Erkenn (2008) 68:129–148 DOI 10.1007/s10670-007-9082-x ORIGINAL ARTICLE
A Dilemma About Necessity Peter W. Hanks
Received: 16 February 2007 / Accepted: 3 August 2007 / Published online: 21 September 2007 Springer Science+Business Media B.V. 2007
Abstract The problem of the source of necessity is the problem of explaining what makes necessary truths necessarily true. Simon Blackburn has presented a dilemma intended to show that any reductive, realist account of the source of necessity is bound to fail. Although Blackburn’s dilemma faces serious problems, reflection on the form of explanations of necessities reveals that a revised dilemma succeeds in defeating any reductive account of the source of necessity. The lesson is that necessity is metaphysically primitive and irreducible. Keywords
Necessity Metaphysics of modality Simon Blackburn
1 Introduction The problem of the source of necessity is the problem of explaining what makes necessary truths necessarily true. For example, what makes it necessarily true that squares have four sides? One familiar answer cites facts about linguistic conventions.1 According to conventionalism, it is necessary that squares have four sides because of linguistic conventions about the expressions ‘‘square’’, and ‘‘four 1
See Carnap (1947), Ayer (1946), and Sidelle (1989).
Earlier versions of this paper were presented at the Northwest Philosophy Conference at Reed College in Oct. 2003, the Central Division APA in April 2004, the Joint Session of the Mind/Aristotelian Society in July 2004, and Dorit Bar-On’s seminar on realism and anti-realism at UNC Chapel Hill in Oct. 2006. I am grateful to the audiences at these presentations. Special thanks to Simon Blackburn, Barry Stroud, two anonymous referees, and Maria Francisca Reines. P. W. Hanks (&) Department of Philosophy, University of Minnesota-Twin Cities, 831 Heller Hall, Minneapolis, MN 55455-0310, USA e-mail:
[email protected]
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sides’’. Alternatively, an essentialist appeals to the nature or essence of being a square.2 For the essentialist, it is necessary that squares have four sides because part of what it is to be a square is to have four sides. In this paper I am going to argue that the problem of the source of necessity has no interesting solution. The best we can hope for are explanations of necessary truths that cite other necessary truths, but this simply pushes the problem back to the source of these other necessary truths. If this is right it shows that necessity is metaphysically primitive, irreducible, and sui generis. We might still engage in the project of mapping out the relations between necessary truths, but we would have to stop trying to render necessity intelligible by showing how it is grounded in some more basic set of facts. Simon Blackburn has presented a dilemma intended to refute any reductive, realist account of the source of necessity (Blackburn 1987). Although Blackburn’s dilemma faces serious problems, a revised form of his dilemma can be used to show that any reductive account of the source of necessity is bound to fail. I will start with Blackburn’s dilemma and its problems, showing how a careful understanding of the form of explanations of the source of necessity leads to a revision in the dilemma. This revised dilemma avoids all the problems facing Blackburn’s dilemma. I will also argue that some recent accounts of necessity that seem to avoid the dilemma in fact do not. The kind of necessity at issue in this paper is what philosophers call ‘‘broadly logical necessity’’. Broadly logical necessity includes logical necessity as in, for example, ‘‘Necessarily, if p and q, then p’’, as well as what is sometimes called conceptual necessity, as in ‘‘Squares necessarily have four sides’’. Philosophers disagree about whether there is another kind of necessity, metaphysical necessity, which would be expressed in a claim like ‘‘Necessarily, water is H2O’’. The disagreement is about whether there is a coherent notion of metaphysical necessity, and if there is, whether it is different from broadly logical necessity.3 I won’t take a stand on this issue in this paper.
2 Blackburn’s Dilemma Suppose we explain hp by appealing to q. The facts cited in the explanation are themselves either contingent or necessary. But they cannot be contingent, since then the necessary truth to be explained would not be necessary. If q could have been otherwise, and it explains why hp, then p also could have been otherwise, which contradicts what we set out to explain. This is the contingency horn of Blackburn’s dilemma. On the other hand, if q is necessary then we have not explained the source of the necessity of p. We have not shown what the necessity of p consists in because we have appealed to another fact that is itself necessary. The necessity of q is simply transferred to p, and so to understand the necessity of p we need an account of the necessity of q. But the facts cited in the account of the necessity of q cannot be contingent, for the reasons just cited, and so they must also be necessary and now we are embarked on a regress. This is the necessity horn of Blackburn’s dilemma. 2
See Fine (1994), Hale (2002), Jubien (1993), Peacocke (1997, 1999), and Shalkowski (2004).
3
See McFetridge (1990), Hale (1996, 1999), and Shalkowski (2004).
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Contingency horn: q is contingent p
Contradicts p because q
Necessity horn: q is necessary Regress Blackburn’s dilemma
As Blackburn explains, ‘‘[e]ither the explanandum [sic4] shares the modal status of the original, and leaves us dissatisfied, or it does not, and leaves us equally dissatisfied,’’ (Blackburn 1987, 54). He takes this dilemma to refute any ‘‘truthconditional approach’’ to necessity, where a truth-conditional approach is one that explains necessary truths by providing the conditions that make them necessarily true. However, there are a number of problems for Blackburn’s dilemma—two for the contingency horn, and one for the necessity horn.5 But as we will see, these problems can all be avoided.
