) Zombies presuppose epiphenomenalism. John Perry (2001) has suggested that the assertion that zombies are conceivable presupposes epiphenomenalism, the thesis that consciousness plays no causal role. If we thought that consciousness plays a causal role, we would not find zombies conceivable. In Chalmers (2004b) I argue that this claim is simply false. Its falsity is demonstrated by the fact that many non-epiphenomenalist views are compatible with the conceivability of zombies. For example, many type-B materialists (such as Hill, Loar, Papineau, and so on) accept that zombies are conceivable, and that consciousness plays a causal role. These philosophers deny that zombies are possible, but that is a different stage of the argument. Furthermore, the Russellian monist view is a non-epiphenomenalist view that we have seen is compatible with the conceivability of zombies in the relevant sense. Finally, even Cartesian interactionist dualism, on which consciousness certainly plays a causal role, is compatible with the conceivability (and possibility) of zombies. On such a view, physically identical beings without consciousness will presumably have large causal gaps in their functioning (or else will have some new element to fill those gaps), but there is nothing obviously inconceivable about such causal gaps. (For more on this, see Chalmers 2004b.)

(5) The judgments of zombies. It is an admittedly strange feature of zombies that they appear to make claims about consciousness that are indistinguishable from the claims of conscious beings, and that they even make parallel judgments, if judgments are functionally understood. I called this "the paradox of phenomenal judgment", and argued that while it is strange (many strange things happen in other possible worlds), it does nothing to undermine the coherence of zombies. Thomas (1998) argues that we have to choose between saying that zombie's claims are true, meaningless, insincere, or mistaken, and that each of these options is untenable. Others (Kirk 1999, Lynch forthcoming) have argued that the coherence of zombies undermines our knowledge of consciousness, since we will then be unable to distinguish ourselves from zombies. In Chalmers (2003b) I argue that an appropriate account of the content and epistemology of our phenomenal judgments shows that there is no problem here.

(6) Zombies are not positively conceivable. Some (e.g. Ashwell 2003, Marcus 2004) have argued that while zombies may be negatively conceivable, they are not positively conceivable. To positively conceive another creature, one must conceive of some combination of physical processes and conscious states. But conceiving of physical processes clearly does not suffice to conceive of a zombie (since conscious beings may have the same processes), and in conceiving of a zombie it is out of the question to conceive of conscious states. So we can form no positive conception of a zombie.

In response, I think it is clear that when we conceive of zombies we conceive of the absence of consciousness. There is no more problem with clearly and distinctly imagining a situation in which there is no consciousness than in imagining a world in which there are no angels, or in imagining a world with one particle and nothing else. The argument here appears to require the idea that absences are never positively conceivable, or at least that to positively conceive an absence always requires conceiving something else in its place. But the cases above suggest that such a claim is clearly false. The claim may turn on misinterpreting the notion of positive conceivability: presumably there is a sense in which conceiving of an absence is negative conceiving, but this is not the sense that is relevant here.

A general point about the arguments above: Many of these arguments, especially 4-6, turn on considerations that are specific to the conceivability of zombies, and do not apply to the conceivability of inverts and the like. One should keep in mind that for the anti-materialist argument, one does not need to consider beings as remote from us as zombies, or even as remote as full-scale inverts. It suffices if we can conceive of a being whose conscious experience is for just a moment slightly different from that of an actual physical duplicate's: perhaps they experience a slightly different shade at a point in the background of their visual field. Any problems that are specific to zombies then will not apply.

5 Hard-to-Classify Objections

Here I consider three objections to the argument that are not straightforwardly classifiable as objections to premise (1) or premise (2).

(1) The conditional-concepts objection.

David Braddon-Mitchell, John Hawthorne, and Robert Stalnaker have independently put forward versions of the following intriguing objection. The conceivability of zombies is compatible with materialism, if the concept of consciousness has a certain conditional structure. Suppose that 'consciousness' functions as follows: if dualism is true in the actual world (that is, if a relevant sort of nonphysical property is instantiated), then 'consciousness' picks out a nonphysical property; and if physicalism is true in the actual world (that is, if no relevant nonphysical property is instantiated but a relevant sort of physical property is instantiated), then 'consciousness' picks out a physical property. Then if dualism is actually true, we should accept that zombies are possible. And it is at least conceivable that dualism is actually true, in that we cannot rule out the truth of dualism a priori. It follows that it is conceivable that zombies are possible. But this conceivability is entirely compatible with the claim that dualism is actually false, so that in fact zombies are impossible.

In response: Let us say that S is meta-conceivable when it is conceivable that S is possible. Then this objection shows that the meta-conceivability of zombies may be compatible with materialism. But the relevant premise of the conceivability argument was not that zombies are meta-conceivable, but that zombies are conceivable. That is, the premise (at least in the negative conceivability version) asserts that we cannot rule out a priori that P&~Q obtains in the actual world, not that we cannot rule out a priori that P&~Q obtains in some possible world. But there are good reasons to accept this premise, and the considerations above does nothing to undermine them. So these considerations do not threaten the argument.

Hawthorne and Stalnaker do not discuss the claim that zombies are conceivable (as I am understanding that claim here), and they say nothing to undermine either that claim or the claim that conceivability in this sense entails possibility, so their discussion leaves all the premises in the argument above intact. Braddon-Mitchell, by contrast, makes clear that he accepts premise 2 but denies premise 1. He says that the apparent conceivability of zombies is just a "shadow" of their metaconceivability: that is, we are apt to conflate the claim that zombies are conceivable with the claim that they are metaconceivable, and we mistakenly take the good reasons for the latter to be reasons for the former. He does not say anything to argue directly that zombies are inconceivable, however. On the face of it, even once we distinguish the two notions, the grounds for saying that zombies are conceivable (e.g., that there is no a priori contradiction in the idea) are as strong as ever.

