Romeo, René and The Reasons Why: What Explanation Is* Carrie Jenkins, University of Nottingham Department of Philosophy, University Park, Nottingham, NG7 2RD [email protected] This is a draft of a paper submitted for publication in the Proceedings of the Aristotelian Society © 2008. Please cite only the published version. Abstract This paper suggests that our everyday explanation talk exhibits a number of important dimensions of variation, then proposes a functionalist account of explanation to help accommodate them. The functional role of explanations is given in terms of answering why-questions, which in turn is spelled out in terms of the provision of information about non-inferential consequence. Realizers of the explanation role can be found by considering various consequence relations, including (for example) relations of causal and nomic consequence. 1 Five Dimensions Do not be alarmed. This paper does not consist in a trawl through objections to the deductivenomological model, the inductive-statistical model, the statistical relevance model, the causalmechanical model, and so on. Instead, it aims to do two things. The first is to suggest that our everyday explanation talk exhibits a substantial array of dimensions of variation, which can be helpfully clarified and categorized. Each of the dimensions should be fairly well known to those familiar with the literature on explanation, but cataloging them, and seeing how they interact, is I think illuminating. The second is to put a functionalist view on the table which I think can help us make sense of these dimensions of variation, and some other features of explanation, in a productive way. Here is my first dimension of variation: Dimension 1: why-explanation vs. how-explanation, that-explanation, what-explanation ... and other things like explication, exposition, clarification and excuses. My first point is that one can explain why, how, that, what, who, when and so on. One can also explain a concept in the sense of analyzing it or explain a word in the sense of giving its meaning; for clarity, let’s refer to these sorts of explanations as ‘explications’. Or one can explain in the sense of giving an exposition of, as when one explains one’s new theory to one’s colleagues or explains what will be in next week’s test. Furthermore one can be asked for explanation when what is required is clarification and/or further details: for instance, if I go to a difficult physics lecture that I don’t really follow, I might ask my companion on the way home to explain—clarify for me—what the physicist was saying in the lecture. I might then ask her to further explain—meaning expand upon—the bit about wormholes. Or one can be asked to explain oneself; that is, excuse one’s * I draw on many extremely helpful conversations with Daniel Nolan throughout this paper. Thanks are also due to Richard Baron, Mark Bradley, Marco Dees, Alan Hájek, Renée Hájek, Denis Robinson, David-Hillel Ruben and Jonathan Schaffer for useful discussions, emails and/or other forms of input. I also received valuable feedback when I presented the paper to members of the Nottingham Metaphysics Group and the Aristotelian Society. Shortly before his unexpected death in November 2007, Peter Lipton sent me some excellent written comments on a late draft which lead to substantial improvements in the final version. Professor Lipton’s undergraduate lectures in Cambridge first inspired my interest in the subject of explanation, and I would like to dedicate this paper to his memory.

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behaviour. Many uses of ‘I can explain everything!’ carry connotations of moral exculpation (rather than, say, grandiose scientific or philosophical ambition). For the rest of this paper, I’ll be talking about explaining why. This is a central use of explanation-talk, and one that has attracted a lot of attention from philosophers. One reason for this may be that a lot of other explanation talk (when it is not simply explication or clarification talk or something similar) is very closely related to explanation why. When one explains what made one raise one’s arm, one explains why one raised one’s arm. When one is asked why one is going home early and explains that one is tired, one explains why one is going home early. I’m not saying that all explanations-what and explanations-that boil down to explanations-why, but merely that many are at least closely related to explanations-why. Explanation-talk without question words attached is also often to do with explanation-why. When I explain the presence of mice in the kitchen, I explain why there are mice in the kitchen. A large class of explanation-talk which doesn’t seem to be obviously related to talk of explanation-why is talk of explanation-how. When I explain how I got out of the trap, I don’t seem to be explaining why I got out of it, or why I was able to get out of it. Maybe I am giving a certain kind of explanation of why I am now out of the trap. But other how-explanations don’t seem to respond well to a similar treatment; explaining how dogs digest their food doesn’t amount to explaining why anything. It is at least an open question whether explanation-how has much to do with explanation-why. However, another reason for focusing on why-explanation is that it presents special challenges to the philosopher. How-explanation can be assimilated to describing a means or method: explaining how X phi-d amounts to giving X’s method of phi-ing. Explication, clarification and excuse-giving are also not too difficult to understand philosophically, at least well enough to count as having a sound grasp of what they amount to. But explanation-why has provoked philosophers to provide many different, and conflicting, accounts of what it is, and the debate is ongoing. Let me now introduce a second dimension of variation, which is (like all the following dimensions) a dimension of variation within the class of explanations-why. Dimension 2: acts of explaining (or successful acts of explaining) vs. sentence tokens or types (or sets thereof) vs. propositions (or sets thereof) vs. facts or events or objects. Natural language usage does not straightforwardly indicate a single ontological category to which explanations belong. Sometimes, explanations are things people do. They are acts of explaining; acts, that is, of uttering (attempted) explanations.1 For instance, when I say that in the physics lecture the explanation of why black holes are black came ten minutes before the question session, this seems to be what’s going on. Clearly the explanation is something located in time. Moreover I can say that the explanation took ages, bored the audience, and was therefore reprehensible, further suggesting that the explanation is an act of the lecturer’s. Sometimes acts of (attempted) explanation which are not very successful get counted as explanations, and sometimes they don’t. For instance, it seems OK to say that the lecturer’s explanation of why black holes are black didn’t work because what she said about black holes just wasn’t true. It was still an explanation, just one that didn’t work. But it also seems OK to say that because what she said about black holes wasn’t true, she did not explain why black holes are black. What she said provided no explanation of that fact at all. (It is also worth noting that various different kinds of success in an act of explanation can be relevant here; more on this in the discussion of dimension 5 below.) On the other hand, it sometimes looks like explanation talk refers to specific bits of language: token sentences (or sets of sentences).2 When I say that the lecturer wrote up her 1 Sometimes these acts are acts of providing an argument, sometimes not. 2 Sometimes these sentences are structured to form an argument, sometimes not. The same goes for sentence types, and propositions.

