A note on Morato on modality and explanation

A note on Morato on modality and explanation (This is a draft, so please do not quote or cite without permission. Comments welcome!) Abstract: This brief note critically assesses the central arguments in Morato’s (2014) recent contribution to the growing literature on contingent necessity-makers. In particular, I demonstrate that (i) neither of Morato’s two novel arguments against contingentism succeed, since both turn on false premises; and, (ii) Morato’s case for a radical ‘trans-world’ view about the nature of explanation in modal contexts is inconclusive at best. Blackburn (1987) offers a dilemma for any realist attempt to explain the source of necessity. Suppose we explain p’s necessity by appeal to some q. Being true, q itself must be either necessary or contingent. But if q is necessary, then we’ve a ‘bad residual must’ that we can’t eliminate. Meanwhile, if q is contingent, then we’ve ‘strong pressure to feel that the original necessity has not been explained or identified, so much as undermined.’ Consequently, either the explanans ‘shares the modal status of the original, and leaves us dissatisfied, or it does not, and leaves us equally dissatisfied’ (Blackburn 1987: 54). And while Blackburn intended this dilemma to motivate abandoning realism in favour of quasi-realism about modality, few have been moved. This is in part due to the fact that Blackburn does little beyond what is sketched above to flesh out the dilemma’s two horns. This has led to a cottage industry of constructing – or, more charitably, reconstructing – the two horns, alongside evaluating how best to respond to them.1 Recently, Morato (2014) has weighed in on these matters. Specifically, after surveying the recent literature concerning the dilemma’s contingency horn, he details two novel reconstructions. He goes on to show how would-be contingentists should respond to them, and, in the process, makes a case for a fairly radical ‘trans-world’ view about the nature of explanation in modal contexts. This brief note critically assesses Morato’s contribution to this debate. In particular, after spelling out his two reconstructions and his response thereto (§1), I go on to show (§2) that his response, which involves denying the intra-world factivity of explanation, is inconclusive at best. I then (§3) demonstrate that his reconstructions turn upon false premises (though not the ones Morato suggests). The general upshot is that while Morato is no threat to contingentists, he isn’t much help either. §1. Morato’s two arguments & his response thereto Morato’s first, ‘simple’ reconstruction of Blackburn’s contingency horn features two central assumptions. The first is: (Ex-Nec) ‘□p because q’ is true in a world wi iff, for every w, p because q in w2 Morato claims that (Ex-Nec) follows from the standard, ‘worldly’ definition of necessary truth – that ‘□p’ is true in world w iff for every w, p in w – and a straightforward ‘disquotation’ principle: (Ex-Rel) ‘p because q’ is true in world w iff (p because q) in w Meanwhile, the second key assumption, which falls out of the factivity of explanation, is: (Truth-Ans) For all worlds w, ((p because q), in w → q in w) 1 See e.g. Hale (2002, 2013), Hanks (2008), Lange (2008), and Cameron (2010). This and the following two principles are slightly modified from (Morato 2014: 336). I have replaced all instances of ‘b explains a’, with ‘a because b’ and, flipped the ‘p’s and ‘q’s to better correspond to the order of presentation. Neither alteration changes anything of substance. Per standard, I assume that ‘because’ – like the notion of explanation it is meant to express – is factive, irreflexive, antisymmetric, and transitive. 2 With these in place, Morato then offers the following argument. Assume, for reductio, that □p because q, where q is only contingently true. As q is contingent, there is a world wi where q is false. Given that p is necessary, p is true in wi. By (Truth-Ans), it follows that it’s not the case that p because q in wi. So, by (Ex-Nec), it follows that, contra the initial assumption, it is not the case that □p because q. Thus, given (Ex-Nec) and (Truth-Ans), contingent necessitymakers are impossible.3 Morato’s second, ‘even simpler’ reconstruction starts with the thought that (Ex-Rel) is compatible with contingent explanatory relations – i.e., with ‘p because q’ being true in some world w1, but false in w2. Since this might be ‘objectionable’ to those who think explanations have some ‘modal force’ (337), he suggests a replacement: ‘p because q’ is true in world wi iff p because q in wi and, for every w where p is true, p because q Employing this principle, Morato offers his second argument: (Ex-Rel-Strong) Assume that a contingent proposition, q, explains □p. [By (Ex-Rel-Strong)], if q explains □p, then q explains □p in every possible world in which □p is true. Given that □p is true in every possible world, then [by (Truth-Ans)] q is true in every possible world, therefore q is necessary, contrary to our assumption. (338) Both of these are, prima facie, compelling reconstructions of Blackburn’s contingency horn. And, if sound, they would certainly entail