These proponents could suggest that the conditional account predicts that zombies are inconceivable, and that it has independent support. At least on Braddon-Mitchell's version of the account (Hawthorne and Stalnaker are not explicit about this), it is an a priori conceptual truth that if PT is the case, then Q is the case, as he takes the conditional account to be an a priori conceptual analysis of phenomenal concepts. Braddon-Mitchell supports this claim by arguing that if an oracle told us that the world is purely physical, we would respond by accepting physicalism about phenomenal consciousness, rather than denying that it exists. (Hawthorne makes a similar observation.)

In response: I think that although the observation about our reaction to oracles is correct, it gives no support to the conditional concepts analysis. As Alter (forthcoming) has noted, the observation is grounded in the fact that we are more certain that we are conscious than we are of any philosophical thesis about consciousness. And our certainty that we are conscious is plausibly a posteriori knowledge, justified by experience. If so, then (as Alter argues), our inference from PT to Q in the oracle situation is partly grounded in this a posteriori knowledge, rather than being a priori. So the oracle observation does not support the thesis that it is a priori that if PT is the case, Q is the case. Furthermore, that thesis is undermined by both the zombie intuition itself and the knowledge-argument intuition that someone who knows PT would not thereby be in a position to know (through a priori reflection) what it is like to see red. So we have good reason to reject the conditional analysis of phenomenal concepts.

(2) The zombie parity objection.

Balog (1999) has suggested that there must be something wrong with the argument, on the grounds that if zombies are possible, they could make a parallel argument to the conclusion that materialism is false in their world. This conclusion would be incorrect, as materialism is true in their world. So something must be wrong with the zombie's argument. As the argument is valid, it must have a false premise. But Balog argues that if the premises of the original argument are true, then the premises of the zombie's argument are true. It follows that one of the premises of the original argument is false. Balog locates the problem in the equivalent of premise 2, the inference from conceivability to possibility, but this specific claim is not needed to undermine the original argument.

In response, I think it is not correct that if the premises of the original argument are true, the premises of the zombie's arguments are true. A tacit premise of the original argument is Q itself, stating for example that someone is phenomenally conscious. (As discussed earlier, this could either be built in as an explicit premise, or it can function as part of the support for premise 4.) The corresponding premise of the zombie's argument will be its claim 'Someone is phenomenally conscious'. I think that this claim is false. For example, in a debate between zombie realists and zombie eliminativists, the zombie eliminativists (who say 'No-one is phenomenally conscious') are correct. (For support for this claim, based in an analysis of phenomenal concepts, see Chalmers 2003b.) If this is right, then the zombie's argument has a false premise where the original argument has a true premise, and the failure of the zombie argument does nothing to undermine the original argument.

(3) The indexical objection.

A fairly common move in response to the conceivability argument (see e.g. Ismael 1999, Perry 2001) is to suggest that it is undermined by an analogy with indexicals. Even if I have complete objective knowledge of the world, I may lack indexical knowledge, such as the knowledge that it is 8pm now. So it is conceivable that all those objective truths obtain and that it is not 8pm now. But it does not follow that the fact that it is 8pm now is some ontologically further fact about the world, so that materialism is false. Likewise, it does not follow from the conceivability of zombies that materialism is false.

One might take this to be an objection to premise (2), the inference from conceivability to possibility. But in fact the point is compatible with premise (2). Premise (2) says that if P&~Q is conceivable, it is 1-possible. The analog version for time says that if P&~N is conceivable (where N is "It is 8pm now"), then P&~N is 1-possible. But P&~N is 1-possible, in that there is a centered world verifying P&~N: a world physically identical to our world, with the center placed somewhere else. In terms of the current argument, the objection is rather that from the fact that there is a centered world verifying P&~N, it does not follow that there is an uncentered world satisfying P&~N (or satisfying anything in the vicinity), and such an uncentered world is what is needed for materialism to be false. By analogy, something similar goes for P&~Q. So if we accept the analogy, we should deny premise (3).

In my main argument for premise (3) above, I assumed the thesis that Q has the same primary and secondary intension. If that thesis is correct, the indexical objection will not apply, as centering is irrelevant to the intensions of such sentences. If there is a centered world verifying P&~Q, then the corresponding uncentered world will also satisfy ~Q (and any difference between the primary and secondary intensions of P will lead at worst to Russellian monism). However, a proponent of the indexical objection may hold that phenomenal concepts are themselves indexical concepts, which have distinct primary and secondary intensions (for example, the primary intension of "I" picks out the individual at the center of a centered world, while the secondary intension of "I" picks out the same individual in all worlds). If so, then Q will have distinct primary secondary intensions. When I considered this possibility earlier, I noted that the argument still goes through but that there is a small loophole in the argument due to centering. In effect, the proponent of the indexical objection is exploiting this loophole in order to resist the argument.

To make considerations about indexical concepts maximally explicit, one can modify the formal argument. The modified argument invokes the sentence PTI, a conjunction of P, T, and I. Here P and T are as before (the "that's-all" truth T is built in explicitly here for completeness). I is a conjunction of relevant indexical truths, such 'I am x', 'Now is y', and so on, where x and y are descriptions picking out unique individuals and times (see Chalmers and Jackson 2001 for more on this). The modified argument runs as follows:

(1) PTI&~Q is conceivable (2) If PTI&~Q is conceivable, then PTI&~Q is 1-possible (3) If PTI&~Q is 1-possible, then PT&~Q is 2-possible or Russellian monism is true. (4) If PT&~Q is 2-possible, materialism is false. (5) Materialism is false or Russellian monism is true.