3 First Problem for the Contingency Horn The first problem for the contingency horn is that if the facts cited in the explanation of the necessity of p are contingent, that only shows that p is not necessarily necessary. If hp because q, and q could have been otherwise, then hp could have been otherwise—i.e., not necessarily hp (:hhp). But the success of the contingency horn requires that if q could have been otherwise then p itself could have been otherwise, i.e., :hp. In order to get from :hhp to :hp one must assume the characteristic axiom of S4, i.e., hp . hhp. Contingency horn: q is contingent p p because q
S4:
p
p
p First problem for the contingengy horn
4
I think Blackburn must have meant ‘‘explanans’’ here, instead of ‘‘explanandum’’. The problem is about whether the fact doing the explaining (explanans) has the same modal status as the original (explanandum).
5
See Hale (2002) and Van Cleve (1999). Hale raises all three problems, Van Cleve only the problem for the necessity horn.
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This is a problem because the characteristic axiom of S4 is not something that the defender of a contingency account of necessity will accept. If one thinks that the source of necessary truths is to be found in contingencies then one should deny that necessary truths are necessarily necessary. This problem can be avoided by paying closer attention to the form of explanations of necessities. An explanation for hp will be an explanation of why it is that p. The form of the explanation looks like this: (p because ðp because r). There is a general reason for expecting explanations of necessities to have this form. Necessary truth is a mode of truth. Propositions that are necessarily true are true in a certain way. It should be no surprise, then, that an explanation of a proposition’s truth should explain why it is necessarily true. If we can understand what makes a proposition true, we should also be able to understand why it is true in a particular way. A close look at the conventionalist and essentialist accounts sketched above reveals that they have this form. The conventionalist explains why it is true that squares have four sides by appealing to the fact that squares have four sides solely in virtue of linguistic conventions. For example, Carnap held that: The concept of logical necessity, as explicandum, seems to be commonly understood in such a way that it applies to a proposition p if and only if the truth of p is based on purely logical reasons and is not dependent upon the contingency of facts. (Carnap 1947, 174, my emphasis) Essentialist accounts also follow this pattern. An essentialist says that squares have four sides because, e.g., the property of being a square contains the property of having four sides. It’s then necessary that squares have four sides because squares have four sides solely on the basis of this relation between properties. If this is right then the contingency theorist explains hp by explaining p on the basis of certain contingent facts corresponding to r. If r could have been otherwise then p itself could have been otherwise. Since r is contingent, it follows that :hp. But this contradicts hp, which is what we set out to explain in the first place. Nowhere in this line of reasoning do we need to appeal to the characteristic axiom of S4. Contingency horn: r is contingent p because r p because (p because r )
p
Reply to first problem for the contingency horn
Note that the first step in the reasoning is an inference from ‘‘hp because (p because r)’’ to ‘‘p because r’’. This is justified by the general principle that ‘‘B because A’’ implies A, i.e., falsities cannot explain anything.
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This solution requires a revision in our original understanding of Blackburn’s dilemma. As we originally understood it, the dilemma arises because q in the explanation ‘‘hp because q’’ is either contingent or necessary. But if I am right then q is of the form ‘‘p because r’’, and what matters for the dilemma is whether r is contingent or necessary. Contingency horn: r is contingent Contradicts
p
p because (p because r)
Necessity horn: r is necessary Regress Blackburn’s dilemma - revised
4 Second Problem for the Contingency Horn The second objection to the contingency horn comes in two parts. The general point is that, even if we grant the characteristic axiom of S4, the contingency horn still relies on a questionable principle about explanation (Hale 2002, 302–303). The two parts of the objection correspond to two versions of this principle. Let’s call the first version the Strong Principle of Explanation: ‘‘B because A’’ implies ‘‘if A had not been the case then B would not have been the case’’. The claim is that the Strong Principle of Explanation is required for taking the first step in the reasoning on the contingency horn. That is, in order to get from the contingency of q to :hhp we need the counterfactual ‘‘If q had not been the case then hp would not have been the case’’. The Strong Principle of Explanation provides the justification for this counterfactual. Contingency horn: q is contingent Strong Principle of Explanation p because q
if q had not been the case then not have been the case
p would
p S4:
p
p
p Second problem for the contingency horn (part 1)
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The problem is that the Strong Principle is false. One can say ‘‘B because A’’ and still think, without inconsistency, that B might have come about by some other means. That the barn burned down because the cow kicked over the lantern does not imply that had the cow not kicked over the lantern then the barn would not have burned down. Perhaps the barn was also struck by lightning.6 The second part of the objection concerns a weaker principle of explanation to serve in place of the Strong Principle. Call this the Weak Principle of Explanation: ‘‘B because A’’ implies ‘‘if A had not been the case then B might not have been the case’’. Suppose we say ‘‘hp because q’’. By the Weak Principle, it follows that if q had not been the case then hp might not have been the case, and from this and the contingency of q it follows that hp might not have been the case, i.e., e:hp.7 Of course, this is equivalent to :hh p. Given the axiom of S4, which we are still assuming for the sake of argument, we have :hp. Contingency horn: q is contingent Weak Principle of Explanation p because q
if q had not been the case then not have been the case
p might
p p S4:
p
p
p Second problem for the contingency horn (part 2)
The problem for this line of reasoning is supposed to be that the Weak Principle of Explanation only applies to explanations of contingencies (Hale 2002, 303). If one is explaining a necessary truth, and if, as we are supposing in this context, one is allowed the axiom of S4, then one will deny that there are any circumstances in which that necessary truth might not have been the case. Given the principle of S4, 6
Cf. Hale (2002, 302).