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explanation of why black holes exist on the whiteboard, that it was three feet long, blue, and easy to read, I seem to be talking about the linguistic tokens she produced. On other occasions it seems to be linguistic types that we are talking about, as when I say that the physics lecturer and my school physics teacher gave the same explanation of why black holes exist, down to the very word. Sometimes it seems to be propositions (or sets of propositions), as when I say that my physics teacher and my French friend’s physics teacher gave the same explanation, but expressed it in different languages. Or when I say that the explanation of why I raised my arm is that I wanted to ask a question. Sometimes, but not always, certain kinds of success are relevant to which bits of language count as an ‘explanation’ and which do not. Sometimes, for instance, the sentence token on the lecturer’s whiteboard counts as an explanation although it is not true, simply because she intended it as an explanation. On other occasions it is said to be no explanation at all, because it is not true. Sometimes explanations seem to be less representational and more worldly things: not the sorts of things that are true or false, but rather the sorts of things that take place or obtain, such as facts or events. I can say that the explanation of why there are mice in the kitchen is the fact that food is left out overnight. Or that what explains the bang is the explosion: that is, an event. On other occasions objects may be referred to as explanations, as when I say that Mr Smith’s broken steering wheel is the explanation of his car crash, or when I ask you what explains why you survived the thugs’ attack, and you pull out your handgun and say ‘This’.3 It is also noticeable that certain locutions are much less susceptible to interpretation in terms of acts of explaining, or other related kinds of explanation, than others. For instance, it is hard to see how the sentence ‘The spark explains the fire’ could be making a claim about someone’s having engaged in an act of explaining a fire by citing a spark, or how it could be true just in virtue of someone’s having used a sentence or proposition concerning the spark to explain the fire.4 What should we say about there being such a large range of ontological categories into which the things that get called ‘explanations’ can (apparently) be put? Are all these things really explanations or only some? Are some of them the core cases of explanation while others are explanations only derivatively (in something like the way in which one might think propositions are central cases of truth-bearers and sentence tokens are truth-bearers only derivatively)? Is our word ‘explanation’ ambiguous as between the various ontological categories? Or is it semantically general? I am too wedded to common sense to deny that all the kinds of things which it is commonsensical to call explanations really are explanations, so I shall assume that they are.5 Moreover, if ‘explanation’ is ambiguous between the categories it must be polysemy, rather than mere homonymy, that we are dealing with. For there are clearly strong connections between the various uses of ‘explanation’ that we’ve been considering. Whatever is going on here is not comparable to the ambiguity of ‘bank’. But even polysemy is less plausible than semantic generality, I think. One clue that we may be looking at semantic generality is that it sounds fine to say that one explanation of the car crash is the broken steering wheel and another is the fact that the driver was drunk. But I should note that a certain amount of indeterminacy in the semantics of ‘explanation’ is to be expected, and also that not all the evidence immediately supports semantic generality. For 3 This lovely example is due to Daniel Nolan. 4 Thanks to Philip Percival, Harold Noonan and other members of the Nottingham Metaphysics Group here. 5 For a very different take on the question of what ontological category explanations belong to, see chapter V of D.-H. Ruben 1990, Explaining Explanation (London: Routledge). Here Ruben argues that only facts stand in the explanation relation. I find Ruben’s position unpersuasive. For instance, it is assumed that sentences are not explanations because ‘they do not explain ... in the conceptually primary sense’ (p. 160). There is no argument for this lack of primacy, nor is its relevance to the question of whether sentences are explanations made plain. The argument against events is that ‘explanation’-involving sentences that talk as if events are explanations are not transparent; different ways of referring to the same event e can change the truth-value of a sentence claiming that e is the explanation of something (see pp. 162-4). Again, however, the relevance of this is hard to see. ‘Belief’-involving sentences about Superman are similarly opaque, but that is no reason to deny that it is Superman whom Lois believes can fly.

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instance, it sounds bad to say that one explanation of the car crash is the broken steering wheel and another is the fact that the steering wheel is broken. However, one reason this sounds bad, I think, is that for many purposes those two things should really be counted as the same explanation, rather than two different ones. What this shows is that a single use of ‘explanation’ must be able to cover both an object and a fact (which certainly does not discredit the thesis of semantic generality). That notwithstanding, I think it likely that the term ‘explanation’ can be more or less semantically general on different occasions of use; on some uses things from many ontological categories may fall within the extension of ‘explanation’; on others only a few categories, or perhaps only one category, will be included. Is one ontological kind the primary kind of explanation? Some things suggest that acts of explaining may be (or at least, may once have been) the core referents of the word ‘explanation’. The word is derived from the Latin ‘explanare’, meaning to lay out (on a flat surface), to make flat or level, or to unfold. The act of laying something out or unfolding it might thus be thought of as the core kind of explanation;6 one can easily see how propositions, sentences and other tools for ‘unfolding’ could then come to be called explanations by extension. Similarly for the facts, events or objects referred to in acts of explaining. And insofar as the word shapes and/or is shaped by our concept of explanation, the linguistic primacy of acts of explaining might well evince conceptual primacy too. On the other hand, from a less linguistic/conceptual and more metaphysical perspective, it is somewhat tempting to suggest that facts, events and objects are the fundamental explanatory things. On this view, our linguistic representations and acts of explaining count as explanations because, and insofar as, they correspond in the right way (or at least attempt or purport to correspond in the right way) with these metaphysically more fundamental things. I shall not take a firm line yet on either linguistic/conceptual or metaphysical fundamentalness; indeed, by the end of the paper I will only make a tentative suggestion. Dimension 3: real explanation vs. all-in-the-mind explanation vs. genuine-understanding explanation. One conception of explanation has it that whether p explains q is a matter of how things stand in reality; usually mind-independent reality. I’ll call this ‘real’ explanation. This conception is in play when we say that nobody could ever possibly know the explanation of the big bang, or that there must be some explanation of the behaviour of dark matter but there’s no way for us finite beings to understand it. A second conception, which I’ll call ‘all-in-the-mind’ explanation, has it that whether p explains q is a matter of whether p helps us feel like we understand q. This conception may be in play when we say that there are lots of good (that is, satisfying) explanations of quantum decoherence but only one of them can be true. On one understanding of how inference to the best explanation works, we generally start out ignorant of the mind-independent facts inferred to, and assess the candidate explanations for mind-only explanatoriness. (‘Potential’ explanations—see dimension 4—can play similar roles to all-in-the-mind explanations. More on these in a moment.) A third conception, which combines elements of the first two, is what I’ll call ‘genuineunderstanding’ explanation. On this conception, p explains q just in case p helps us genuinely understand q—that is, p helps us feel like we understand q, where that understanding counts as genuine because of (a) how p and q are related in (usually mind-independent) reality and (b) the fact that we are appropriately epistemically connected to the obtaining of that relationship. All three of these characterizations are vague and sketchy, and deliberately so. Too much precision would, I think, do violence to the vagueness and sketchiness of our natural language usage and the corresponding concepts. But I hope, at least, that the three conceptions are recognizable.