that contingent necessity-makers are impossible. However, Morato rejects them. Both, according to him, turn on a flawed premise. Specifically, Morato suggests that, as it requires that q must be true in world w to explain something therein, (Truth-Ans) entails that ‘(mere) possibilities cannot explain anything’. Consequently, he thinks we’ve good reason to reject (Truth-Ans) – and, by extension, the above arguments – if we can prove that ‘a plausible conception of explanation is compatible with the idea that possibilities could occupy the role of explanantia’ (340). Morato offers two counter-arguments to (Truth-Ans). First, he claims there are counter-example cases ‘in a great number of philosophical contexts’, though he mentions only two specific instances: (i) modal arguments, where an actual truth (e.g. the non-identity of a statue and lump of clay) is explained by a non-actual possibility (e.g. the lump survives being smashed but the statue doesn’t); and (ii) discussions of moral responsibility, where the actual moral responsibility of an agent is explained in terms of ‘non-actual courses of actions available to him at the moment of [a] choice’ (341-2). His second argument against (Truth-Ans) starts with the idea that we occasionally want to explain the possibility of something even when it is in fact false, which we do by showing that the relevant claim is compatible with what is actually true. So, to explain how it would have been possible for [Morato] to be elected in Parliament in the last general elections, what I need to do is explain how [his] actual properties before the last general election were not incompatible with [his] possible becoming a member of Parliament. (341) Consequently, we’ve a proposition – i.e. that Morato is elected – whose possible truth we’d like to explain, which we do by e.g. appealing to metaphysical compatibility. Thus, says Morato, we’ve a prima facie counter-example to (Truth-Dum) (p because q is true in wi) → (p is true in wi) 3 Morato credits Cameron (2010) with a similar argument, though Cameron doesn’t use anything like (Ex-Nec). But there is a kind of symmetry within the explanans and explanandum roles. For suppose that (a) p in w1 because q in w2, (b) ¬q in w1, and (c) ¬p in w2. Relative to w2, the explanation in (a) is an instance of an actual truth, q, explaining a mere possibility, p. However, relative to w1, (a) is an instance of an actual truth being explained by a mere possibility. So the above scenario is also a counter-example to (Truth-Ans). For these reasons, Morato rejects (Truth-Ans). And, as (Truth-Ans) plays a role in both, he also rejects his two arguments against contingent necessity-makers. §2. On Morato’s case against (Truth-Ans) While Morato’s discussion is interesting, I find it flawed. He claims that his reconstructions fail because of the falsity of (Truth-Ans); I contend that his cases against (Truth-Ans) are inconclusive at best. Meanwhile, I agree with Morato that his reconstructions fail. However, this isn’t for the reason he specifies; instead, other key premises turn out to be false. First, we should be clear that, contra Morato, (Truth-Ans) is perfectly compatible with possibilities serving as explanantia; for example, the actual truth of ‘I’m not necessarily an only child because I possibly have a sister’ isn’t a counter-example, since the explanans is itself actually true. We would have a counter-example if we could show that there are true explanations involving a mere possibility, where q is a mere possibility in w iff q is false, though possibly true, in w. However, this only undercuts (Truth-Ans) if the false ‘q’ serves as the explanans – the conjunction ‘¬q and q’ won’t do, because, provided q is merely possible in w, the conjunction is true in w. This is because (Truth-Ans) is only incompatible with scenarios where we’ve a true explanatory claim where the explanans is false at the world of assessment. That is, (Truth-Ans) is false iff ‘((p because q) and ¬q)’ is true at some world w. This also highlights why rejecting (Truth-Ans) is a bold move: doing so allows for cases where ‘((p because q) and ¬q)’ are true in a given world. This flies in the face of what we might call intra-world factivity, which states that ‘p because q’ is true in w only if both ‘p’ and ‘q’ are true in w. As it is extremely plausible, abandoning intra-world factivity isn’t a move to be taken lightly. So the burden of proof is on Morato to motivate this radical step. The problem is that Morato’s arguments do not provide genuine counter-examples to (Truth-Ans). In the modal argument case, the explanans isn’t a false (but possibly true) claim, but a true possibility claim – the relevant explanation isn’t ‘Statue and Lump are distinct because Statue persists and Lump doesn’t’; it’s ‘Statue and Lump are distinct because possibly, Statue persists and Lump doesn’t’. Similarly, the explanation in the moral responsibility case is something like, ‘A is morally responsible for her actions because possibly, A behaves otherwise’. Here the explanans is not the false (but possibly true), ‘A behaves otherwise’, but the true possibility claim, ‘(A behaves otherwise)’.4 In other