Conceivability, 2-D Modal Semantics, and Modal Epistemology

Conceivability, Two-Dimensional Modal Semantics, and Modal Epistemology TUOMAS E. TAHKO ABSTRACT The combination of conceivability and two-dimensional modal semantics purports to be very powerful: it upholds modal rationalism, explains a posteriori necessity, and even accounts for metaphysical impossibilities—all this while committing to only one modal space, conceptual modality. In this paper I will examine whether conceivability and two-dimensional modal semantics can produce a complete account of modal epistemology and argue that they cannot. We will see that the framework is not able to accommodate metaphysical modality or to deal with metaphysically substantial, essentialist statements. I will first introduce the framework and draw attention to some of its details and then point out the problems that it faces in regard to certain examples.

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Our inquiry begins with the distinction between conceptual and metaphysical modality. The majority view is, following Kripke (1980), that the distinction is genuine and that there are some things which are conceivable, i.e. conceptually or epistemically possible, but metaphysically impossible. To avoid launching into Kripke exegesis, we will abstain from analysing Kripke's own position, instead we will refer to the established interpretation.1 It might be appropriate to examine the nature of conceptual possibility (in terms of the Kripkean line) before we proceed. Presumably, conceptual possibility is grounded in concepts and our epistemic access to it is via conceivability—thus the obvious link between conceivability and conceptual possibility. But a clarification is needed, because the notion of epistemic modality is often used as if it was synonymous with conceptual modality, yet it seems that there is a way to distinguish them. One of Kripke's passages about the nature of epistemic possibility goes as follows:

If I say, ‘Gold might turn out not to be an element,’ I speak correctly; ‘might’ here is epistemic and expresses the fact that the evidence does not justify a priori (Cartesian) certainty that gold is an element. I am also strictly correct when I say that the elementhood of gold was discovered a posteriori. If I say, ‘Gold might have turned out not to be an element,’ I seem to mean this metaphysically and my statement is subject to the correction noted in the text. (Kripke 1980: 143n.)

Here the ‘might’ is epistemic because it does not need to be true in any (metaphysically) possible world that gold is not an element. Given that the sentence ‘Gold is an element’ is (necessarily a posteriori) true, it is not (metaphysically) possible that Gold might have turned out not to be an element. To generalize: for a proposition to be epistemically possible, it does not need to be metaphysically possible, and on the 1 Proponents of this general line of thought that is usually referred to as ‘Kripkean’ are many, recent accounts include Hughes (2004) and Soames (2005).

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other hand, if both terms in a true identity sentence are rigid designators, then the identity-relation in question has to be metaphysically necessary. So, the sentence ‘Gold might have turned out not to be an element’ seems to make a metaphysical claim, when it should only be making an epistemic claim, as in the case ‘Gold might turn out not to be an element’. This is the kind of correction that Kripke refers to in the quoted footnote. Now, it does not appear to be conceivable, at least not any more, that gold is not an element, given the a posteriori knowledge that we have about its elementhood. So, what is at issue here is our understanding of conceivability: is it in some sense conceivable that Gold might turn out not to be an element? Some would like to say that it is always conceivable that things might have been otherwise, while others would insist that conceivability is restricted by the current a posteriori framework. Plausibly, we can distinguish between different types of conceivability here, as Yablo (1993) and Chalmers (2002a) have done. Kripke does not give an explicit account of these matters and there does not seem to be any general convention about the relationship between conceivability and conceptual or epistemic modality. The major issue, in any case, is whether we should fix conceivability in terms of how the world might be before we have any a posteriori knowledge, or how the world might be given the a posteriori framework.2 One way to read this distinction to the concepts of epistemic and conceptual possibility is to apply the ‘a priori’ version to epistemic possibility and the ‘a posteriori’ version to conceptual possibility. This is by no means the only way, but it would seem to be consistent with Chalmers (2002a: 156159): his ‘primary conceivability’ corresponds with the ‘a priori’ version and ‘secondary 2 Yablo (1993) suggests a number of different subscripts for different sorts of conceivability, which I do not find particularly helpful. Chalmers (2002a) thinks that there might be up to eight types of conceivability; it is his distinction between primary and secondary conceivability that reflects the issue at hand, and I will focus on these. See also Hughes (2004: 86 ff.).