6 See e.g. P. Achinstein 1983, The Nature of Explanation (Oxford University Press).

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Dimension 4: Actual vs. potential explanations.7 Hempel8 introduced the term ‘potential’ explanations for arguments which are in all respects D-N explanations, except that their premises need not be true. To adapt this usage to our purposes, we’ll use the term for things which are in all respects explanations except that they are not true, do not obtain, do not exist, or whatever. Sometimes it can seem that explanation-talk is used in such a way that potential explanations count as explanations; this is a(nother) sense in which one might say that there are lots of good explanations of quantum decoherence but only one of them can be true. Similarly, inference to the best explanation might be understood as inference to the best of a bunch of potential explanations, of which perhaps only one is true, but all of which are nonetheless explanations. On other occasions, it looks as if merely potential explanations are not being counted as explanations, as when one says that the explanation of Smith’s being late home isn’t that he was at his office working, although that would be a good explanation if he had indeed been at the office. The relationship between potential explanation and all-in-the-mind explanation is not obvious. Maybe the two notions are very close, so that whether something is a (good) potential explanation is all to do with how satisfying it is to us. On the other hand, maybe the two diverge quite radically, and whether something is a (good) potential explanation is affected by additional, or just different, factors (as on Hempel’s account for instance). We need not settle this issue here. Dimension 5: Explanations vs. good explanations vs. the best explanation vs. the explanation. Sometimes we talk as if the only explanations are good explanations; sometimes bad ones count as explanations too. Certain positions along dimension 3 lend themselves to one or other way of talking better than others. For instance, if we are talking about all-in-the-mind explanation, an explanation can fail to be good by failing to generate enough understanding. But if we are talking about what I’ve called real explanation or about genuine-understanding explanation, it is less clear that there could be an explanation which was not a good explanation. Even with real explanation, however, we might be able to make sense of a notion of betterness for explanations; for instance, one might think that citing two events which are causally upstream of the explanans will often make for a better real explanation than citing only one of them. Perhaps by thinking about a cut-off on such a scale of betterness, we could make sense of how a real explanation could yet be a bad explanation. What counts as a ‘good’ explanation is a highly context-sensitive matter. That is to say, the context of utterance of the word ‘good’ (and, for that matter, ‘explanation’) has a huge impact on extension. There are many different kinds of explanatory goodness, corresponding to different ways of evaluating explanations, and we rely on context to supply the relevant one (or more accurately, the relevant combination of different ones). For example, explanations might be evaluated for: relevance for their audience, understanding-generation, truth (or verisimilitude), provision of new information, provision of the desired kind of information, clarity, brevity, and so on.9 In addition, for each way of being good, how good an explanation has to be in order to 7

Thanks to Marco Dees and to Peter Lipton here. C. Hempel 1965, ‘Aspects of Scientific Explanation’, in his Aspects of Scientific Explanation And Other Essays in the Philosophy of Science (London: Collier-Macmillan), pp. 331-496. See p. 338. 9 See also pp. 226-7 of D. Lewis 1986, ‘Causal Explanation’, in his Philosophical Papers Volume II (Oxford University Press), pp. 214-40. 8

