THE SOURCE OF NECESSITY

Bob HaleUniversity of Glasgow

A little more than four decades ago, Michael Dummett gave what I havealways found a compelling statement of the central philosophical problem aboutnecessity: “The philosophical problem of necessity is twofold: what is its source,and how do we recognise it.”1 I shall take it that the kind of necessity in ques-tion here is what is sometimes calledabsolutenecessity, where to say that anoperator ‘▫’ expresses a kind of absolute—as opposed to merely relative—necessity means, approximately, that it is true that▫p only if there is no senseof ‘possible’ in which it is possible that not-p.2 In this paper, I shall be mainly—indeed, almost entirely—concerned with the first part of this problem. In myfinal section, I shall canvass and offer some defence of a quite simple sugges-tion about how Dummett’s first question may be accepted at face value anddirectly answered. But before we can usefully and sympathetically consider thatsuggestion, a good deal needs to be done to prepare the ground. In contrastwith Dummett’s second question, which merely demands what any credible phi-losophy of necessity clearly owes—an account of our knowledge of it—and socannot be refused,3 it is far less clear what the demand for the source of neces-sity is after and, in consequence, less clear that, or in what sense, it must beaccepted. In particular, it might be heard as calling for a reductive explanationof necessity—an explanation, in terms whose modal status is itself unproblem-atic (and so without appeal to any supposed necessities), of necessity in gen-eral, or how there can be such a thing as necessity at all. If the demand isunderstood this way, it is—for reasons which some of what I shall be arguingshould help to bring out—at least very doubtful that it can be met; but it is, Ishall suggest, equally doubtful that we must then accept it. But if, as I think,there is some other way in which the demand for the source of necessity can beunderstood—and perhaps, when so understood, cannot be refused—it is far fromobvious what it is. The difficulty here arises, in part, because while—subtleand sophisticated philosophical disputes about the nature of scientific explana-tion notwithstanding—we have a reasonable working grip on what, at least insimple and straightforward cases, constitutes an explanation, when the explanan-

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dum is some particular or generalcontingency, it is much less clear what shouldcount as explainingwhat could not but be(or have been) as it is. This in turn ispartly because there is no non-trivial counterfactual dependence of any neces-sity on anything else. But as we shall see in the next section, there are furtherconsiderations which might lead us to suppose that any attempt to explain ne-cessity in general is doomed to failure. So at least part of my preparatory dis-cussion will be taken up with arguing that we need not embrace that pessimisticconclusion.

Blackburn’s Dilemma

Simon Blackburn gives a more elaborate but, even if less pithy, equallyforceful formulation of Dummett’s problem in a relatively recent article. Elab-orating what he calls the ‘truth-conditions approach’ to necessity, he writes:

By making judgements of necessity we say things, and these things are true orfalse. Perplexity arises because we think there must therefore be something whichmakesthem so, but we cannot quite imagine or understand what this is. Nor do weunderstand how we know about whatever this is: we do not understand our ownmust-detecting faculty. Elucidating the truth-condition, and our access to it, isthegoal of philosophy, ... The problem is that of the fugitive fact, and the solution is tocapture the nature of the fact in an intelligible way. This answer would tell us whatsuch truthsconsist in: the answer would be obtained by establishing thetruth-conditionsfor such judgements. It would give us an ‘account’ of the states of af-fairs in which their truth consists, or of what it is thatmakesthem true. The accountwould have an explanatory role as well: fully established, it would explain why itis necessary that twice two are four, ...4

In contrast with Dummett, however, Blackburn is not here speaking for him-self. He is, rather, seeking to capture the essence of the problem of necessity asother philosophers standardly conceive it. But so to conceive it is, in Black-burn’s view, fatally tomisconceive it. He proceeds to pose what he takes to bea lethal dilemma confronting any attempt at a ‘direct’ solution of the sort de-scribed in the passage quoted—that is, roughly, one which takes Dummett’squestions at face-value and accepts their evident presuppositions that thereissuch a thing as necessity (i.e. there are some statements which hold true ofnecessity) and that it is indeed a possible object ofknowledge.

If we ask what makes it so thatA must be the case, we may be given a local proof,a proof ofA from B. This is satisfactory if we already understand whyB must beso, ...but if our concern is with the whole area, then we then turn to scrutinize thatunderstanding. Attention just shifts to whyB must be the case, for our philosophi-cal concern is with necessity in general, not withA in particular. Suppose an even-tual answer cites some truthF, and so takes the form: ‘▫A becauseF’. ...