7
I am assuming, with Hale, a Lewisian analysis of counterfactuals. On Lewis’ analysis, the counterfactual ‘‘if q had not been the case then hp might not have been the case’’ is true if and only if either hq (the vacuous case) or :hp in at least one of the closest :q-worlds. Because e:q, :hp holds in at least one accessible :q-world, and so e:hp. See Lewis (1973a) and Hale (2002, 317). The same result follows on a Stalnakerian analysis of counterfactuals. On Stalnaker’s account, the counterfactual ‘‘if q had not been the case then hp might not have been the case’’ and e:q imply that :hp is true in the closest accessible :q-world, and hence e:hp. See Stalnaker (1968, 98–112). One reason for preferring Lewis’ account is that, as Lewis points out, Lewis (1973a, 79–80), for Stalnaker, if the antecedent is not impossible, the ‘‘would’’ and ‘‘might’’ counterfactuals come out equivalent. This would obliterate the difference between the Strong and Weak Principles of Explanation. For a response, see Stalnaker (1981).
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if one thinks p is necessary then, so long as q is contingent, one should reject any counterfactual of the form: if q had not been the case then hp might not have been the case.8 If hp, then by the principle of S4 it follows that hhp, and hence there are no circumstances in which hp might not have been the case. The upshot of this is that the Weak Principle of Explanation only applies to explanations of contingencies. But the contingency theorist is attempting to explain a necessary truth and so cannot make use of the Weak Principle. Furthermore, the Weak Principle may be false even for contingencies, for the same reason that the Strong Principle is false.9 Suppose the barn burned down because the cow kicked over the lantern, but the barn was also struck by lightning, and the lightning would have caused the barn to burn down even if the cow hadn’t kicked over the lantern. Then it is not true that the barn might not have burned down had the cow not kicked over the lantern. The Weak Principle seems to fall victim to the same kinds of causal preemption examples that falsify the Strong Principle.10 These considerations need to be modified in order to apply to the revised form of the dilemma. As we have seen, the form of the explanation offered by the contingency theorist is ‘‘hp because (p because r)’’. The contingency theorist is thus committed to explaining p by appealing to r—and it is to this explanation that the Strong or Weak Principle applies in deriving the contingency horn. Contingency horn: r is contingent p because r p because (p because r)
Strong / Weak Principle of Explanation if r had not been the case then p would / might not have been the case p/
p
p Second problem for the contingency horn - revised
Note that, as before, there is no need for the axiom of S4. Revising Blackburn’s dilemma in the way I have suggested doesn’t seem to help here. The revised contingency horn requires either the Strong Principle or the Weak Principle, but these principles are either false or at best, in the case of the Weak Principle, only apply to explanations of contingencies. Even though the explanation ‘‘p because r’’ is not directly an explanation of hp, the contingency theorist still regards p as necessary and thus can refuse to apply the Weak Principle to this explanation. 8
If q is necessary then the counterfactual is vacuously true.
9
I am indebted here to Marc Lange and to an anonymous referee. Another problem case for the Weak Principle was suggested to me by Scott Soames. Suppose one explains that Socrates died because he drank the hemlock. Surely this does not commit one to the claim that had he not drank the hemlock then he might not have died.
10
See Lewis (1973b) for the notion of causal preemption.
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However, it may be that the Strong and Weak Principles are false for some kinds of explanations but true for others. Causal preemption examples show that these principles do not apply to causal explanations.11 But the explanations involved in accounts of the source of necessity are not causal explanations. When a conventionalist says that it is true that squares have four sides solely because of linguistic conventions she is not citing the causes of the fact that squares have four sides. Her explanation is more like a reductive scientific explanation that cites the facts that ground or constitute another set of facts. Suppose we want to explain why an aggregate of gas molecules has a certain temperature. A causal explanation would cite the event or fact that caused the aggregate to have this temperature, e.g., the fact that the aggregate was placed next to a heat source. A different kind of explanation cites the mean molecular kinetic energy of the gas molecules in the aggregate. The mean molecular kinetic energy does not cause the aggregate to have a certain temperature. Rather, it grounds or constitutes the fact that the aggregate has a certain temperature. Let’s call this second kind of explanation a grounding explanation. The explanation given by the conventionalist, and more generally, the explanations given in accounts of the source of necessity, are grounding explanations. These explanations provide the facts that make it the case that certain things are true, not by finding the causes of those truths, but by finding the facts that ground them, that account for holding of these truths in a non-causal sense. It is a difficult and interesting task to clarify the relation of grounding involved in grounding explanations. It is likely that it is a catch-all for a number of relations, e.g., identity, realization, supervenience, metaphysical determination. Sorting this out goes beyond the scope of this paper. What we do need to decide, however, is whether the Strong and Weak Principles apply to the particular kinds of grounding explanations given in accounts of the source of necessity. It’s plausible to think that these principles hold for reductive scientific explanations. Take the Strong Principle (which, if it applies, would imply that the Weak Principle also applies). If the mean molecular kinetic energy of the gas molecules had been different, then the temperature of the aggregate would have been different. In general, if a fact f can be scientifically reduced to a fact g, then if g had not obtained than f would not have obtained. This is because the grounding relation involved in scientific reduction is the relation of identity. The mean molecular kinetic energy in an aggregate of gas molecules is the temperature of that aggregate. This is why if the mean molecular kinetic energy were different then the temperature would have to be different. In the case of explanations of necessities, however, the grounding relation is not identity. The conventionalist, for example, does not intend to identify the fact that squares have four sides with the fact that there are certain conventions. It would be too quick, therefore, to generalize from the case of reductive scientific explanations to grounding explanations of necessities.