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qualify as ‘good’ can depend significantly on the context of utterance. Appreciating this range of dimensions of explanatory goodness helps us deal appropriately with the fact that it is prima facie harder to see how certain positions along dimension 2 are compatible with taking there to be some explanations which are bad ones. Explanations which are acts or sentences can surely be bad, but how could explanations which are facts be bad explanations?10 After all, facts are just facts: they are all equally good in the sense that they all obtain, are the case, or whatever. There are no facts which fail to obtain; failure to obtain results in non-facthood. However, other kinds of explanatory goodness can still apply to fact explanations. Context of utterance may determine that the fact that the cheese is always left out in the kitchen overnight counts as a ‘better explanation’ of the presence of mouse droppings in the kitchen than the fact that there are mice living in the kitchen skirting board. It might be, for example, that we are in a context where the fact that there are mice living in the skirting board is already known to all concerned. What counts as ‘the best’ explanation can also be importantly context sensitive, since different explanations might be best for different purposes and for different people. Adopting a position along dimension 3 will almost certainly have significant consequences for what counts as a ‘good’ or ‘best’ explanation. Sometimes we talk of ‘the’ explanation of something. Yet it is commonly agreed that almost everything—perhaps everything—is susceptible of more than one explanation. My decision to buy a cake at 1.50pm today can explain my purchasing a cake at 2pm, but so can my hunger at 1.50pm, and so can my long-standing belief that cakes taste good. In some contexts talk of ‘the’ explanation might amount to the same as talk of ‘the best’ explanation thing for current purposes. On other occasions, it might amount to the same as talk of ‘the (most) relevant’ explanation for current purposes. On others, it might mean little more than talk of an explanation. Note that none of this context sensitivity gives us any reason to be mind-dependence antirealists about explanation. What depends on context (and hence on the intentions, interests and so on of the utterer and/or audience) is what is expressed by terms like ‘good explanation’ and ‘best explanation’, not what counts as a good or best explanation once these aspects of meaning are settled. Perhaps it is worth mentioning briefly here that I will not be dealing in the notion of an ‘explanation-sketch’ (as described by Hempel11). That notion appeared in the literature on explanation in the course of attempts to rescue certain accounts of explanation from counterexample. If you start off convinced that all explanations are deductive arguments but are later taxed with the fact that many of the things we ordinarily call ‘explanations’ consist of far less, you might be tempted to say that what’s explicitly given in such cases is merely a sketch of a real explanation, which is hovering in the background of the explanation sketch. For myself, I regard the ordinary-language felicity of describing something as an explanation as pretty good evidence that it is an explanation. Defeasible evidence, of course, but pretty good defeasible evidence. While I’m happy to grant that some explanations are sketchier than others, I do not think there are good enough grounds to regard the sketchy ones as non-explanations. 2 A Functionalist Proposal Given that there are all these different dimensions of variation in our use of the term ‘explanation’, and all these different positions along each dimension, one might be tempted to consider a pluralist view, according to which there are many different kinds of explanations (considering especially dimensions 2 and 3) which are distinct from each other. There are also further differences between explanations that we have not focused on yet but which will be significant below: for instance, there is an important difference of some kind between causal explanations and the explanations given in 10 11

Thanks to Daniel Nolan and Harold Noonan here. Hempel 1965, p. 423ff.

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mathematics, and it is far from clear that this difference amounts to a difference along any of the dimensions of variation so far introduced. However, it would be nice to have a theory more unifying than a pure pluralism; for there are clearly substantial connections between the various things that count as explanations. Functionalism offers us a promising way of dealing with the intuition that there are many categories of explanation that are in some ways the same sort of thing and in other ways very different sorts of things. When I say ‘functionalism’, the term should be understood quite loosely; I don’t propose to characterize explanation with a set of input-output rules, or anything like that. I just mean that explanations play a certain role in our lives, and our concept of explanation is importantly connected to our understanding of that role. But many different sorts of things can—and do—play that role. That is to say, there are many different sorts of realizers of the explanation role. And ontologically speaking, explanations are nothing over and above these various things that play the explanation role. What sort of role do explanations characteristically play? My starting point here is the suggestion that explanations are things that can provide answers to why-questions. The related view that explanations are answers to why-questions is familiar from the work of such authors as Hempel,12 Bromberger,13 and Van Fraassen,14 but I do not say quite that (and nor do I follow Bromberger or Van Fraassen in their attempts to formalize why-questions and their answers15). Instead, I want to suggest that although some explanations (such as acts of explaining and sentences) are well-described as answers to why-questions, others may be things (such as facts and objects) which get cited in answers. I will count all these as things that can provide answers to whyquestions, but it is not felicitous to call all of them answers in themselves. I also want to operate with determinedly informal notions of a why-question and an answer to a why-question. It seems to me extremely likely that our everyday notions of explanation are vague, complex and unlikely to succumb to any straightforward formalization, and it is these everyday, fuzzy, notions that I’ll be trying to throw some light on. It is worth noting here that what counts as an ‘answer’ to a why-question is context-sensitive in similar ways to what counts as an explanation. For example, sometimes only good answers count, sometimes bad ones count too. But it is less clear that the contextual behaviour of ‘answer’ lines up perfectly with that of ‘explanation’. For instance, it sounds fine to say that Peter gave me an answer when I asked him why he was late, but what he said was no explanation of his lateness. This isn’t crisp evidence of a mismatch in the behaviour of ‘answer’ and ‘explanation’ since it is always possible that the context shifts over the course of the sentence, but I think it is somewhat unhappy to have to say that that’s what’s going on. Instead, I would prefer to think of things this way. When I talk about ‘answers’ to why-questions in characterizing the role of explanations, I would like the reader to think about all the things that can fall within the extension of ‘answer to a why-question’ in its various (possible) contexts of use. I hope thereby to fix the range of things that can fall within the extension of ‘explanation’ in its various (possible) contexts of use. It would be a further claim, which I am not making, that the things within that range which fall within the extension of ‘answer’ and ‘explanation’ are the same within every (or indeed any) context of use.16 So what kind of thing can be used to answer a why-question? The dimensions of variation which are operative for explanation are operative here too. Sometimes we talk as if only good answers count as answers at all, sometimes as if bad answers are also answers. Sometimes 12

Hempel 1965, p. 334. S. Bromberger 1966, ‘Why-Questions’, in R. Colodny (ed.) Mind and Cosmos: Essays in Contemporary Science and Philosophy (University of Pittsburgh Press); reprinted in B. Brody (ed.) Readings in the Philosophy of Science (Englewood Cliffs, NJ: Prentice Hall), 1970, pp. 66-87. 14 B. Van Fraassen 1980, The Scientific Image (Oxford University Press). 15 Some of the classic problems for Van Fraassen’s approach are outlined in P. Kitcher and W. Salmon 1987, ‘Van Fraassen on Explanation’, in Journal of Philosophy 84, pp. 315-30. 16 Many thanks to Daniel Nolan and other members of the Nottingham Metaphysics Group for pressing me to clarify this. 13