Here premise (2) is an instance of the general principle discussed earlier, and premise (4) is as before. The case for the modified premise (3) is more or less the same as that for the earlier premise (3). The main difference is this version removes the residual loophole in the case for premise (3) at the end of section 3, after we relaxed the assumption that Q has the same primary and secondary intensions. That loophole involved the suggestion that a centered world w verifying PT&~Q need not differ in any objective respect from the actual centered world W, since it might differ only in the location of the center. That loophole is now removed: if both w and w verify PTI, then they cannot differ only in the location of the center, as I specifies that location.[*] So w and w will differ in objective respects despite both verifying PT, and the rest of the argument will go through as before.

*[[ Strictly speaking, there is an exception for cases of wholly symmetrical worlds where individuals cannot be picked out by any unique objective descriptions. But there is no reason to think that the actual world is such a world, and any such symmetries play no role in the judgment that PTI&~Q is conceivable. ]]

As for the modified premise (1), this premise follows from the observation that adding indexical information does not close the epistemic gap between PT and Q. For example, I can coherently conceive that PT is the case, that I am x, that now is y, and that someone else is a zombie. (Note that this is a disanalogy with indexical cases: PTI&~N is not conceivable, where N is a claim about what time it is now.) Likewise, if we give Mary in her black-and-white room the same sort of indexical information, she will still not be in a position to know what it is like to be red. The epistemic gaps are just as wide as they were before. So the modified premise (1) is as plausible as the earlier version.

At this point, an opponent may suggest that phenomenal concepts are primitive indexical concepts, quite independent of other indexical concepts such as I and now. For example, phenomenal concepts might involve a primitive phenomenal indexical 'E', which picks out a phenomenal state of the experiencer in a way analogous to that in which 'I' and 'now' pick out the speaker and time. If so, then the full indexical truth I must include claims of the sort 'E is such-and-such', where the right-hand-side is an independent specification of the referent. And the opponent might suggest that this right-hand-side could specify a physical or functional property. That is, the indexical truth I might include a claim of the form 'E is PP', where PP picks out a physical or functional property instantiated by the subject. (Hawthorne 2002 makes a suggestion along these lines.) But if so, PTI&~Q may well be contradictory. Say that Q is 'Someone instantiates E'. P will entail that 'Someone instantiates PP', and in conjunction with I will entail 'Someone instantiates E'. If so, then PTI&~Q is not conceivable after all.

I think that this interesting suggestion founders at the first stage: there is good reason to believe that our core phenomenal concepts are not indexicals. I think it is plausible that there are indexical phenomenal concepts such as E, which we might gloss as this phenomenal property, picking out a phenomenal property that the subject is currently having. But as I argue in Chalmers (2003b), these concepts are distinct from our core phenomenal concepts, such as the pure phenomenal concept of phenomenal redness. Crucially, any identity claim involving pairs of such concepts is cognitively significant. For example, the thought this phenomenal property is R, involving an indexical concept and a phenomenal concept of phenomenal redness, is as cognitively significant as a thought such as this shape is circle, involving an indexical and a geometric concept of circularity. If so, the phenomenal concept is distinct from the indexical concept.

One can also make a direct case against any analysis of phenomenal knowledge as indexical or demonstrative knowledge, as follows. The epistemic gaps associated with indexicals always disappear from an objective perspective. Say that I am physically omniscient, but do not know whether I am in the USA or Australia (we can imagine that there are appropriate qualitative twins in both places). Then I have am ignorant of the truth of 'I am in Australia', and discovering that I am in Australia will constitute new knowledge. But if someone else is watching from the third-person point of view and is also physically omniscient, they will have no corresponding ignorance concerning whether I am in Australia: they will know that A is in Australia and that B is in the US, and that is that. There is no potential knowledge that they lack: from their perspective, they know everything there is to know about my situation. So my ignorance is essentially indexical, and evaporates from the objective viewpoint. The same goes for indexical ignorance concerning what time it is: when I am ignorance of the truth of 'It is 3am now', a physically omniscient historian in later years will have no corresponding ignorance about whether it was 3am then. Demonstrative ignorance concerning what "this" is works in a similar way. In all these cases, the ignorance disappears from the objective viewpoint. An objectively omniscient observer can know everything there is for them to know about my situation, and there will be no doubts left for them to settle.

The epistemic gaps associated with phenomenal knowledge behave quite differently. Consider Mary in her black-and-white room, ignorant of what it will be like for her to see red for the first time. In this case, a physically omniscient observer may have precisely analogous ignorance: even given his complete physical knowledge, he may have no idea what it will be like for Mary to see red for the first time. So this ignorance does not evaporate from the objective viewpoint. The same goes even more strongly for knowledge of what it is like for others to see red. For any observer, regardless of their viewpoint, there will be an epistemic gap between complete physical knowledge and this sort of phenomenal knowledge.

This suggests strongly that phenomenal knowledge is not a variety of indexical or demonstrative knowledge at all. Rather, it is a sort of objective knowledge of the world, not essentially tied to any viewpoint. If so, then any analysis of phenomenal concepts as indexical concepts will fail.

(4) Objections to two-dimensional semantics

One general sort of resistance to the two-dimensional argument comes from resistance to the two-dimensional framework as I have set it out. If one does not think that the notion of a primary intension is coherent, then most of the premises of the argument will not even be meaningful, let alone true. This sort of objection is too broad in scope to be covered in this paper; see Chalmers (2006b) for some replies to objections. Here, I will just note that much prominent resistance to two-dimensional semantics is really resistance to the claims that the intensions it postulates are the semantic content of utterances, or that they are what is said, or that they are what is ascribed in propositional attitude ascriptions, or some such similar thesis. But the arguments in this paper need no such thesis. All they need is that sentences or utterances can be associated with primary intensions in the way I describe. Nothing turns on whether this association yields a sort of "semantic content", can be used for attitude ascriptions, and so on. All that matters is that the relation of verification between worlds and utterances is well-defined (and then, of course, that it makes the premises true).