11 Soames’ Socrates example, in note 9, makes a similar point. To say that Socrates died because he drank the hemlock is to give a causal explanation for Socrates’ death.
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Still, there is reason to be confident that the Strong and Weak Principles do apply in general to the grounding explanations given in accounts of the source of necessity. The problems for the Strong and Weak Principles, when applied to causal explanations, stem from the existence of multiple potential causes for the fact or event being explained. This should be evident from causal preemption examples, where one potential cause preempts another. If c caused e, but there are other potential causes for e, it doesn’t follow that if c had not occurred then e would or even might not have occurred. In the case of the grounding explanations of necessities, however, there are good reasons to deny that there are multiple potential grounds for the fact being explained. Suppose there are two potential grounds, g1 and g2, for a fact f. The problem is what to say if both g1 and g2 obtain. One cannot happily say that one or the other is the sole ground for f, since the choice is arbitrary. (In the case of causes, on the other hand, there will be reasons for choosing one potential cause over the other, e.g., one of the causes occurred first.) Nor is it plausible to say that g1 and g2 together are the ground for f, since that commits one to an embarrassing form of over determination. How could it be that g1 wholly accounts for f while at the same time g2 also wholly accounts for f? There are only two ways to avoid having to face these questions. One can either deny that g1 and g2 are compossible, in which case it could not happen that both g1 and g2 obtain, or deny that there are multiple potential grounds for f at all. In the case of grounding explanations for necessities, however, the first of these options is desperate and implausible. Suppose a contingency theorist holds that the fact that squares have four sides can be grounded either in conventions or in, e.g., contingent facts about the geometry of space. How could she possibly justify the claim that these two potential grounds are not compossible? Incompossibility arises out of logical, conceptual, or metaphysical inconsistency, and it is hard to see how multiple potential grounds for a given fact f could be logically, conceptually, or metaphysically inconsistent. The only plausible route for a theorist giving an account of the source of necessity is to deny that there are multiple potential grounds at all. The result of all of this is that there is no reason not to apply the Strong Principle of Explanation (and hence also the Weak Principle) to the grounding explanations given in accounts of the source of necessity. A theorist who gives such an account explains p by citing r, where this is a grounding explanation. As we have seen, the theorist must also deny that there are any potential grounds for p other than r. In other words, there is no other way for p to be the case than for r to be the case. It follows that had r not been the case, then p would not have been the case. The Strong Principle of Explanation therefore applies to grounding explanations of necessities and therefore can be used to derive the contingency horn of the dilemma. It is worth noting that the interest of the contingency horn extends beyond merely refuting conventionalism. This is because the contingency horn applies to any account of the source of necessity in terms of contingent truths—not just those that
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appeal to linguistic conventions. For example, we cannot hold with Descartes that necessary truths are the results of God’s decisions.12 If God could have decided otherwise then necessities turn out not to be necessary. Nor can we explain the source of necessity by appealing to deep yet contingent features of human nature, e.g., Kantian forms of intuition, or Wittgensteinian forms of life.13 Even if we cannot conceive of these being otherwise, so long as the facts of human nature to which we appeal in explaining necessities are contingent then we have undermined the necessity of the truths we set out to explain. The consequences of the contingency horn are very general and quite devastating.
5 Problem for the Necessity Horn The problem for the necessity horn depends on a distinction between what we can call, following Hale, ‘‘transmission’’ and ‘‘non-transmission’’ explanations. As Hale puts it, ‘‘in any transmission explanation of a particular necessity, appeal is made not simply to the truth of at least one further necessary truth, but to its necessity,’’ (Hale 2002, 310). On the other hand, in a non-transmission explanation no use is made of the fact that the explanans is necessary. Another way to put this is that a transmission explanation depends for its success on the fact that its explanans is necessary and a non-transmission explanation does not. Now, if all explanations of necessities in terms of other necessities are transmission explanations then the necessity horn of Blackburn’s dilemma succeeds as originally formulated. This is because transmission explanations could never locate the source of necessity. At best, they could only explain how some necessary truths depend on others. The question is whether all such explanations are transmission explanations.14 Hale provides two examples of what he takes to be non-transmission explanations of necessities:
12 ‘‘The mathematical truths, which you call eternal, have been established by God and depend on him entirely, just as all other creatures do ... he has established these laws in nature as a king establishes laws in his kingdom,’’ Descartes’ Letter to Mersenne, 15 April 1830, (Kenny 1970). Frankfurt argues that this commits Descartes to the view that nothing is necessary (Frankfurt 1977). Geach and Curley respond that it only commits him to the view that necessities are not necessarily necessary (Geach 1973; Curley 1984). Van Cleve defends the Frankfurt position using the same considerations I have used against the first problem for the contingency horn (Van Cleve 1994). 13 I intend no interpretive claims about Kant or Wittgenstein. My only claim is a hypothetical one. If Kant tried to explain the source of necessity by appealing to contingent features of our cognitive capacities then he is stuck on the contingency horn (and mutatis mutandis for Wittgenstein and forms of life, cf. Cavell (1979, 118–119)). As Russell read Kant, the antecedent of this conditional is true, and he argued that this commits Kant to the view that the truths of arithmetic and geometry are not necessary Russell (1959, 87). Van Cleve defends Kant with essentially the first problem for Blackburn’s contingency horn, but then rebuts this defense with the same move I have made against the first problem (Van Cleve 1999, 37–41). Thanks to Robert Greenberg for bringing this to my attention. 14
Cf. Van Cleve (1999, 143).