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answering a why-question is a matter of providing information about how things stand in reality; sometimes it is a matter of generating a feeling of understanding; often it is about both. We can use sentences (both types and tokens) to answer why-questions; we can use (cite) facts or objects; we can use certain speech-acts. One point I think is illuminating is that there is a connection between answers to whyquestions and the notion of consequence.17 The first point to note is that why-questions seek reasons: when we ask why something happened, we want to know for what reason(s) it happened. If I ask you why the cup fell off the table, you might tell me that the reason it fell off is that there has just been a small earthquake. Another way of responding to a why-question is to say: ‘No reason’. Although why-questions seek reasons, however, they do not seek reasons in the sense of reasons to believe (justifications, warrants etc.) or reasons for action (pragmatic, prudential or moral reasons). So what is a ‘reason’, in the required sense? Reason talk can sound teleological or purposive. This is evinced by the fact that the word ‘for’ is always close by when reason talk is in play. Asking why the cup fell off the table amounts to asking: ‘For what reason did the cup fall?’ But there need be no purposes or ends involved; suppose, for instance, that the reason the cup fell off the table is simply that there was an earthquake. These appearances of ‘for’ should not be mistaken for symptoms of (misplaced) teleology. They in fact signal something else. In many European languages the word for ‘why’ is equivalent to ‘for what’; in French, for instance, we have ‘pourquoi’. In archaic English, the word ‘wherefore’ is used to mean ‘why’. ‘Wherefore art thou Romeo?’ is not, despite popular misconception, an enquiry about Romeo’s location, but rather the beginning of a musing on the import of his bearing the name he does. There is even an archaic word ‘whyfor’ with the same import. We also, mainly in written English, sometimes use ‘for’ by itself to mean ‘because’, as in: ‘There is no need to be anxious, for everything is as it should be’. So what is all this ‘for’ talk doing? A clue is that this kind of use of ‘for’ is interestingly related to the word ‘therefore’. And ‘therefore’ is obviously closely related to ‘wherefore’. Considering archaic forms makes this easiest to see: the question ‘Wherefore have you to this castle come?’ is well answered by ‘I would speak with you; therefore am I here.’ What’s going on here is that a why-question (‘Why have you come to this castle?’) is answered by the giving of a reason or explanation (‘I want to talk to you; that’s why I’m here’). The ‘wherefore’–‘therefore’ link is, however, apt to mislead unless we are careful. The connection might, at first blush, suggest that inference is central to explanation and the answering of why-questions. After all, ‘therefore’ is widely used to mark an inference. But this would be a mistake. To see what kind of mistake, notice the difference between two possible readings of Descartes’s ‘I think, therefore I am’.18 On the first reading, an inference is being drawn from ‘I think’ to ‘I am’. On the second, Descartes is claiming that thinking is his raison d’être. (Descartes intended the first reading. It’s not entirely clear—at least to me—whether he also intended the second.) Clearly, ‘therefore’ is serving two very different purposes in these different readings of the cogito. On the first reading, it serves to mark an inference. On the second reading, it serves to indicate an explanatory relationship. Given the difference between these uses of ‘therefore’, we would do well to be wary of assuming that the ‘wherefore’-‘therefore’ link vindicates what is sometimes called the inferential conception of explanation.19 However, the double life of ‘therefore’ reveals why the inferential conception can seem very natural. Notice that other related words play a similar double role; ‘for’ is sometimes used to mark an inference instead of an explanation, as in: ‘p; for q and if q then p’. ‘Since’ can mark inferences (‘Since he has spots, he has measles’) or an 17

Some suggestive moves in this direction may be found in W. Salmon 1978, ‘Why Ask “Why?”? An Inquiry Concerning Scientific Explanation’, in Proceedings and Addresses of the American Philosophical Association 51, pp. 683-705, and in J. Hintikka and I. Halonen 1995, ‘Semantics and Pragmatics for Why-Questions’, in Journal of Philosophy 92, pp. 636-57. 18 Both ‘Je pense, donc je suis’ and ‘Cogito, ergo sum’ are susceptible of the same two readings. Thanks to Renée Hájek and Mark Bradley respectively for confirming this. 19 See e.g. Salmon 1978 for this nomenclature.

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explanatory connection (‘Since he has measles, he has spots’).20 Similarly for ‘as’. And even ‘because’ looks like it can sometimes be used as an inference marker, as in: ‘He must be at home, because his car is in the drive’.21 Instead, let’s look at what happens if we take ‘therefore’ as meaning roughly the same as ‘consequently’. We employ many notions of consequence: inferential consequence is one, but only one among many. There are also causal consequences, logical consequences,22 nomic consequences, modal consequences, things which ‘follow naturally’ in a variety of informal senses, intended consequences, and ‘results’ and ‘outcomes’ of various other kinds. Inferential consequence is the relation of premise(s) to conclusion in an inference (which inference may be good or bad). Non-inferential consequence is not characterized in terms of inference (though of course, when a non-inferential consequence relation obtains this may help explain what is good about the corresponding inference). I would like to suggest that explanation requests seek information about consequence relations of non-inferential kinds. Suppose (to use a familiar kind of example23) we both see a shadow cast by a tower, and infer from the length of the shadow that the tower is 50 feet tall. If I ask you to explain why the tower is 50 feet tall, citing the length of the shadow seems like a terrible attempt at an explanation, even though the tower’s height is a good inferential consequence of the shadow’s length. Instead you might cite the intentions of the architect, showing what the tower’s height is an intentional consequence of. Or you might cite the current trend for towers of height 50ft, showing what the tower’s height is a probabilistic consequence of. These would have a much better shot at being good explanations. I propose, therefore, that we think of questions of the form ‘Why p?’ as requests to be told of what p is a (non-inferential) consequence. We ask ‘Why p?’ because we want to know a reason for p, which is to say that we want to know what p is a consequence of in one of these noninferential senses. The ‘reason’ talk surrounding explanation and why-questioning, and the related appearances of ‘for’ discussed above, are used to signal neither teleology nor inference, but rather the presence of one (or more) of these other consequence relations. An important aspect of the characterizing role for explanations, then, is this: Why-explanations of p are things that show of what p is a non-inferential consequence, or things of which p is a non-inferential consequence.24 Explanations which are acts of explaining are covered by the first disjunct, and explanations which are facts or events are covered by the second. Explanations which are sentences or propositions could be covered by either. It is not immediately obvious, however, how explanations which are objects are covered by either disjunct. What might it mean to say that an object has p as a consequence, or reveals of what p is a consequence? My suggestion is that when p is explained by an object O, what is going on is that p is a consequence of O’s being as it is (in some contextually salient respect). We can say that p 20