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conceivability’ with the a posteriori version. However, the labels ‘conceptual’ and ‘epistemic’ are often used interchangeably. To simplify matters, I will here only consider the stronger (i.e. a priori) interpretation of conceivability and continue to use the words ‘conceptual’ and ‘epistemic’ interchangeably—this should cause no serious problems, as the stronger interpretation is the one that seems to be taken for granted in connections where the distinction is not made explicit (cf. Jackson 1998). It seems that the stronger version of conceivability has to be grounded in something that is purely a priori, or, more accurately, everything that is not ruled out by a priori reasoning is conceptually possible. Chalmers (2002a: 158) further separates this kind of negative definition from a positive one—the latter requires that we can coherently imagine a situation (as if it was actual) that would verify the possibility in question. To get to the bottom of this, we need to bring in two-dimensional modal semantics, because much of what Chalmers says about conceivability draws on it. Very roughly, the idea is that where traditionally modality is seen as ‘considering something to be possible counterfactually’, there is another way to think about it, namely to ‘consider something to be possible actually’ (cf. Chalmers 2006a, 2006b). These different ways to think about modality are supposed to reflect metaphysical and conceptual or epistemic modality, respectively. This gives the two-dimensionalist a tool to talk about metaphysical necessities as if they were not true in the actual world, i.e. the epistemic possibility that Hesperus is not Phosphorus is not ruled out by a priori reasoning and thus there is a perfectly clear sense in which Hesperus is not Phosphorus (and, indeed, a clear sense in which it is conceivable). This is not in conflict with the Kripkean idea of metaphysical necessity, or so Chalmers (2006b) argues. Accordingly, Chalmers endorses the idea that there are two distinct ways to understand modalities, what he calls the primary and the secondary intension, and here

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it is the secondary intension that is supposed to correspond with the traditional understanding. We should take a closer look at these secondary intensions and what they amount to. Chalmers (2002b: ch. 7) argues that what is relevant for the Fregean view of language are the epistemic intensions, i.e. the primary intensions, and so epistemic modality; whereas Kripke's case involves secondary intensions and thus metaphysical modality. Two-dimensional semantics is supposed to be able to accommodate both of these cases, but we are primarily interested in the latter. Unfortunately, because Chalmers takes the case of secondary intensions to correspond with the classic Kripkean story, he does not say a great deal about them. It seems, however, that the difference between primary and secondary intensions lies in their epistemic status; here is how Chalmers puts it in terms of primary and secondary conceivability (which correspond with primary and secondary intensions, respectively):

Unlike primary conceivability, secondary conceivability is often a posteriori. It is not secondarily conceivable that Hesperus is not Phosphorus, but one could not know that a priori. To know this, one needs the empirical information that Hesperus is actually Phosphorus. This aposteriority is grounded in the fact that the application of our words to subjunctive counterfactual situations often depends on their reference in the actual world, and the latter cannot usually be known a priori. (Chalmers 2002a: 159.)

The story that is starting to emerge here goes as follows. Conceptual or epistemic possibility is purely a priori and (primary) conceivability is a guide to it—everything that is not ruled out by a priori reasoning is possible in this sense. Metaphysical possibility, however, is restricted by a posteriori information. According to Chalmers, when we talk about Hesperus and Phosphorus counterfactually the application of our words depends on their reference in the actual world, which is plausibly in the realm of a posteriori knowledge. This is a fairly simple picture, as the only difference between 5