For example, a critical paper by Bealer (2002) focuses all of its arguments on the semantic theses, and gives no argument at all against the claim that statements can be associated with primary intensions or against the claim that they satisfy the CP theses. Something similar applies to a book on two-dimensionalism by Soames (2004), which is mostly devoted to arguing against certain two-dimensional analyses of attitude ascriptions, and spends very little time arguing against the underlying association of statements with primary intensions. Setting arguments of this sort aside, the majority of other arguments against two-dimensionalism are really arguments against specific theses such as the associated conceivability-possibility premise, and are addressed below. So henceforth I will assume the coherence of the framework, and will defend the specific theses.

6 Objections to Premise (2)

Finally, we come to the crucial premise (2). It is this premise that bridges the epistemic and modal domains, and it is this premise and associated principles that have attracted the most in-depth philosophical discussion.

Premise (2) says that if P&~Q is conceivable, P&~Q is 1-possible. This premise can be seen as an instance of the general conceivability-possibility thesis CP:

CP: If S is conceivable, S is 1-possible.

Here, "conceivability" should be understood as ideal primary conceivability, of either the negative or positive variety (I always take "ideal primary" as understood from here on). The two versions of the thesis that result are equivalent to theses CP- and CP+, discussed earlier. Thesis CP- is equivalent to the claim that if ~S is not a priori, S is 1-possible. The positive version CP+, holding that if S is positively conceivable, S is 1-possible, is somewhat weaker than the negative version, as positive conceivability entails negative conceivability but the reverse is not obviously the case. Much of my discussion will apply equally to both CP+ or CP-, so I will often just speak of CP, except where the distinction is relevant.

The case for premise (2) largely derives from the case for CP, and from here on I will mostly focus on the general principle rather than the specific premise. Of course if it turns out that the general principle needs to be restricted to a certain class of sentences to be plausible, then the question will arise as to whether P&~Q falls into that class.

Why believe CP? In the first instance, the thesis is plausible because there are no clear counterexamples to it. Principles linking conceivability and possibility have been widely accepted in the history of philosophy, but have more recently been questioned because of various counterexamples, such as the Goldbach case (both Goldbach's conjecture and its negation are conceivable but only one is possible) and especially the Kripke cases ('Hesperus is not Phosphorus' is conceivable but not possible). But CP accommodates these examples straightforwardly, with the idealization accommodating Goldbach cases, and the primary/secondary distinction accommodating Kripke cases. If it handles these cases, then the central sources of resistance to conceivability-possibility principles is undermined. But of course, there may be other possible sources of resistance.

7 Strong Necessities

Before proceeding, it is useful to clarify CP by making clear what a counterexample to it would involve.

According to the two-dimensional analysis, ordinary Kripkean a posteriori necessities such as 'water is H 2 O' and 'Hesperus is Phosphorus' have a necessary secondary intension but a contingent primary intension. That is, such statements are 2-necessary but 1-contingent: there are centered possible worlds (a Twin Earth world, or a world with distinct morning and evening stars) that verify their negations. When S is an a posteriori necessity of this sort, with a contingent primary intension, we might say that S is a weak a posteriori necessity.

By contast, we can say that an a posteriori necessity is a strong a posteriori necessity, or just a strong necessity, iff S has a necessary primary intension. Strong necessities are a posteriori necessities that are verified by all centered metaphysically possible worlds. It is not easy to give examples of strong necessities, as all of Kripke's a posteriori necessities appear to be weak necessities. But I will discuss some putative candidates in what follows.

It is easy to see that CP- is equivalent to the thesis that there are no strong necessities. If S is negatively conceivable but not 1-possible, then ~S will be a strong necessity. If S is a strong necessity, then ~S will be negatively conceivable but not 1-possible.

Insofar as CP+ is potentially weaker than CP-, the relationship between CP+ and the thesis that there are no strong necessities is not as clear. Certainly any counterexample to CP+ will yield a strong necessity, but the reverse is not obviously the case. To handle this, we might define two classes of strong necessities, according to whether they provide counterexamples to CP+ or merely to CP-. Let us say that a negative strong necessity is a statement S such that S is 1-necessary and 2-necessary but ~S is negatively conceivable. The latter condition is equivalent to the requirement that S is not a priori, so negative strong necessities are equivalent to strong necessities as defined above. A positive strong necessity is a statement S such that S is 1-necessary and 2-necessary while ~S is positively conceivable. Then all positive strong necessities are negative strong necessities, but the reverse is not trivially the case. CP- and CP+ are then equivalent to the theses that there are no negative strong necessities and that there are no positive strong necessities respectively.

What would a strong necessity involve? To get an idea, consider a philosophical view on which it is metaphysically necessary that an omniscient being (e.g. God) exists, but on which it is not a priori that such a being exists. Then according to this view, 'An omniscient being exists' (or O) is an a posteriori necessity. Like all a posteriori necessities, O is 2-necessary, and ~O is negatively conceivable (and also positively conceivable, if we add the plausible claim that it is positively conceivable that there is no omniscient being). If O were an ordinary a posteriori necessity, then O would be 1-contingent: there would be a metaphysically possible world verifying ~O. But if there is no omniscient being, then it seems that there is no such world. 'There is an omniscient being' does not seem to have any difference in its primary and secondary intensions, so if a world satisfies O, it verifies O. So given that O is 2-necessary, O is 1-necessary. It follows that if this philosophical view is correct, then O is a strong necessity: it is at least a negative strong necessity, and given the positive conceivability claim above, it is a positive strong necessity.