Thanks to Harold Noonan for spotting this one. Interestingly, this effect seems to be harder to achieve without the use of the epistemic modal ‘must’. Maybe that is because the word ‘because’ is more strongly associated with explanation by default, and can revert to its inferential use only when the presence of an inference is clearly signalled, for instance by the use of an epistemic ‘must’. 22 It take it that logical consequence relations obtain independently of the drawing of corresponding inferences. It might be that logical consequence relations are – or correspond to – certain kinds of normative facts about inference. Nonetheless, inferential consequence in my sense is a non-normative notion. Thanks to Øystein Linnebo here. 23 Cf. Van Fraassen 1980, pp. 132-4. 24 This part of my view bears some similarities to Ruben’s claim that explanation is linked to the existence of metaphysical determination or dependency relations in the world (Ruben 1990, chapter VII). However, I intend something more liberal; on my view, there could be kinds of consequence relevant to explanation which do not correspond to determination or dependency relations in Ruben's metaphysically robust sense. For instance, certain kinds of mind-dependence anti-realists about modality could still regard modal consequence as relevant to explanation if they adopted my view. 21

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is ‘a consequence of O’ in this (somewhat extended) sense. The ‘consequence’ locution is not quite so happy when applied to objects as in the other cases, but other cognate locutions sound fine: p can be due to O, for instance. I shall therefore use ‘consequence’ in the case of objects too, in order to avoid complicating the letter of the account by introducing other, more grammatically comfortable, terms for the same thing. 3 Realizers of the Explanation Role If consequence plays a key part in characterizing the explanation-role, then we might expect there to be many different realizers of that role. For, in addition to the already-noted fact that things from various different ontological categories can play the role, there are many different kinds of noninferential consequence. These include causal consequence, nomic consequence, probabilistic consequence, logical consequence, mathematical consequence, modal consequence (of various strengths), and many others besides. I shall say a few words about each of the types of consequence just listed, in order to give a flavour of how these different consequence relations can be relevant to explanation, and how the kind of functionalism I am interested in can accommodate what is appealing about extant work on causal explanation, covering-law explanation, and the like. It should be comparatively uncontroversial that causal consequence is relevant to explanation. Very often, an explanation of an event or fact will cite a cause or causes of that event or fact. When I say the earthquake explains why the cup fell off the table, I seem to be citing something of which the cup’s falling is a casual consequence. It also seems fairly clear that nomic consequence can be relevant to many explanations, including many non-causal explanations. For example, if you ask why the statue melted when at room temperature, I might answer ‘Because it was made of ice’. The statue’s melting when at room temperature is a nomic consequence of its being made of ice, though the consequence relation invoked here is clearly not causal. (The statue’s being made of ice does not cause it to melt.) The amount of attention paid to causal and covering-law models of (scientific) explanation is testimony to the large number of explanations that invoke relations of causal and nomic consequence, especially in the sciences. My functionalist proposal enables us to accommodate the many insights of causal and covering-law accounts, whilst fitting them into a bigger picture which allows for other kinds of explanation as well (such as mathematical explanation). To give an example, the kind of functionalism I am interested in could incorporate something like Lipton’s account of causal explanation.25 The functionalist can acknowledge, with Lipton, the importance of contrast in selecting, from among the many causes of an event, those which are explanatory in a certain context and/or for a certain audience. And we might even accept Lipton’s particular account of how contrast functions to select causes that are explanatory. Lipton’s account is then viewed as an account of one kind of realizer of the explanation role: the causal realizers. (Of course, much of what he says might also be helpful in our quest to understand the other realizers too, and the role-property itself.) Because the role has other realizers besides causal realizers, we can take on board Lipton’s persuasive counterexamples to the view that all explanation is causal explanation (see p. 208), and make a positive suggestion as to what it is that these noncausal explanations have in common with causal ones. There are (at least) two kinds of ‘probabilistic consequence’ relation that can be relevant to explanation. When I say that p is a probabilistic consequence of q, I might mean that, given q, p is probable. Or I might mean that, given q, it follows that p is more probable than it would otherwise have been. Both relations have been thought to be important for understanding explanation; see Hempel’s Inductive Statistical model of explanation (Hempel 1965) and Salmon’s Statistical Relevance model (Salmon 1971) respectively. Again, the functionalist account I am suggesting 25

See P. Lipton 1990, ‘Contrastive Explanation’, in D. Knowles (ed.) Explanation and Its Limits (Cambridge University Press); reprinted in D. Ruben (ed.) Explanation, Oxford Readings in Philosophy (Oxford University Press), 1993, pp. 207-45.