conceptual or epistemic modality and metaphysical modality is their different epistemic status. However, the Kripkean picture about the difference between these types of modality seems considerably more substantial. Indeed, it appears that there is an argument available here for the likes of Frank Jackson, who would rather see the Kripkean metaphysical modality to be reduced to conceptual modality altogether.3 Here is how it goes: the sentence ‘Hesperus is Hesperus’ is clearly purely a priori and necessary, it reflects the primary intension. The supposed metaphysical necessity, ‘Hesperus is Phosphorus’, requires a posteriori information, but is there anything else that separates it from sentences like ‘Hesperus is Hesperus’? According to Jackson (1998: 69-70), this difference in epistemic status is all that there is to it. Moreover, there is nothing else than the empirical discovery that Hesperus is in fact Phosphorus that differentiates these sentences. If this is the case, it would seem that the type of modality that is in effect in the case of ‘Hesperus is Hesperus’ is quite sufficient for the case of ‘Hesperus is Phosphorus’ as well. There is a difference between these cases, but ‘The difference lies, not in the kind of necessity possessed, but rather where the labels “a priori” and “a posteriori” suggest it lies: in our epistemic access to the necessity they share’ (Jackson 1998: 69-70). I see no route out of this for anyone who adopts this version of two-dimensionalism.4 The question that we are faced with now is how can the two-dimensionalist account for metaphysical possibilities? Chalmers suggests the following5: [P]rimary conceivability is an imperfect guide to secondary possibility, but is a much better guide to primary possibility. In all the Kripkean cases in which S is primarily conceivable, S is also 3 Presumably, so does Chalmers. 4 The version of two-dimensionalism at hand is sometimes dubbed ‘epistemic’. Here I will focus strictly on this version, whose main proponents are Chalmers and Jackson. 5 Where S is ‘primarily possible’ when its primary intension is true in some possible world, and S is ‘secondarily possible’ when its secondary intension is true in some possible world.

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primarily possible (or at least, Kripke’s discussion gives no reason to deny this). There is a (centered) possible world satisfying the primary intension of ‘Hesperus is not Phosphorus’ (e.g., a world where heavenly bodies visible from the center in the morning and the evening are distinct), of ‘heat is not the motion of molecules’ (e.g., a world where something else causes heat sensations), and so on. These worlds are all first-class metaphysical possibilities. (Chalmers 2002a: 165.)

So Chalmers thinks that the Kripkean picture is perfectly compatible with the idea that conceivability is a guide to possibility, as long as primary conceivability is aligned with primary possibility and secondary conceivability with secondary possibility. It is crucial here that Chalmers does not decouple primary and secondary possibility in the sense that the Kripkean framework decouples metaphysical and conceptual possibility. Presumably this is because otherwise the two-dimensional framework would be incapable to deal with metaphysical possibilities—as Chalmers puts it in the passage quoted above, primary possible worlds are ‘first-class metaphysical possibilities’. To the apparent worry that the two-dimensional framework accommodates both the metaphysical possibility and impossibility of statements such as ‘Water is XYZ’, Chalmers replies as follows:

One might worry about how a metaphysically possible world (the XYZ-world) can verify a metaphysically impossible statement (‘Water is XYZ’). But two-dimensional evaluation makes this straightforward: ‘Water is XYZ’ is true at the XYZ-world considered as actual, but false at the XYZ-world considered as counterfactual. The metaphysical impossibility of ‘Water is XYZ’ reflects the fact that it is false at all worlds considered as counterfactual. But this is quite compatible with its being true at some worlds considered as actual. (Chalmers 2006a: 82.)

Let us see whether the two-dimensional evaluation holds water. A core assumption in

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this evaluation is that there is a sense in which we can consider the XYZ-world to be actual. This assumption is grounded in the idea that we do not know which world is the actual world, given empirical defeasibility. Quite simply, then, if we adopt the scenario that the XYZ-world is the actual world, then we have a clear sense in which ‘Water is XYZ’ is possible, while we can still say that ‘Water is XYZ’ is metaphysically impossible in the sense where the XYZ-world is considered as counterfactual and we assume that our best current science is correct (i.e. that water is not XYZ in the actual world). Now, if we look at how ‘Kripkeans’ generally analyse the case of ‘Water = H2O’, we have something on the following lines6:

1. ‘Water’ is a directly referential term and it refers to a substance. 2. Substances have the same molecular structure in all possible worlds. 3. In the actual world, the molecular structure of water is H2O. 4. ‘Water = H2O’ is a posteriori necessary.