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h(Vixens are female foxes) because being a vixen just is, or consists in, being a female fox. h(The conjunction of two propositions A and B is true only if A is true and B is true) because conjunction just is that binary function of propositions which is true iff both its arguments are true. (Hale 2002, 312)
As Hale intends it, (1) makes appeal to the fact that the property of being a vixen and the property of being a female fox are identical. (2) makes appeal to the identity conditions for conjunction. It is plausible to hold that in each case the facts doing the explaining are necessary. But (1) and (2) are supposed to be non-transmission explanations because neither makes an appeal to the necessity of its explanans. Because of this, Hale thinks that these explanations provide illuminating accounts of the sources of necessity of the explananda. The fact is, however, that (1) and (2) are transmission explanations in disguise. Let’s focus on (1). As Hale himself points out,15 the form of (1) is: (p because ðp because rÞ That is, necessarily vixens are female foxes because vixens are female foxes because being a vixen just is being a female fox. If this is really a non-transmission explanation then it should not matter whether r is necessary—the explanation should still succeed even if we regard r as contingent. Hale puts it like this: An explanation of this kind works—explains why it is necessary that p—by claiming that p’s truth is a consequence of, or is ensured by, the nature of the identity-conditions of something involved in that truth (e.g., what it is to be an object of a certain kind, or what it is to be a particular function, or relation, etc.). It is quite widely held that truths about the nature or identity-conditions of things are necessary, in a strong or absolute sense. I think this is right…. But—crucially—it seems to me that the claim that explanations like [1] and [2] succeed as explanations of necessity does not depend on the correctness of this further claim. (Hale 2002, 312, my emphasis) So it should not matter to the success of (1) whether the further claim that its explanans is necessary is correct or not. And that means that it should still succeed even if we take the explanans to be contingent. It is easy to see that (1) fails if we regard its explanans as contingent. The problem is essentially the same one that arises on the contingency horn. Suppose, per impossible, it could have been that the property of being a vixen was not identical with the property of being a female fox. If vixens are female foxes because these properties are identical, then had those properties not been identical then
15 ‘‘What allows us to regard what’s explained as the necessity of p is that fact that the truth of p is explained in a special way, in terms of some fact about what it is to be …, where [being] … is integral to the proposition that p,’’ (Hale 2002, 312).
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vixens would not have been female foxes.16Given our supposition that these properties might not have been identical, it follows that it is not necessary that vixens are female foxes. But the explanation cannot succeed in explaining why necessarily vixens are female foxes if it has the consequence that it is not necessary that vixens are female foxes. So we cannot regard (1) as a successful explanation if we take its explanans to be contingent. This means that (1) makes implicit use of the fact that its explanans is necessary, and that makes it a transmission explanation. It has the form: (p because ððp because rÞ and (rÞ On reflection, I think it is clear that this is how explanations of necessities in terms of other necessities must work. To say that p is true because of r and to leave it open whether r is necessary or contingent also leaves it open whether p is necessary or contingent. And that means that we have not accounted for the necessity of p. To capture the necessity of p, therefore, we must also include the necessity of r in our explanation. Consequently, any successful explanation of a necessity in terms of another necessity must be a transmission explanation, but transmission explanations cannot reveal what necessity consists in, and so we cannot explain the source of necessity by appealing to other necessities. Hale anticipates this line of response, but it is hard to make sense of his reply. He argues that: … even if (one agrees that) an explanation ‘hp because q’ of the kind suggested cannot be correct unless (one thinks that) q is itself necessary—so that the necessity of the explanans is in a sense presupposed—it does not follow that it is presupposed in a relevant way, i.e., in a way that compromises the explanation. It would do so if the explanation worked by transmitting the necessity of the explanans to the explanandum, but that it does not do. (Hale 2002, 314) Here Hale concedes that explanations like (1) and (2) presuppose the necessity of their explanans, in the sense that these explanations would not be (regarded as) correct if their explanans were not (regarded as) necessary. What is unclear is why he doesn’t think that this shows that these are transmission explanations. A transmission explanation appeals to or presupposes the necessity of its explanans in such a way that the success of a transmission explanation depends on the necessity of its explanans. Therefore, if (1) and (2) pressuppose the necessity of their explanans and succeed only if their explanans are necessary then they are transmission explanations. Why does Hale think otherwise? His thought must be 16
Here I have made implicit and essential use of the Strong Principle of Explanation, which, I have argued, applies to the grounding explanations given in accounts of the source of necessity. In the absence of this principle we cannot get from the contingent identity of these properties to the possibility that there are vixens that are not female foxes. The properties might be contingently identical yet necessarily coextensive, in which case it would not be possible for there to be vixens that are not female foxes. The argument here depends not only on the contingent identity of these properties but also the fact that their identity explains the fact that vixens are female foxes, where this explanation is a grounding explanation.