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allows us to accommodate the intuitions behind these accounts, without succumbing to the objection that they do not cover all the cases. They can be recast as accounts of one class of realizers of the explanation role, rather than accounts of explanation per se. Logical and mathematical consequence can also be relevant to explanation; when my student asks why P ⊃ (Q ⊃ P), I can answer his question by showing that it is a logical consequence of (P v ~P). When asked why there are no even primes other than 2, we can answer by saying that every even number other than 2 is divisible by some number other than itself and 1, namely 2. One thing that is thrown into sharp relief in the literature on mathematical explanation is that it is far from obvious that it suffices for the provision of a mathematical explanation of p that one merely provide a proof that p.26 It might be thought that this raises problems for my account; the quest for an explanation of p cannot be a quest to know of what p is a consequence, for knowing that p is a consequence of our mathematical axioms often doesn’t satisfy our need for an explanation. In fact, this problem has analogues with regard to the other realizers already discussed; for instance, contra Lewis (1986) it is not plausible that citing any old cause (or part of the causal history) of p can count as providing an explanation of p. Similarly, not all kinds of nomic consequence are explanatory, as the well-known counterexamples to the covering-law models show (see Woodward 2003 for a good summary of some of these). These phenomena are, however, entirely compatible with the account I am offering. In addition to the above-noted ability of that account to incorporate insights like those of Lipton with regard to which causes count as explanatory, it is an important part of that account is that what counts as an ‘explanation’ (and what counts as a ‘good’ one) is highly sensitive to the interests of the speaker and audience. In order to assess what counts as an ‘explanation’ we depend on the context of utterance to settle such matters as which of the dimension 3 notions of explanation is in play, what kinds of consequence relation are salient, how much the audience knows already, and so on.27 Of special relevance to the current worry is the issue of how context makes particular consequence relations salient. When we ask ‘Why p?’ we are asking ‘Of what is p a consequence?’, but we are not interested in just any old consequence relation. A good answer to ‘Of what is p a consequence?’ is one that tells us of what p is a consequence-of-the-kind-we’re-interested-in. Similarly, when I ask ‘What are you going to do tomorrow?’, I’m not interested in hearing that you plan to breathe in and out all day. A good answer to ‘What are you going to do tomorrow?’ is one that tells me which things-of-the-kind-I’m-interested-in you’re going to do tomorrow. What kinds of consequence we are interested in varies enormously from person to person, time to time, and explanans to explanans. But there are some obvious guiding principles. Generally, people aren’t interested in hearing about the obtaining of consequence relations they already know to obtain. Notice, however, that this is very different from saying they aren’t interested in hearing facts they already know in answer to why questions. If you ask ‘Why p?’, it could be very informative to be told ‘q’ in response, even if you already know q. For you might not have been aware that p was a consequence (of the kind you’re interested in) of q. Often, people seem to have in mind some kind of contrast which makes particular consequence relations interesting to them.28 In addition, the various factors listed by Lewis29 as determining what counts as a ‘good’ explanation can all also have an impact on what counts as an ‘explanation’. Finally, let me say a bit about modal consequence. Many good explanations take the form of 26

See e.g. M. Steiner 1978, ‘Mathematical Explanation’, in Philosophical Studies 34, pp. 135-51. I do not mean to say that for everything p of which q is a consequence there is some possible context in which p counts as ‘explanatory’ of q. For instance, it is hard to see how q can be ‘explanatory’ of itself given any context of utterance of the explanation talk, yet q is a logical consequence of itself. My view is that background knowledge and other features of context impose certain restrictions on what will count as ‘explanatory’; but for all that says, it may be that some such constraints are imposed by every possible context. Thanks to Peter Lipton for pressing me to clarify this point. 28 See Lipton 1990 for a discussion of this kind of phenomenon in the causal case. 29 See Lewis 1986, pp. 226-7. 27

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showing that something is, in some (perhaps quite restricted or conditional sense) necessary. Why did you go to Sainsbury’s today? Because you had to: Waitrose was shut and you were out of milk. Why did Jimmy own up to stealing the books? Because the teacher’s threat to punish the whole class made it impossible for him to stay silent. Why aren’t there any square circles? Because that just can’t happen. The modalities involved in these three examples are of quite different kinds. The first is clearly a very restricted modality; it was only necessary for you to go to Sainsbury’s today if you were to have milk for breakfast and didn’t want to go shopping for it in another town. The second might be read as saying either that it was impossible for Jimmy to stay silent given that he is a good person, or that it was impossible for him to stay silent given his unwillingness to endure the bad opinion of his classmates. The third example looks more like an explanation appealing to an unrestricted modality. Since p is a consequence of □p, regardless of how restricted or general a modality the box represents,30 these explanations all function by showing of what the explanans is a consequence. The consequence relation involved here might be logical; in any case, it is not particularly distinctive. But it is also worth noting that many other explanations work rather like the ones just mentioned but make the modality less obvious. Why did you go to Sainsbury’s today? Because Waitrose was shut and you were out of milk. In this case, the explanandum is not a consequence of the explanans in anything like a logical sense. However, what we do know is that, across a salient range of worlds (the close worlds where you have milk for breakfast without shopping in another town), all the explanans-worlds are explanandum-worlds. That is what I mean by saying that sometimes explanations invoke modal consequence relations. What I’m calling ‘modal consequence’ is basically strict implication, but the modalities involved (that is to say, the degree of strictness) may vary. Nomic consequence might be thought of as a special case of modal consequence: modal consequence where the salient range of worlds consists of those worlds which obey our laws of nature. Similarly for mathematical and logical consequence. However, all these kinds of consequence are sufficiently significant for the theory of explanation to merit their own categories for the purposes of exposition. (Maybe probabilistic consequence could be understood in terms of worlds too, although this is more controversial.) Another point worth mentioning is that something akin to modal consequence, when combined with consideration of impossible worlds,31 may be of value in understanding certain kinds of explanation. Perhaps, for instance, one difference between an explanatory mathematical proof and a non-explanatory one is that when (and only when) P is an explanatory proof of s, s is true in all the contextually salient possible and impossible worlds where P’s premises and inference rules are true. A few other kinds of consequence, which may or may not be reducible to special cases of the ones I’ve already mentioned, are dispositional consequence, deontic consequence, legal consequence and intentional consequence. I gave an example of an explanation involving intentional consequence on p. 8 above. Examples of explanations that seem to me to involve dispositional consequence include the following. Why did the salt dissolve? Because it was placed in water. Why did the glass break? Because it was dropped. And so on. It is worth noting that some realizers of the explanation role may be unavailable for certain kinds of explanandum.32 For instance, it is not very plausible that there are causal explanations of mathematical explananda. On the other hand, some might think (although I do not think this myself) that particular events have only causal explanations. One of the interesting issues thrown into relief by the kind of functionalism I am interested in, but which I do not claim to have addressed here, is that of saying in general what kinds of realizers are available for which kinds of explananda. 30 Of course, some uses of the box are not covered by this rule (known as T); deontic boxes, for instance, are not likely to obey it. The boxes I refer to represent alethic modalities. 31 See e.g. D. Nolan 1997, ‘Impossible Worlds: A Modest Approach’, in Notre Dame Journal of Formal Logic 38, pp. 535-72. 32 Thanks to Philip Percival here.