What we are interested in is the second premise. What makes ‘Water = H2O’ a metaphysical necessity, is exactly the assumption behind the second premise, namely that substances have their molecular structure by necessity; the molecular structure of a substance is part of its essence. The two-dimensionalist could perhaps accommodate this idea by making it a constraint for ‘water’ that it picks out a substance which is watery and has its molecular structure essentially, and similarly for the XYZ-world: XYZ is a substance which is watery and has its molecular structure essentially. However, this point rests solely on empirical defeasibility, that is, talk of the XYZworld can be meaningful only if it is considered as actual. Yet, the interesting part of the 6 Cf. Hughes 2004, Soames 2005, Salmon 2005.

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story is not the actual molecular structure of water, but the essentialist assumption concerning the nature of chemical substances.7 Here the two-dimensional framework gives us some very strange results. Consider how statements concerning the nature of chemical substances like water come out in the two-dimensional framework: ‘Water has its actual molecular structure in all possible worlds’. This statement is true (if it is true) in all possible worlds regardless of whether the world is considered as actual or counterfactual. It states something about the nature of a substance regardless of what the molecular structure of that substance in fact is. Compare that with ‘All water is water’, which is also true in all possible worlds regardless of whether the world is considered as actual or counterfactual (cf. Jackson 1998: 85). What has happened here is that we have avoided the complications introduced by empirical defeasibility (the third premise) altogether: ‘Water has its actual molecular structure in all possible worlds’ only concerns the second premise. Yet, without empirical defeasibility there is nothing in the twodimensional framework that distinguishes trivialities like ‘All water is water’ from substantial metaphysical statements like ‘Water has its actual molecular structure in all possible worlds’. Both of these statements come out as true in all possible worlds considered as actual and counterfactual. Moreover, both statements appear to be a priori, and our epistemic access to them is supposedly via conceivability. Anyone who takes essentialism seriously will surely find this result problematic, but I believe that the problem is independent of any essentialist assumptions. Already on the face of it, the statements ‘Water has its actual molecular structure in all possible worlds’ and ‘All water is water’ seem substantially different, namely, it appears that establishing the truth of the first statement requires considerably more effort than establishing the 7 Which, I should add, is controversial even within the Kripkean framework, as Lowe (2007) has pointed out.

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truth of the second one. I do not wish to deny that the first statement, if it is true, is a priori, but I am not convinced that conceivability is enough to establish its truth. Why would this be a problem for the two-dimensional framework?8 Well, if there is a difference between the two statements and if the two-dimensional framework is unable to accommodate that difference, as we saw above, then the framework is not complete —in fact, it might be fundamentally unable to accommodate the difference between the statements. However, we need to examine the statements in more detail to establish that there indeed is a difference between them. The difference, I wish to suggest, lies in the nature of the a priori content underlying the statements ‘Water has its actual molecular structure in all possible worlds’ and ‘All water is water’. In the case of ‘All water is water’ it is clear that the statement is true simply in virtue of its semantic content; certainly, no reflection about the nature of water is required. The case of ‘Water has its actual molecular structure in all possible worlds’ is not quite as self-evident though. It appears to rely on the general principle that chemical substances have the same molecular structure in all possible worlds. How do we arrive at this principle, then? Strictly in terms of semantics? Surely not: semantics cannot rule out the possibility that exactly the same chemical properties could emerge from different molecular structures—perhaps a different organization of the fundamental forces would enable this possibility. This, it appears to me, is an open question, one that can be settled only by a thorough analysis of the natural laws that are responsible for the forming of chemical substances, and, especially, whether these laws

8 Once again, my concern is the two-dimensional framework in terms of how Chalmers and Jackson use it; the problems that we will observe may be artefacts of the particular metaphysical and epistemological assumptions that Chalmers and Jackson combine with the two-dimensional framework—most importantly that we are dealing with only one modal space, i.e. conceptual modality.