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that in a transmission explanation the necessity of the explanans is ‘‘presupposed in a relevant way,’’ (Hale 2002, 314), and the necessity of the explanans in (1) and (2) is not presupposed in the relevant way. But what could this relevant way be, other than that the necessity of the explanans is required for the success of the explanation? An analogy may be helpful here. Suppose I explain p by appealing to q, and in doing so I presuppose that q is known to my audience. I might also hold that the success of the explanation depends on the fact that q is so known. But, assuming that p is not about knowledge, there is little temptation in this case to say that knowledge of q figures crucially in the explanation of p. The success of the explanation of p depends on the knowledge of q in the sense that if the audience does not know q then they may not accept or understand or be convinced by the explanation. But the audience’s knowledge of q is not crucial for q’s ability to explain why p is the case. If q explains p, then it does so whether or not q is known. If the presupposition of necessity required for explanations like (1) and (2) were like this, then Hale would be justified in claiming that this kind of presupposition does not make these explanations transmission explanations. It should be clear, however, that the presupposition of the necessity of the explanans in (1) and (2) is not like the presupposition that q is known. It is not that the explanans must be necessary in order for these explanations to be accepted or understood by an audience. Rather, the explanans must be necessary in order to account for the necessity of what is being explained. As we have seen, if the explanans were not necessary it would turn out that the explananda are also not necessary, and that would mean that the explanans fail to account for the necessity of the explananda not just in a pragmatic or epistemic sense, but in a stronger metaphysical sense. The necessity of the explanans must be presupposed in order for them to count, metaphysically, as successful explanations of the necessity of their explananda. This must be the relevant sense of presupposition for transmission explanations. Since the necessity of the explanans in (1) and (2) is presupposed in this sense, these explanations are transmission explanations, despite what Hale says to the contrary.
6 Modified Conventionalism The revised dilemma depends on the claim that philosophical accounts of the source of necessity have the form ‘‘hp because (p because r)’’, and when r is necessary, hr also shows up in the explanans. In particular, I have argued that conventionalism and essentialism have this form. But one might reply that the only plausible kind of conventionalism is what Dummett has called ‘‘modified conventionalism’’ (Dummett 1959), and modified conventionalism does not appear to have this form. Full-blooded conventionalism is the thesis that for every necessary truth p there is a separate convention that establishes the truth of p.17 As Quine pointed out, fullblooded conventionalism has to face the fact that there are an infinite number of 17 The term ‘‘full-blooded conventionalism’’ is also Dummett’s. He has argued that full-blooded conventionalism can be found in Wittgenstein’s writings on the foundations of mathematics, but this is controversial. See (Dummett 1959) and (Stroud 1965).
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necessary truths, and so establishing the truth of each by a separate convention would require an infinite number of conventions (Quine 1936). This forces the retreat to modified conventionalism. This is the view that there are conventions that establish the truth of each member of some finite subset, U, of necessary truths. The truth of any other necessary truth outside of U is established by the fact that it follows from U. For example, it may be directly stipulated by convention that ‘‘Squares have four sides’’ is true, and hence it is necessarily true. But the truth of ‘‘Squares have internal angles summing to 360’’ is not directly established by convention. This counts as true because it is a logical consequence of the convention establishing the truth of ‘‘Squares have four sides’’ and other conventions regarding geometrical and logical expressions. The modified conventionalist explains the necessity of the truths in the base class U by the fact that their truth is secured directly by convention. Explanations of the necessity of truths in the base class have exactly the form I have claimed for them. The trouble comes from those necessary truths outside of U. The modified conventionalist’s explanation of the necessity of these truths appears to have the form ‘‘hp because p is a logical consequence of conventions C1...Cn’’. This objection disappears upon closer scrutiny. Suppose that p0 is not a member of the base class U, that p is a member of U and so the truth of p is established directly by convention, and that p0 is a logical consequence of p. The modified conventionalist explains the necessity of p0 as follows: p0 is necessary because p0 is true because (i) p is true by convention, (ii) for all q, q0 , if q is true by convention and q0 is a logical consequence of q, then q0 is true, and (iii) p0 is a logical consequence of p. The second clause, (ii), amounts to an additional convention added to the original list of conventions for members of U. Taken together, these conventions establish by stipulation the truth of the members of U and anything that follows logically from the members of U. This still leaves something out because the conventionalist also intends to establish the relation of logical consequence by convention. This means that clause (iii) will have to be spelled out in terms of conventions for logical expressions.18 However this is ultimately executed, it should be clear that the form of the explanation is ‘‘hp0 because (p0 because r)’’, where r is a conjunction of (i–iii). This brings out the fact that for the modified conventionalist, the truth of sentences outside the base class is established indirectly by convention and logic. As Dummett put it, for the modified conventionalist, ‘‘although all necessity derives from linguistic conventions that we have adopted, the derivation is not always direct,’’ (Dummett 1959, 169).
18 Quine’s regress arises because the conventions that determine what follows logically from what at the same time determine the meanings of logical expressions (Quine 1936). But the conventions must themselves employ logical expressions whose meanings are supposed to be fixed by these same conventions. Hence, these conventions have to be applied to themselves in order to apply them in determining the relation of logical consequence, and this leads to the regress. The problem is not merely epistemic—it is not that we cannot use the conventions to find out what follows from what. The problem is metaphysical—the conventions are incapable of establishing that anything follows from anything else. Thanks to Bill Hanson for clarification on this point.