One could put the matter by saying that there is an epistemically possible scenario verifying ~O, but no metaphysically possible world verifying ~O. Here a scenario can be understood as corresponding to a maximal a priori coherent hypothesis, in the way that worlds correspond to maximal metaphysically possible hypotheses. (I give a formal treatment of scenarios in Chalmers (2004a, forthcoming), but here I will leave the notion intuitive. (One might call this sort of scenario a negative scenario, since it corresponds to a maximal negatively conceivable hypothesis. One could also define a positive scenario so that it corresponds to a maximal positively conceivable hypothesis.) The notion of scenarios is not defined in terms of metaphysical possibility, and in particular it is not assumed that scenarios correspond to metaphysically possible worlds. But nevertheless it is plausible that there is an intimate relationship.

For any a posteriori necessity S, there will be a scenario verifying ~S. For example, as 'water is H 2 O' is not a priori, there will be a scenario verifying 'water is not H 2 O'. That is, there will be some maximal a priori coherent hypothesis H (perhaps involving the assumption that the watery stuff is made of XYZ, and so on) such that if we accept H, we should accept 'water is not H 2 O'. For ordinary a posteriori necessities, these scenarios will correspond closely to centered metaphysically possible worlds, so that there will be a centered world verifying ~S. For example, 'water is not H 2 O' is verified by a centered XYZ-world, where the individual at the center is and has always been surrounded by clear, drinkable XYZ in the oceans and lakes. There is little reason to doubt that such a world is metaphysically possible, and there is an intuitive sense in which it qualitatively matches the scenario that we imagine when we entertain the hypothesis that water is not XYZ.[*]

(I will leave the notion of correspondence (or of qualitative matching) between scenarios and worlds at an intuitive level here, as it is not needed to play a formal role in the arguments. One might formalize it by requiring that scenarios be described in a limited vocabulary consisting of semantically neutral terms and indexicals, in the form D&I, where D is an semantically neutral statement and I is a conjunction of indexical statements. Then a scenario characterized by D&I will correspond to a centered world w iff D is true of w and iff I is true (in the obvious sense) of the individuals at the center of W.)

When S is a strong necessity, by contrast, there will be a scenario verifying ~S, but this scenario will correspond to no metaphysically possible world. (When S is a positive strong necessity, there will be a positive scenario verifying ~S; when S is a negative strong necessity, there will be a negative scenario verifying ~S.) For example, given the theist view outlined above, there will be a (negative and positive) scenario verifying 'There is no omniscient being', involving some maximally detailed hypothesis under which there is no such being. But on this view, there is no centered world that corresponds to this scenario, and there is no centered world that itself verifies 'There is no omniscient being'. We might put this intuitively by saying that on this view, the space of (centered) metaphysically possible worlds is smaller than the space of epistemically possible scenarios, at least in the relevant respect. On this view, there are scenarios that correspond to no world.

To bring this back to the mind-body case: take the paradigmatic type-B materialist who holds that premise (1) is true, premise (2) is false, and materialism is true. On this view, the material conditional P⊃Q (which is itself the negation of P&~Q) is a strong necessity. The truth of materialism implies that it is 2-necessary, the truth of (1) implies that it is a posteriori and its negation is 1-conceivable, but the falsity of (2) implies that its negation is 1-necessary. On this view, there will be a scenario verifying P&~Q, including various specific zombie scenarios. But these scenarios will correspond to no metaphysically possible world.

Note that the analog of CP with scenarios instead of worlds is close to trivial: if S is conceivable in the relevant sense, there will automatically be a scenario verifying S (at least if the notions of a scenario and of verification are unproblematic). Even a type-B materialist and a believer in strong necessities can accept that principle. They must simply deny that all scenarios correspond to worlds. So CP might be seen as equivalent to the thesis that for every scenario, there is a corresponding world.

(In Chalmers 2004a, the Core Thesis of epistemic two-dimensional semantics says that S is a priori iff S has a necessary 1-intension. If 1-intensions are defined over scenarios, then the resulting Weak Core Thesis is independent of CP, makes no claim about metaphysical possibility, and need not be disputed by believers in strong necessities. If 1-intensions are defined over centered worlds, then the resulting Strong Core Thesis is equivalent to CP and must be disputed by believers in strong necessities. The Strong Core Thesis can also be understood as the thesis of Metaphysical Plenitude: that every negatively conceivable statement is verified by some centered world. So the nexus of the debate over premise (2) might be phrased in terms of either CP, the Strong Core Thesis, or the thesis of Metaphysical Plenitude.)

My view is that for every scenario there is a corresponding world, and that there are no strong necessities. In The Conscious Mind, I gave the following reasons for this: (i) strong necessities cannot be supported by analogy with other a posteriori necessities; (ii) they involve a far more radical sort of a posteriori necessity than Kripke's, requiring a distinction between conceptual and metaphysical possibility at the level of worlds; (iii) they lead to an ad hoc proliferation of modalities; (iv) they raise deep questions of coherence; (v) strong necessities will be brute and inexplicable; and (vi) the only motivation to posit a strong necessity in the mind-body case is the desire to save materialism. I still accept most of these reasons, but there is more to say.

In the last decade or so, numerous objections to CP have been proposed. These objections fall into a number of classes. The first, and largest, involves attempts at exhibiting clear cases of strong necessities. The second involves attempts at explaining how there might be strong necessities in the phenomenal case (if not elsewhere), by analyzing the nature of phenomenal concepts. The third involves general philosophical objections. I will take these in turn.

8 Are There Strong Necessities? I: Examples.

I will discuss a number of putative counterexamples to CP in turn. The first five involve a posteriori identities. The next four involve are tied to issues about the a priori and a priori entailment, and involve potential challenges to CP-. The last five, suggested especially by Yablo (1999, 2002), involve challenges to CP- and CP+.