Now eitherF will claim just that somethingis so, or it will claim that some-thing mustbe so. If the latter, there is no problem about theform of the explana-tion, for one necessity can explain another. But as we have seen there will be the

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same bad residual ‘must’: the advance will be representable as ‘if we see whythismust be so, we can now see whythat must be as well’ And there is no escapefrom the overall problem that way. Suppose instead that F just cites that some-thing is so. If whatever it is does nothaveto be so, then there is strong pressureto feel that the original necessity has not been explained or identified, so much asundermined.5

We can put the intended dilemma like this: To give the ultimate source of anynecessity, we must either appeal to something which could not have been other-wise (i.e. is itself necessary) or advert to something which could have beenotherwise (i.e. is itself merely contingent). But any appeal to another necessitymust fail to provide the desired explanation, since it merely shifts the question;while adverting to a contingency is equally hopeless, because, by resting thesupposed necessity on a mere contingency, we deprive it of the very necessitywe sought to explain.

How should we respond to this dilemma? Blackburn’s own view is that weshould do so by scrapping altogether the approach to modality which leads usinto it, in favour of the kind of ‘quasi-realist’ alternative he has sought to pro-mote in other areas, and especially in morals—modal statements should be seen,not as attempts to capture the denizens of some special realm of modal facts,but as expressions or projections of our own attitudes or, perhaps, of our imag-inative capacities and incapacities. I am not going to discuss here whether, ifthe dilemma is good, this would be the best response to it. Since I don’t thinkthe dilemma is good, and can think of no other good reason why we should nottake modal statements at face-value, as articulating distinctively modal facts orfalsehoods, I don’t think weshouldabandon the truth-conditions approach. Ofcourse sticking to that approach requires finding a positive solution to Dum-mett’s problem. I shall try to show that seeing why Blackburn’s dilemma is lesscompelling than it may at first appear puts us on the right track. More pre-cisely, I shall try to show that the first—necessity—horn of his dilemma cru-cially overlooks the possibility of a certain kind of explanation. But it will beboth instructive, and useful for my purposes, to begin by scrutinizing theother—contingency—horn.

Conventions and Contingency

One—sometime very popular—proposed answer to Dummett’s first ques-tion tries to locate the source of necessity in linguisticconventions. Elaboratinghis dilemma, Blackburn contends that this kind of account must impale itselfon its second horn.

... suppose a theorist claims that twice two must be four because of a linguisticconvention ...Suppose it is denied that there is any residual necessity, that wehaveto make just those conventions, ... . Then ...there is a principled difficulty aboutseeing how the kind of fact cited could institute or be responsible for the necessity.

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This is because, if good, the explanation would undermine the original modal sta-tus: if that’s all there is to it, then twice two does not have to be four ...6

If—the thought goes—the alleged or supposed necessity, e.g. that 21254, re-ally does depend upon a convention governing the use of the words in whichwe state it, and the existence of that convention is a merely contingent matter,then it can’t after all be necessary that 21254; had there been no such conven-tion, it would not have been necessary, and might not even have been true, that21254.

Prescinding, for the time being, from some difficult but ultimately crucialquestions about what kind of explanation we may properly and sensibly de-mand, either of specific necessities or, more problematically, of necessity ingeneral, it is hard to see how this objection could dislodge a determined con-ventionalist. Let us suppose, as the conventionalist will surely grant, that it is acontingent matter what conventions are in force. I shall assume7 that the con-ventionalist’s position is not intended to be deflationary—so that her claim isthat it really is necessary that twice two is four, say, but that it is so simplybecause we subscribe to certain conventions. But how, on these assumptions, isthe conventionalist supposed to wind up committed to ‘undermining’ the neces-sity, rather than explaining it? Let▫p be the necessity to be accounted for, andq a statement to the effect that the relevant convention is in force. The conven-tionalist holds that▫p becauseq, and agrees that it is merely contingently truethat q, i.e. that whileq, L¬q. Let us further suppose8 that our conventionalistholds not only that the fact thatq is sufficient to ensure that▫p, but that had itnot been the case thatq, it would not have been necessary thatp. Even so,these premisses would commit her only to denying that it isnecessarilyneces-sary thatp (i.e. to ¬▫▫p).9 It would follow from that that¬▫p only on theassumption of the characteristic S4 principle that what is necessary is necessar-ily so. Since that is scarcely a principle which the conventionalist can be ex-pected to accept, the objection pretty directly begs the question against her.10