words, both cases are explanations of the form ‘(p because q) in w’, not ‘(p in wi) because (q in wii)’. And given that, in both cases, the explanans is true, neither tells against (Truth-Ans). Anticipating this move, Morato counters that the distinction between ‘(p because q) in w’ and ‘(p in wi) because (q in wii)’ collapses, because ‘p and p have the same content, [and] therefore should be credited with the same explanatory potential’ (345). I must confess that I have some difficulty wrapping my head around the idea that p and p have the same content, as they frequently differ in truth value, and certainly differ in entailments. However, setting this aside, it is clear that there is an explanatory difference between possibility claims like p and their non-modalized correlates like p, for there are cases where p is (at least) a partial explanation for p, though p is never a partial explanation for itself. For example, it is plausible that ‘(Ohle is a dog) because Ohle is a dog’ is actually true, though ‘Ohle is a dog because Ohle is a dog’ is necessarily false. This difference in 4 In effect, the objection here is a version of Morato’s ‘Third Problem’ (2014: 345). explanatory potential gives us good reason for thinking that there is a distinction between ‘(p because q) in w’ and ‘(p in wi) because (q in wii)’. However, there is another line of response Morato might take. Early in his article, Morato stipulates that, ‘for simplicity’s sake’ (328fn1), his principles are all restricted to propositional atoms. Obviously, such a restriction would block the above counter-examples: no possibility claim could be an explanans (or explanandum). But this highlights the fact that Morato’s restriction does much more than merely reduce complexity – in fact, this stipulation does most of the heavy lifting, making the principles look more plausible than they actually are. So, why, other than simplification, ought we restrict ourselves to just propositional atoms? As it turns out, Morato does offer some further motivation for his restriction. Specifically, he claims that limiting the principles to propositional atoms is ‘motivated by the assumption that to explain a modal formula is to explain the corresponding non-modal formula in the possible worlds quantified over by the modal operator’ (340fn15), which he formalizes as ‘p because q’ is true in w iff for some world w, p because q in w However, as the right-hand-side states the truth conditions for ‘(p because q)’, this entails ‘p because q’ is true in w iff (p because q) Yet this is false: generally, an explanation for something’s modal status need not be the same as a (possible) explanation of that thing. For example, many think that while the truth of Socrates is wise explains the truth of (Socrates is wise or ¬(Socrates is wise)), the former does not explain the latter’s modal status.5 And, more to the point, while ‘Ohle is a dog because Ohle is a dog’ is necessarily false, ‘(Ohle is a dog) because Ohle is a dog’ is plausibly true. Further, it is natural to explain iterated modalities by appeal to simpler modal formula – for example, p by p, or □□p by □p. Yet Morato’s restriction rules these explanations out. This, in combination with the above, means there’s little reason to accept the restriction. And once the restriction goes, Morato’s first argument against (Truth-Ans) looks inconclusive at best. A similar point applies to Morato’s second argument against (Truth-Ans): if we have a scenario where (i) ‘p because q’ is true, (ii) ‘p’ is false, and (iii) ‘p’ is true, then we’d also have a counter-example scenario to (Truth-Dum) and hence also to (Truth-Ans). However, Morato has not satisfied the antecedent – condition (ii) is not met. This is because what is explained isn’t a false non-modal claim, but rather a true possibility claim. Or, to put the point another way, the explanation is of the form ‘(p because q) in w’, and the explanandum is the (true!), ‘(Morato was elected)’. This fits with Morato’s ‘symmetry’ point – depending on which world you’re evaluating from, either the explanans or the explanandum will be a possibility – but leaves (Truth-Ans) unharmed. Consequently, the second argument is also inconclusive. These failures render Morato’s suggested abandoning of (Truth-Ans) unmotivated. But, again, this isn’t problematic since embracing (Truth-Ans) does not, pace Morato, entail that possibilities cannot play a role in explanations. All it means is that there are no worlds where ‘((p because q) and ¬q)’ is true – a consequence we should like, since it means we don’t have to forsake the intra-worldly factivity of explanation. If it did, the debate would be over: we’d have a straight counter-example to Blackburn’s contingency horn. Though c.f. Wildman (ms) for further discussion. 