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are metaphysically necessary. It may indeed be the case that chemical substances have the same molecular structure in all possible worlds and that we can know this a priori. In fact, I am inclined to think that if we are able to know this at all, we would know it a priori. But not everything that is knowable a priori can be established by semantic means, or, at any rate, the truth of the proposition under investigation now cannot be established by semantic means. The definition of ‘chemical substance’, or ‘water’, for that matter, in no way implies that substances must have the same molecular structure in all possible worlds. Moreover, I do not think that conceivability can be of any help here. The manner in which we saw Chalmers to define conceivability, namely that what is not ruled out by a priori reasoning is conceivable, seems to assume that a priori reasoning is simply conceptual analysis (cf. also Jackson 1998). Same goes for the positive definition of conceivability, namely imagining a situation (as if it was actual) that would verify the possibility in question. Neither account of conceivability could establish the truth of ‘Water has its actual molecular structure in all possible worlds’; as we just saw, conceptual or semantic information cannot rule out counterexamples to this statement. We can now present a dilemma for the two-dimensionalist. On the one hand, if statements like ‘Water has its actual molecular structure in all possible worlds’ are indeed a priori, then the a priori content must have different grounds than the a priori content underlying statements like ‘All water is water’, and hence the two-dimensional framework will be unable to accommodate a crucial part of modal epistemology because it classifies these statements in the same way. On the other hand, if the twodimensionalist denies that there is a more substantial sense of the a priori, then she must deny the apriority of statements like ‘Water has its actual molecular structure in all possible worlds’ because they cannot be analysed in the same way as statements like

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‘All water is water’. This would seem to render the two-dimensional framework inconsistent because both statements are nevertheless true in all possible worlds considered as actual and counterfactual. The upshot of this is that we should seek for an alternative method of dealing with substantive metaphysical statements. Here my sympathies are with Kit Fine (1994) and the idea that metaphysical modality is grounded in essences. Moreover, I believe that we can gain knowledge about metaphysical modality and ultimately about essences by a priori means, where ‘a priori’ is not reducible to semantic information (cf. Tahko 2008). A full account of modal epistemology has to be able to accommodate metaphysically substantial, essentialist statements. This, I wish to suggest, is not possible in the conceivability cum two-dimensional modal semantics framework.

References Chalmers, D. 2002a. Does Conceivability Entail Possibility? In Gendler, T. S. & Hawthorne J. (Eds.) Conceivability and Possibility. Oxford: Oxford University Press (pp. 145-200). Chalmers, D. 2002b. On Sense and Intension. Philosophical Perspectives 16. Chalmers, D. 2006a. Foundations of Two-Dimensional Semantics. In Garcia-Carpintero, M. & Macia, J., (Eds.) Two-Dimensional Semantics: Foundations and Applications. Oxford University Press. (pp. 55-140). Chalmers, D. 2006b. Two-Dimensional Semantics. In Lepore, E. & Smith, B. (Eds.) The Oxford Handbook of Philosophy of Language. Oxford: Oxford University Press. (pp. 574-606). Fine, K. 1994. Essence and modality. In Tomberlin, J. E. (Ed.) Philosophical Perspectives 8. Atascadero, CA: Ridgeview. (pp. 1-16). Hughes, C. 2004. Kripke: Names, Necessity, and Identity. Oxford: Oxford University Press.

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Jackson, F. 1998. From Metaphysics to Ethics: A Defence of Conceptual Analysis. Oxford: Oxford University Press. Kripke, S. 1980. Naming and Necessity. Cambridge, Mass.: Harvard University Press. Lowe, E. J. 2007. A problem for a posteriori essentialism concerning natural kinds. Analysis 67.4, 286-92. Salmon, N. U. 2005. Reference and Essence, 2nd ed. New York: Prometheus Books. Soames, S. 2005. Reference and Description: The Case against Two-Dimensionalism. Princeton: Princeton University Press. Tahko, T. E. 2008. A New Definition of A Priori Knowledge: In Search of a Modal Basis. Metaphysica, 9.2, 57-68. Yablo, S. 1993. Is Conceivability a Guide to Possibility? Philosophy and Phenomenological Research 53, 1-42.

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