(1) Kripke cases: It is occasionally proposed that some Kripkean a posteriori necessities are in fact strong necessities. In particular, it is sometimes proposed that coextensive names such as 'Cicero' and 'Tully' may have the same primary intension as well as the same secondary intension. If so, 'Cicero is Tully' is a strong necessity (as it is clearly a posteriori).

In response: When we entertain the hypothesis that Cicero is not Tully, this hypothesis corresponds to specific scenarios that we can elaborate. In particular, the relevant scenarios may involve the hypothesis that the causal chains associated with names 'Cicero' and 'Tully' pick out different historical individuals. A scenario like this certainly corresponds to a centered metaphysically possible world: there are certainly worlds where the causal chains associated with these words functions in this way. And it seems clear that if we discovered that our world were such a world, we would reject the hypothesis that Cicero is Tully. So such a world seems to verify 'Cicero is not Tully' (although it may not satisfy 'Cicero is not Tully'). Worlds like this can be found for any Kripkean a posteriori necessity S (as Kripke himself pointed out, in effect), and such worlds will always verify ~S.

One might resist the claim that the world in question verifies S by rejecting the claim that there is an a priori entailment (for the speaker in question) from a description of the world in question to S. In response, I think that the sort of considerations in Chalmers and Jackson (2001) strongly suggest that these entailments are a priori at least in principle. But even if one rejects this claim, there is clearly remains some distinctive epistemic relation between the world in question and 'Cicero is not Tully': in particular, it remains the case that if one accepts (hypothetically) that the actual world is qualitatively just like the world in question, and reflects on this hypothesis, then one will reject the claim that Cicero is not Tully. (Note that this is quite unlike the situation that the theist thinks obtains in the God case, where there is no world that stands in this inferential relation to 'There is no God'.) So if one rejects a priori entailments, one can use this sort of inferential relation to define primary intensions, and ordinary Kripkean necessities will always have a primary intension that is false at some world.

(2) Essential modes of presentation. Block (??) and Tye(??) have suggested that one might get counterexamples to CP via identities in which each expression picks out an identity via an essential property. For example, let Q be a quantum-mechanical description that happens to pick out H 2 O. Then 'Q=H 2 O' is a posteriori (since the quantum-mechanical and chemical descriptions are not conceptually connected), but each picks out the referent via an essential property (which corresponds to the primary intension), so 'Q=H 2 O' will be 2-impossible. Kallestrup (forthcoming) also argues that a posteriori microphysical identities such as 'Q=H 2 O' will be strong necessities, on the grounds that microphysical terms have identical primary and secondary intensions.

In response: It is arguable that microphysical and chemical expressions pick out their referents by contingent properties, for reasons described earlier. Further, an entity can have more than one essential property, so that if a substance is picked out by distinct essential properties, the corresponding primary intensions will differ and the sentence will not be 1-possible. Finally, it is pretty clear that the scenario one has in mind when one conceives of the falsity of 'Q=H 2 O' (say, a world where something with the structure of Q yields quite different chemical-level properties due to different quantum-mechanical laws) will itself correspond to a possible world W that verifies 'Q is not H 2 O'. So unless one gives independent reason to think that there is no such world w (perhaps because one holds the strong view of the necessity of laws of nature, discussed under objection (12) below), there is little reason to deny the natural view that 'Q' and 'H 2 O' have distinct primary intensions. If so, there is no counterexample here.

(3) Distinct homophonous expressions. Block (2006) has suggested a case analogous to the 'Cicero=Tully' case above in which the same orthographic expression is used on each side. E.g., perhaps one has acquired the term 'chat' on two separate occasions for two separate species. One may then lose any associated information, but still recognize that they are distinct expressions, so that 'chat=chat' will not be a priori. But let us say, the two expressions 'chat' pick out the same referent. Then 'chat=chat' will be necessary, but both sides will have the same primary intension. At least, the explanation above, suggesting a primary intension along the lines of "the thing causally connected to my use of 'chat'", suggests that the sentence will be 1-necessary.

In response: Even here, there will be a centered world corresponding to the scenario one has in mind when one entertains the falsity of the hypothesis one expresses with 'chat=chat'. Such a centered world involves distinct causal chains from each of the two uses of 'chat' to distinct entities. Here the two uses can at least be distinguished indexically, with a primary intension along the lines of "the thing causally connected to this use of 'chat'". (If necessary, these indexicals can be grounded in direct indexical reference to token mental states, along the lines below.)

(4) Demonstratives: Schiffer (2004) suggests a worry about identities involving perceptual demonstratives, such as 'that=that'. In most such cases, there is no problem: the conceivable falsity of such a claim corresponds to a scenario in which the item causing a certain sort of experience in one differs from the item causing a different sort of experience, and this scenario will correspond to a centered world, such that if one discovered this world to be actual then one would reject 'that=that'. But there are cases in which the relevant experiences are indistinguishable, such as Austin's "Two Tubes" case (1989) in which one simply sees two red dots in a symmetrical visual field, or a case where one sees many dots and has no way to pick out any one of them by description. Then the model above involving different sorts of experience will not apply.

In response: Again one will have to invoke indexicals here, so that the primary intension of each 'that' will be roughly equivalent to that of 'the cause of this experience', for different phenomenal indexicals 'this'. In this case, the phenomenal indexical must be considered a primitive indexical akin to 'I' and 'now'. Formally, evaluating the primary intension of such an indexical requires a centered world where the center includes not just a subject and a time, but certain marked experience tokens, to which the distinct phenomenal indexicals are linked. Then 'that=that' will be false at centered worlds where the two relevant experience tokens marked at the center are caused by different objects. For more on this, see Chalmers (2003b).