5 Of course, Morato rejected (Truth-Ans) in order to block his two anti-contingent necessity-maker arguments. So contingentists might worry that, by embracing (Truth-Ans), they’ve jumped out of the frying pan and into fire. Thankfully, they need not despair – as it happens, there are other reasons for rejecting the two. §3. On Morato’s two reconstructions Take the simple argument. The weak point here is (Ex-Nec). This principle is, I contend, both unmotivated and false. First, what follows from the standard worldly definition of ‘□’ and (Ex-Rel) is not (Ex-Nec), but rather: (Ex-Weak) ‘□p because q’ is true in world wi iff (i) for all w, p in w; (ii) q in wi; and, (iii) (□p because q) in wi And plugging (Ex-Weak) into the simple argument renders it harmless to contingentists. Moreover, (Ex-Nec) is false. In general, any time q is either identical to p or is a conjunction that has p as a conjunct, then (Ex-Nec)’s right-hand-side is, due to the irreflexivity of explanation, necessarily false. So, for example, ‘□(2+2=4) because (□(2+2=4) and, ∀x(□x → □□x)’, is necessarily false. However, it’s natural to think that ‘□□(2+2=4) because (□(2+2=4) and ∀x(□x → □□x))’ is actually true – that is, the necessity plus the generalization explains the necessity’s being necessarily necessary. But this falsifies (ExNec): the right-hand-side is true, the left-hand-side false.6 Consequently, the simple argument is no threat to contingentists. It features a principle, (Ex-Nec), that everyone should reject, as it is both unmotivated and false. What of the ‘even simpler’ argument? Here again, a central premise – namely, (ExRel-Strong) – is both false and unmotivated. First, this principle is obviously false when we consider cases of explanation overdetermination. For example, true existential generalizations are, per standard, taken to be explained by their true instances. Thus ‘there is a dog because Ohle is a dog’ is actually true. However, as Ohle only contingently exists, there is a world w1 where Ohle isn’t a dog, and, in this world, his being one doesn’t explain the existence of dogs. However, suppose Fido is dog in w1. Then the relevant p is true (and is explained by Fido’s dog-hood), though both q and ‘p because q’ are false. Further, we need not restrict ourselves to overdetermination cases for counterexamples. If we assume p only contingently obtains, then ‘p or ¬p because p’ might be true in world w1, though there will be a world w2 where ‘p or ¬p because p’ is false and, instead, ‘p or ¬p because ¬p’ is true.7 Further, (Ex-Rel-Strong) does not in fact capture the idea that explanatory relations have modal force.8 Rather, a plausible principle that does is: (EMF) 6 ‘p because q’ is true in world wi iff (i) ((p because q) in wi); and (ii) for every w where ‘q’ and ‘p’ are true, (p because q) in w Morato might try and reply by leaning on his stipulation that his principles are restricted to logical atoms, but, as I’ve argued earlier, this restriction is problematic. 7 Thanks to an anonymous referee for this example. In fact, cases like this can be used to provide a positive case for contingent necessity-makers, even for absolute necessities; see Wildman (ms). 8 To his credit, Morato (2014: 339) also argues that (Ex-Rel-Strong) is dubious, though he doesn’t offer the above counter-examples. However, (EMF) neuters the even simpler argument – the closest we get to a contradiction is that every world where both □p and q are true is a world where ‘□p because q’ is true, which is perfectly compatible with q’s being contingent. So the upshot is that the ‘even simpler’ argument isn’t a threat either. It features a false premise, the sensible replacement for which leaves the argument impotent. And, more generally, neither of Morato’s novel arguments is problematic for contingentists. §4. Conclusions In summary, it seems that Morato set himself a flawed problem, then offered a flawed solution. Both of Morato’s novel reconstructions rely upon false premises, and therefore are not a threat. Meanwhile, Morato’s proposal to reject (Truth-Ans) turns upon mistakenly conflating the explanatory potential of p and p; and once we are clear about the difference, there is no reason to pursue his strategy of denying the intra-worldly factivity of explanation. Of course, I’ve said nothing here about Morato’s ‘trans-world’ notion of explanation, which suggests a new and interesting way to think about the relationship between explanation and modality. But, to the extent that it depends upon denying (Truth-Ans) (and hence the intra-worldly factivity of explanation), it will be problematic. Similarly, Morato’s challenge to clarify the explanatory difference between modalized and non-modalized claims is a difficult and worthwhile one. However, these larger points do little to take away from the fact that the above arguments in Morato’s paper are, sadly, flawed. Acknowledgements [REDACTED] References Cameron, R. 2010. ‘On the source of necessity’, in B. Hale & A. Hoffman (eds.), Modality, pp. 137-53, Oxford: Oxford University Press. Hale, B. 2002. ‘The source of necessity’. Noûs 36: 299–319. - 2013. Necessary Beings: An Essay on Ontology, Modality, and the Relations Between Them. Oxford University Press. Hanks, P. 2008. ‘A dilemma about necessity’. Erkenntnis 68 (1): 129-48. Lange, M. 2008. ‘Why contingent facts cannot necessities make’. Analysis 68 (298): 120–8. Morato, V. 2014. ‘Explanation and modality: on the contingency horn of Blackburn's dilemma’, Erkenntnis 79: 327-349. Wildman, N. ms. ‘For contingent necessity-makers’. Unpublished manuscript.