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To sum up the main idea of this section, realizers for the explanation role come in bundles. Each bundle corresponds to a different kind of non-inferential consequence relation, and within each bundle are things belonging to various different ontological categories. There is, for instance, a bundle of causal realizers: causes (events, facts, objects), acts of citing causes, sentences which describe causes, propositions which describe causes. All these things can play the explanation role. Then there is a bundle of nomic realizers: things of which the explanandum is a nomic consequence (events, facts, objects), acts of citing these things, and sentences and propositions which describe these things. All these things can also play the explanation role. And so on for the other kinds of consequence. 4 Concluding Remarks Ideally, a more thorough treatment of the notion of consequence than I am able to give in this paper would be desirable.33 I have listed some kinds of consequence, but I have not given any general guidance as to what does and does not count as a kind of consequence. It is clear that the notion has some punch; that is to say, not any old relation counts as a consequence relation. Some that obviously don’t count include looking like, being cooler than, and the universal relation. Some things might be borderline cases of consequence relations: raising probability by a small amount but not very much, for instance. But for now, we must rest content with an intuitive distinction. Let me finish up by returning to a question I raised earlier: is there one ontological category of explanations which is basic? I believe the views developed in the previous sections provide some tentative support for the answer to this question which I previously gestured at, namely that acts of explaining are conceptually basic, but facts, events and objects are metaphysically basic. My suspicion—and let me stress that it is only a suspicion; I have not argued for it—is that our concept of explanation is a role-concept rather than a realizer-concept. I think the concept is closely tied to the role I described above: the role of providing answers to why-questions, that is, providing information as to of what the explanandum is a consequence (of the right kind). And the asking and answering of why-questions, the requesting and provision of information, is a human activity; or at least, that’s what it is first and foremost. Things like sentences and facts can count as answers to why-questions only derivatively, because of their involvement in this human activity. To this extent, I am in sympathy with Achinstein’s34 position (though I would not endorse all of his arguments in its favour). That notwithstanding, various things seem to be, in a certain important sense, more metaphysically fundamental to explanation (at least of the ‘real’ and ‘genuine understanding’ kinds—see dimension 3) than the human activities that characterize the explanation role. The facts, events and objects that make up our world are there first, and it is their being as they are that often makes for the obtaining or not of the various consequence relations that generate realizers for the explanation role. Hence it is the facts, events and objects in our world that often render our attempts at the act of explanation successful or otherwise. Many (perhaps all) acts of explanation are in that sense world-directed, and their goodness as explanations is in that way dependent on how things are in the world. To this extent, I am in sympathy with those who, like Ruben35 insist that explanation is grounded in metaphysical relations in the world, rather than (merely) in anything anthropocentric like the act of explaining. Properly understood, however, this intuition and the act-primacy intuition of Achinstein do not need to conflict with one another. Ruben’s intuition is an intuition about the realizers of the explanation role, Achinstein’s is about the role concept itself.

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Thanks to Peter Lipton here. See Achinstein 1983. 35 See Ruben 1990. 34

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References Achinstein, P. 1983: The Nature of Explanation. Oxford University Press. Bromberger, S. 1966: ‘Why-Questions’. In R. Colodny (ed.) Mind and Cosmos: Essays in Contemporary Science and Philosophy. University of Pittsburgh Press. Reprinted in B. Brody (ed.) Readings in the Philosophy of Science. Englewood Cliffs, NJ: Prentice Hall, 1970, pp. 66-87. Hempel, C. 1965: ‘Aspects of Scientific Explanation’. In his Aspects of Scientific Explanation And Other Essays in the Philosophy of Science. London: Collier-Macmillan, pp. 331-496. Hintikka, J. and Halonen, I. 1995: ‘Semantics and Pragmatics for Why-Questions’. Journal of Philosophy, 92, pp. 636-57. Kitcher, P. and Salmon, W. 1987: ‘Van Fraassen on Explanation’. Journal of Philosophy, 84, pp. 315-30. Lewis, D. 1986: ‘Causal Explanation’. In his Philosophical Papers Volume II. Oxford University Press, pp. 214-40. Lipton, P. 1990: ‘Contrastive Explanation’. In D. Knowles (ed.) Explanation and Its Limits. Cambridge University Press. Reprinted in D. Ruben (ed.) Explanation, Oxford Readings in Philosophy. Oxford University Press, 1993, pp. 207-45. Nolan, D. 1997: ‘Impossible Worlds: A Modest Approach’. Notre Dame Journal of Formal Logic, 38, pp. 535-72. Ruben, D.-H. 1990: Explaining Explanation. London: Routledge. Salmon, W. 1971: ‘Statistical Explanation’. In W. Salmon (ed.), Statistical Explanation and Statistical Relevance. University of Pittsburgh Press, pp. 29-87. ------------ 1978: ‘Why Ask “Why?”? An Inquiry Concerning Scientific Explanation’. Proceedings and Addresses of the American Philosophical Association, 51, pp. 683-705. Steiner, M. 1978: ‘Mathematical Explanation’. Philosophical Studies, 34, pp. 135-51. Van Fraassen, B. 1980: The Scientific Image. Oxford University Press. Woodward, J. 2003: ‘Scientific Explanation’. In E. Zalta (ed.) Stanford Encyclopedia of Philosophy, available online at: http://www.seop.leeds.ac.uk/entries/scientificexplanation/#2.5.

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