(5) Dancing qualia: Hawthorne (2006) suggests a case involving phenomenal concepts, based on the dancing qualia case in The Conscious Mind. Say that Fred starts with identical red experiences in the left and right half of his visual field, forms concepts R1 and R2 (pure phenomenal concepts, in the language of Chalmers 2003b) of the relevant phenomenal property (phenomenal redness) and judges R1=R2. After this the experiences in the right half of his visual field "dance" between red and blue every minute, while they continue to play the same functional role (in The Conscious Mind I argued that this is naturally impossible but allowed that it is logically possible). Fred has been told that this may happen, but when a change happens he is unable to notice it. After four minutes his right-field experience is back to red, and he once again entertains the thought R1=R2. But he is unable to know that this is true through any amount of a priori reasoning, so R1 is not R2 is at least negatively conceivable. But both R1 and R2 have the same primary intension, so R1=R2 is 1-necessary. If so, this is a counterexample to CP-.

In response: This should be treated analogously to a case in which Fred's cognitive processes are tampered with so that they first judge 7+5=12 (with normal processes), then 7+5=14 with abnormal cognition, then back again. If Fred knows this is happening, then when he entertains 7+5=12 he will be unable to know that it is happening through any amount of a priori reasoning. Nevertheless, his thought is still a priori. This is simply a situation in which tampering with cognitive processes renders him less than ideal, so that he is unable to know all a priori knowable truths. (Or, in a closely related version, it is a situation where misleading empirical evidence undercuts his ability to know these.) The dancing qualia case above should be treated the same way.

(6) Ordinary macroscopic truths Another class of examples comes from the suggestion that consciousness is not alone in its failure to be a priori entailed by microphysical truths. Block and Stalnaker (1999) have suggested that many ordinary macroscopic truths, such as "water boils at 100 degrees" (or W), are not a priori entailed in this way. If so, then P&~W is at least negatively conceivable. But P&W is not possible (at least if water and its properties supervene on the microphysical), and it is not clearly 1-possible, either. If it is not, then P&~W is a counterexample to CP-.

In response: Chalmers and Jackson (2001) argue that these macroscopic Ctruths are a priori entailed by P, or at least by PQTI (say what this is, here if not before). Of course P&~Q, P&~T, and P&~I may be negatively conceivable, but the latter two are clearly also 1-possible, while the former is precisely the main topic of dispute. So any failures of entailment by P associated with the failure of entailment to Q, T, or I give no further support to the existence of strong necessities. Such support would require at least a truth M such that PQTI does not a priori entail M, and such that PQTI⊃M is 2-necessary and 1-necessary. The arguments in Chalmers and Jackson 2001 suggest that at no ordinary macroscopic truths M are like this.

In any case, even if one rejects the a priori entailment thesis here, these cases will yield at best exceptions to CP- (i.e. negative strong necessities), not exceptions to CP+ (i.e. positive strong necessities). Even if w above is like Q in that P&~W and even PQTI&~W is negatively conceivable, PQTI&~W is not positively conceivable: "water-zombies" are not positively conceivable in the way that zombies are positively conceivable. So this sort of case leaves CP+ unthreatened.

(7) Unknowable mathematical truths. Perhaps the most challenging cases for CP- are mathematical truths M such that M is true (and so necessarily true and 1-necessarily true), but not knowable, and so not knowable a priori. If there are such cases, M is a negative strong necessity (though not a positive strong necessity, as ~M is not positively conceivable). Here one might appeal to unprovable true mathematical sentences, such as those whose existences is entailed by Gödel's theorem.

In response: Unprovability in a given system does not entail non-apriority. For example, the consistency of Peano Arithmetic is not provable in Peano Arithmetic, but is still plausibly knowable a priori. One can make the case (see Chalmers 2002) that all true statements of arithmetic are knowable a priori at least under an idealization (i.e., our failure to know them a priori is due to certain limitations of our cognitive systems). One might worry about higher set theory, such as the Continuum Hypothesis, but here it is far from clear that such sentence are determinately true or false, and it is also far from clear that they are not knowable a priori under an idealization. So although these cases provide an interesting challenge to CP-, they do not provide clear counterexamples to CP-. And as in the previous case, there is no challenge to CP+ here.

(8) Inscrutable truths. A related class of potential counterexamples to CP- includes special sorts of true sentences M such that according to certain philosophical views, M is not a priori entailed by any underlying qualitative truths, but such that it is necessitated by such truths. In Chalmers (2002) I call these inscrutable truths. Such sentences might include vague sentences such as 'John is bald', under some versions of the epistemic theory of vagueness, according to which such sentences can be true but unknowable even in principle on the basis of underlying qualitative information. Others might include certain moral or metaphysical truths, on views according to which there are true such sentences with no a priori link to underlying qualitative truths. In Chalmers (2002) I argue that there are no compelling counterexamples here, as the views in question should all be rejected. In any case, these cases do not typically go along with the positive conceivability of PQTI⊃~M, and so at best challenge CP-, not CP+.

(9) The deeply contingent a priori. Hawthorne (2004) suggests that some truths may be a priori even though they are false in some possible worlds considered as actual. For example, let E⊃H be a conditional from one's total evidence to a hypothesis it supports. Then there are some grounds for holding E⊃H to be a priori (since the inference from E to H transmits justification and arguably cannot itself be a posteriori). But E⊃H it is certainly not 1-necessary: E&~H is verified by many worlds where the evidence is misleading. If so, E&~H is ruled out a priori (so it counts as inconceivable by the earlier definition), but it is 1-possible. Strictly speaking this sort of case does not challenge CP-, but rather challenges the associated "right-to-left" principle. This is still a worry for the framework, however, and addressing it helps to clarify an important issue.