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7 Analysis vs. Explanation There are other theories of necessity that also seem to pose problems for my claim about the form of explanations of the source necessity. For example, according to David Lewis, squares necessarily have four sides because in every possible world squares have four sides, where possible worlds are concrete universes in alternate dimensions (Lewis 1986). This has the form ‘‘hp because p is true in every possible world’’. On Colin McGinn’s account, (which is easier to grasp if we change examples) Socrates is necessarily human because Socrates instantiates the property of being human in the mode of necessity (McGinn 2000). McGinn’s account has the form ‘‘h a is F because a instantiates F in the mode of necessity’’. According to Ted Sider’s neo-conventionalism, necessary truths are necessary because there are conventions to call them necessary (Sider 2003).19 On this theory, there is a convention to call logical, analytic and mathematical truths necessary. So, provided ‘2 + 2 = 4’ is a mathematical truth, the following sentence will be true: Necessarily, 2 + 2 = 4. Convention can do this much. It need not play any role in making it true that 2 + 2 = 4, or in making this be a mathematical truth. (Sider 2003, 204) This account has the form ‘‘hp because p is a truth of certain kind and there is a convention to call truths of that kind necessary’’. Like Lewis’ and McGinn’s theories, Sider’s theory does not appear to have the form I have claimed for explanations of the source of necessity. To see why there really is no problem here let’s distinguish between an analysis of necessity, an account of the meanings of sentences like ‘‘Necessarily, squares have four sides’’, and an explanation of the source of necessity, an account of what makes it the case that necessarily squares have four sides. The two are distinct. Explanations of the source of necessity are not aimed at saying what we mean by claims about necessity. Traditional conventionalism, for example, is not the view that claims about what is necessary are about linguistic conventions. As Ayer put it, speaking of a priori propositions, ‘‘... those who take a conventionalist view of a priori propositions do not mean to hold the theory that what are commonly said to be a priori propositions are really empirical propositions about the way words are
19 Sider does not label his view ‘‘neo-conventionalism’’. The term is due to Ross Cameron (2008). In unpublished work Sider calls his view ‘‘quasi-conventionalism’’, but I prefer Cameron’s label because it avoids any associations with Blackburn’s quasi-realism (Blackburn 1993).
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used’’ (Ayer 1936, 19).20 So when a conventionalist says that ‘‘Squares necessarily have four sides’’ is true because there are certain linguistic conventions she is not claiming that this sentence means that there are these conventions. The conventionalist account of necessity is in a different line of work than an analysis of the meaning of the word ‘‘necessarily’’. Furthermore, it is a mistake to think that a single theory can be both an analysis of ‘‘necessarily’’ and an explanation of the source of necessity. To hold otherwise is to commit a version of Euthyphro’s error (Plato 1981). Suppose someone claims that ‘‘pious’’ means ‘‘loved by all the gods’’, so that ‘‘x is pious’’ means ‘‘x is loved by all the gods’’. It would then be absurd to go on to explain why x is pious by saying that x is loved by all the gods. This would be to explain why x is pious by saying that x is pious, and that is no explanation at all. Similarly, if ‘‘necessarily’’ means ‘‘true in all possible worlds’’, for example, then it would be absurd to explain why it’s necessary that squares have four sides by saying that it is true in all possible worlds that squares have four sides. That would be to explain why it’s necessary that squares have four sides by saying that it’s necessary that squares have four sides. This shows that one cannot give an analysis of the meaning of the word ‘‘necessarily’’ and then use that very analysis as an account of the source of necessity. An explanation of the source of necessity uncovers the facts in virtue of which necessary truths are necessarily true; it does not simply restate those necessary truths. The theories mentioned earlier are all analyses of ‘‘necessarily’’ and not explanations of the source of necessity.21 In each case, the aim of these theories is to give the meanings of sentences like ‘‘Necessarily squares have four sides’’. McGinn and Sider are explicit about this. McGinn puts his theory by saying that ‘‘modal words function as copula modifiers,’’ (McGinn 2000, 81). Sider asks us to pretend that the only necessary truths are the logical, analytic and metaphysical truths. This allows him to state his theory by saying that ‘‘‘necessary’ just means ‘is either a logical, analytic, or metaphysical truth’,’’ (Sider 2003, 204). Without the pretense the theory is harder to state. Even so, in its final form Sider’s theory will give the meaning of the word ‘‘necessary’’ in terms of a list of various kinds of truths. Lewis is less explicit about the fact that he is analyzing the meaning of modal expressions, but there are good reasons for reading him this way.22 For example, Lewis thinks the truth values of controversial modal axioms can be settled by metalogical considerations about the accessibility relation among worlds. ‘‘Instead of asking the baffling question whether whatever is actual is necessarily possible, we 20 Ayer goes on to say that ‘‘our view must be that what are called a priori propositions do not describe how words are actually used but merely prescribe how words are to be used,’’ (Ayer 1936, 20). So for example, ‘‘Squares necessarily have four sides’’ is an imperative, dictating how the expressions ‘‘square’’ and ‘‘four sides’’ are to be used. This is a rather idiosyncratic account of conventionalism insofar as it departs from the idea that sentences about necessity are made true by conventions. Imperatives are not made true by anything. In any case, Ayer’s form of conventionalism does ultimately seem to be a claim about the meanings of sentences about necessity, and so it counts as an analysis. 21 Contrary to Cameron (2008), therefore, Sider’s neo-conventionalism does not solve the problem of the source of necessity. 22
Here I follow Chihara (1998, 81–82).