In response: There may be a sense in which E⊃H is a priori here, in that it has some justification independently of experience. But there is a sense in which it is not, or at least in which its justification is much weaker than that of many other a priori truths. Intuitively, one cannot conclusively rule out the possibility that E&~H, whereas one can conclusively rule out the hypothesis that 2+2=5 for example. Conclusive justification is the sort that one gets from proof and analysis, rather than from abduction and induction, for example. In the uses of the a priori in the current context, it is always the conclusive a priori that is relevant. By this standard, E&~H is not ruled out a priori. This allows one to accommodate the clear intuition that E&~H is not just 1-possible but 1-conceivable: it is always conclusive apriority that is relevant to matters of conceivability.

(10) Disquotational truths. Yablo (2002) suggests that certain disquotational truths, such as "'sister' means sister", are a priori but are not 1-necessary. It could turn out that 'sister' does not mean sister, in worlds where the term is used differently, and such worlds verify "'sister' does not mean sister".

In response: I think the treatment of this case differs depending on whether one sees 'sister' picking out its referent orthographically (so just a certain orthographic form is required) or semantically (so that a certain meaning is required). If "'sister'" is understood orthographically, then "'sister' means sister" is not a priori: it is substantive a posteriori knowledge that the orthographic item means anything at all. If "'sister'" is understood semantically, then "'sister' means sister" may be a priori, but it is also 1-necessary: cases where the orthographic item is used with a different meaning will be irrelevant to the primary intension of "'sister'".

(11) Response-enabled concepts. Yablo (2002) argues that certain geometric terms such as 'oval' may pick out certain shapes according to the way they trigger certain responses, rather than through a substantive independent grasp. In the actual world 'oval' picks out cassinis (where 'cassini' is defined mathematically), but 'ovals are cassinis' is not knowable a priori. But 'ovals are cassinis' is nevertheless necessary and 1-necessary (a world where cassinis cause oval experiences is not a world where it would have turned out that ovals are cassinis, according to Yablo), so it is a strong necessity.

In response: I think that the actual term 'oval' may embody a geometric understanding, so that 'ovals are cassinis' (or something like it) is a priori. But there might be other terms that could work in Yablo's response-enabled way, though, so I will go along with his treatment of 'oval' as one of them. Under this assumption, we should say that 'ovals are cassinis' is not 1-necessary. If w is a world where Hs cause oval experiences, then (under this model of 'oval') it is a priori that if w is actual, so that Hs cause oval experiences, then ovals are Hs. (What matters for evaluating a primary intension is the a priori connection, not the "turns out" claim above.)

(12) Laws of nature. According to some philosophical views, laws of nature are not just naturally necessary but are metaphysically necessary. Shoemaker (1999) holds such a view, and suggests that it may provide a counterexample to CP.

In response: On some versions of this view, laws of nature follow a version of the Kripkean model. That is, if mass in the actual world obeys certain laws, then nothing in any counterfactual world counts as mass unless it obeys exactly those laws, so any law involving mass will be necessary. This might hold because of the semantics of mass (which require that a counterfactual property have the same nomic role as actual mass in order to qualify as the referent of 'mass'), or it might hold because of the metaphysics of mass (according to which properties such as mass have their nomic profile essentially, as on Shoemaker's view). On these models, we need not deny that there are worlds that correspond to the scenario we conceive when we conceive that mass obeys different laws: it is just that such worlds will contain "schmass" rather than mass. I think that it is implausible that the modal profile of 'mass' and/or the essential properties of mass are this precise (see Fine 2002 and Sidelle 2002 for arguments), but in any case, this model does not provide a counterexample to CP. In this case, a schmass world may verify the hypothesis that the relevant law of nature is false, so laws of nature are not strong necessities.

To yield strong necessities, this sort of view must hold that not only are there no worlds where mass obeys different laws, but there are also no related worlds where something else, "schmass", obeys those different laws. Here, the relevant sort of view is one according to which the fundamental properties and laws of all worlds are the fundamental properties and laws of our world (and on which these laws are not knowable a priori). In effect, this restricts the space of metaphysically possible worlds to the space of naturally possible worlds. If this view is correct, then a fundamental law will be a strong necessity: there will be no world corresponding to the scenario that we conceive when we conceive that is false.

I think that there are no good reasons to accept this extremely strong view of laws of nature, and that there are good reasons to reject it. The best reasons to take the hypothesis that laws of nature are necessary seriously come from the Kripke and Shoemaker models above. But nothing in these models supports the strong view, or yields a strong necessity. Rather, the CP thesis can itself be taken as reason to reject the view.

(13) A necessary God. I have already noted that the existence of strong necessities is entailed by a theist view on which an omniscient being (or an omnipotent being, or a perfect being) exists necessarily but on which the existence of such a being is not knowable a priori. If we say that a god is by definition an omniscient being (or a perfect being, or whatever), then 'A god exists' will be a strong necessity.

In response: I think that theist views of this sort are to be rejected. If the existence of such a god is knowable a priori, then it may exist necessarily. But if it is not, then one should conclude that such a being exists at best contingently. I cannot go over the arguments for believing in a necessary god here, but they all rest on highly contentious premises, and once again, CP itself provides an argument against these views. The best way to defend the existence of a necessary god is to argue that a world without such a being is not even conceivable.

Even if one believes in that the existence of a god provides a strong necessity, it is not clear that this sort of strong necessity undermines the case against materialism. The debate over materialism uses necessity as a criterion of ontological distinctness: the question of whether physical truths necessitate phenomenal truths is relevant precisely insofar as it bears on the question of whether the phenomenal involves nothing ontologically "over and above" the physical. But a variety of necessity in which the existence of a god is necessary will not be well-suited to this role. On such a view, the existence of a god will be necessitated by physical truths, but such a god will presumably nevertheless be ontologically nonphysical. So if the only strong necessities are strong necessities of this sort, connecting ontologically distinct existences, their existence is no help to physicalism. Under this assumption, then if P&~Q is conceivable, Q will be something over and above the physical, either because it is nec