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could try asking: is the relation R symmetric?’’ (Lewis 1986, 19). But, as Lewis points out, this requires holding that ‘‘the modal operators can be correctly interpreted as quantifiers over the indices of some or other frame, restricted by the relation of that frame,’’ (Lewis 1986, 19). In other words, using the metalogical considerations to settle issues about controversial modal principles requires thinking that ‘‘necessarily’’ is correctly interpreted as a universal quantifier over the possible worlds in some system of modal logic. And Lewis clearly does hold that ‘‘modal operators are quantifiers over possible worlds,’’ and that ‘‘there exist frames which afford correct interpretations of the modal operators,’’ (Lewis 1986, 20), namely frames in which the indices are concrete, spatiotemporally disconnected universes. Since these theories are analyses of the word ‘‘necessarily’’, and not explanations of the source of necessity, they pose no threat to my claim about the form of such explanations. This point can be obscured by the fact that Lewis, McGinn and Sider present their theories as reductions of modality. But reductions come in different varieties. A semantic reduction gives the meaning of the word ‘‘necessarily’’ in nonmodal terms. In that sense, it reduces modal expressions to non-modal ones. This is the task that Lewis, McGinn and Sider set for themselves. A metaphysical reduction, on the other hand, is not about the meanings of words. A metaphysical reduction of necessity would show how necessary truths are exhaustively grounded in some more basic set of non-modal facts. The problem of the source of necessity is the problem of finding a metaphysical reduction of necessity. As we have seen, this problem cannot be solved by giving a semantic reduction of the word ‘‘necessary’’. Suppose we hold, following Lewis, that ‘‘necessary’’ means ‘‘true in all possible worlds’’. In that case the problem of the source of necessity becomes the problem of explaining what makes certain truths true in all possible worlds. It is no help to have it repeated that they are true in all possible worlds. It might be replied, however, that we could depart from Lewis, McGinn, and Sider and regard their theories as explanations of the source of necessity. If so, we would not hold, for example, that ‘‘necessary’’ means ‘‘true in all possible worlds’’. We would hold instead that what makes it necessary that squares have four sides is that in every possible world squares have four sides. Wouldn’t that be an account of the source of necessity that does not have the form ‘‘hp because (p because r)’’? It would. But there is a real question about whether this sort of explanation can give us what we want from an account of the source of necessity. The search for the source of necessity starts with puzzlement about what makes certain truths not just true but necessarily true. It is comprehensible why squares have four sides, but what does the necessity of this truth consist in? Sider captures the puzzlement nicely: I can see that this colored thing is extended, and indeed that all colored things I have examined are extended, but where is the necessity, that colored things must be extended? Part of the puzzlement here is of course epistemic, and epistemic reasons for reductionism have already been mentioned. But there is a particularly metaphysical puzzlement here as well. In metaphysics one seeks an account of the world in intelligible terms, and there is something elusive about modal notions. Whether something is a certain way seems
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unproblematic, but that things might be otherwise, or must be as they are, seems to call out for explanation. (Sider 2003, 184) A successful account of the source of necessity would alleviate this puzzlement. It would show us how necessities fit intelligibly into our conception of the world. The problem for accounts of the sort now under consideration, i.e., the modified Lewis, McGinn and Sider accounts, is that they fail to dispel this puzzlement. For example, suppose we hold that what makes it necessary that squares have four sides is that in addition to the actual squares having four sides, all the squares in all possible worlds have four sides. This trades in one puzzling fact for another. Why should all the squares in all the myriad of possible worlds also have four sides? It can’t be an accident that all the actual and possible squares are this way. If it were an accident then we should expect there to be possible worlds in which some squares do not have four sides. There must be some deeper explanation for the fact that all the actual and possible squares have four sides. That deeper explanation, I maintain, will explain why the actual squares have four sides in the first place. It is by understanding the ground for this truth that we will come to understand why all the actual and possible squares have four sides. Similar remarks apply to the modified McGinn and Sider accounts of necessity. Suppose we say, following McGinn, that it is necessary that Socrates is human because Socrates instantiates the property of being human in the mode of necessity. But why should Socrates instantiate this property in that mode, instead of in the mode of contingency? The answer has got to be an account of what makes it the case that Socrates instantiates this property at all. Or, following Sider, we might say that it’s necessary that 2 + 2 = 4 because it is a mathematical truth that 2 + 2 = 4, and there is a convention to call mathematical truths necessary. But what makes it a mathematical truth that 2 + 2 = 4? Here one wants to say something like: it’s a mathematical truth that 2 + 2 = 4 because it’s true that 2 + 2 = 4 solely in virtue of the nature of 2 and 4 and addition. Or perhaps one will appeal to conventions about the words ‘‘2’’ and ‘‘ + ’’ and ‘‘4’’. The point is that an account of why it’s mathematically true that 2 + 2 = 4, and hence, on the modified Sider account, why it’s necessary that 2 + 2 = 4, will be an account of what makes it true that 2 + 2 = 4. The lesson here is that the modified Lewis, McGinn and Sider accounts merely postpone the sort of explanation we need in order to solve the problem of the source of necessity. These modified accounts have the form ‘‘hp because q’’, but the facts cited in these account, i.e., the q’s, are as philosophically puzzling as hp. Alleviating this puzzlement can only come with an understanding of what makes it the case that p. Philosophically satisfying completions of these accounts will have the form ‘‘hp because q, and q because (p because r)’’, and this shows that in the end we are explaining why it is necessary that p by explaining why it is true that p.
8 Conclusion Blackburn used his dilemma in an attempt to defeat reductive, realist attempts to dispel the metaphysical puzzlement about necessities. Although the dilemma as he
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formulated it does not succeed, I have argued that a revised form of his dilemma does refute any reductive account of the source of necessity. Blackburn hoped to use his dilemma to motivate a quasi-realist approach to necessity. Blackburn’s quasi-realism about necessity combines expressivism about modal utterances with an account of how these utterances achieve truth-evaluable status (Blackburn 1987, 62–73). But for subtle reasons that go beyond the scope of this paper, Blackburn ultimately concludes that such a quasi-realist theory of necessity is unsatisfactory. If this is right then we are left back where we started, confronting metaphysical puzzlement about necessity. Perhaps progress on this issue can be made by more careful reflection on the nature of this puzzlement, i.e., by reflection on why we find it hard to fit necessities into our overall metaphysical conception of the world. We might find that this puzzlement is not as serious as it may seem.
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