To be sure, the argument might still be effective—for all that we’ve seenthus far—against anyone who opts for the contingency horn but, unlike theconventionalist, grants that whatever is necessary is necessarily so. But there isa further difficulty. We have so far let pass the assumption that one who ex-plains why it is necessary thatp by appeal to the contingent fact thatq will bethereby committed to endorsing the counterfactual: had it not been thatq, itwould not have been necessary thatp. But the assumption is in fact problem-atic, at best, since there are plausible cases in which we explain whyp, quitecorrectly, by pointing to the fact thatq, but in which it is false that, had it notbeen thatq, it would not have been thatp, because even if it had not been thatq, it would, or might, still have been thatr, which would have sufficed anywayto ensure thatp. The balloon burst because it was hit by my bullet, but evenhad I missed, or not even fired, it would still have burst, since you also firedand hit it and would still have fired and hit, had I not done so. So the generalprinciple on which the argument of this horn, as we have it, relies—that ex-

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plaining ‘B becauseA’ commits one to endorsing the ‘would’-counterfactual;‘¬A ▫r ¬B’—is very much open to question.11 It might be suggested12 thatit would suffice for the argument to appeal to a weaker and, to that extent,more plausible principle, to the effect that explaining ‘B becauseA’ does atleast commit one to endorsing the ‘might’-counterfactual: ‘Had it not been thatB, it might not have been thatA’. It is true, of course, thatL¬B follows fromL¬A and¬A Lr ¬B,13 ( just) as well as fromL¬A and¬A ▫r ¬B. How-ever, even if the more modest principle is right when we are concerned withexplanations ofcontingencies,14 it cannot possibly govern explanations ofne-cessities. For suppose▫B. Then▫¬¬B, whence it is (vacuously) true thatA▫r ¬¬B, and hence false that¬(A ▫r¬¬B), for anyA. That is, if ▫B, it isfalse thatA Lr¬B, whatever propositionA is taken to be. So—assuming, aswe may in this context, that▫B entails▫▫B—▫B entails that ALr ¬▫B isfalse, for everyA. Thus, if we explain ‘▫B becauseA’, we cannot possibly becommitted to¬A Lr ¬▫B.

We should not over-estimate the significance of Blackburn’s failure to fur-nish an effective objection against a specifically conventionalist opponent. Forwhilst it is true enough that conventionalism is not only the most prominent,but also the only obvious, way of trying to live on the contingency horn, thereare other, better-known and more effective, objections to the conventionalistanswer. Quine long ago made the point that word-sized conventions (of nota-tional abbreviation) cannotcreatenecessary truth—or even truth simpliciter—but can at best provide for thetransformationof given necessary truths intoothers. Thus a convention to the effect that, say, ‘bachelor’ means, or is to mean,the same as ‘unmarried man’ enables us to transform ‘No bachelor is married’into ‘No unmarried man is married’. But it is simply a confusion to supposethat the convention is what makes for the truth of the former statement. If theformer is, or expresses, a necessary truth, that it because it is a definitionalcontraction of another necessary truth—the logical truth that no unmarried manis married—the necessity of which is not to be accounted for by reference tothat convention. Of course—since there can be conventions of notational ab-breviation relating to logical vocabulary—conventions of this sort may enableus to transform some logical truths into others. But the same point applies: thesource of the truth, or necessity, of any abbreviated logical truth must be thesame as that of the longer logical truth it abbreviates, and cannot be explainedby appeal to word-sized conventions. The upshot, as Quine stressed, is that ifconvention is to be billed as the mother of necessity, appeal must be made toconventions of a quite different sort—sentence-sized conventions, stipulatingthe truth of complete sentences (or perhaps whole classes of sentences exem-plifying some specified form) appear to be required. But as Quine, andlater—somewhat differently—Dummett argued, the project of grounding allnecessity—or even all logical necessity, narrowly or broadly conceived, andleaving aside other putative species of absolute necessity—in such conven-tional stipulations is equally hopeless.

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Sentence-sized stipulations are likewise inadequate to the task of provid-ing for the conventionally-based truth of all necessary truths because—giventhe potential infinity of such truths—this would require the necessity of mostnecessary truths to be inherited from a base class of directly stipulated truths,by virtue of their being logical consequences of truths in that base class, andthis either merely serves to disclose further necessary truths unaccounted foron the premisses and conclusions model (Dummett) or generates a vicious in-finite regress (Quine). To elaborate a little, let U be our base class of directlystipulated necessary truths andp some necessary truth not in U.15 Then theconventionalist must claim that the necessity ofp is secured by its being a log-ical consequence of (some statements in) U. But then the conditional: Urpwill be a further necessary truth, which we may assume not to be guaranteedby its being either in U or an instance of a form covered by a stipulation inU.16 Since its necessity is not secured by direct stipulation, it must be held toresult from its being, in turn, a logical consequence of statements in U. But thatmerely discloses another necessary truth: Ur(Urp), of whose necessity wehave as yet no account.

Observing that the conditionals Urp, Ur(Urp), along with others inthe impending regress, such as Ur(Ur(Urp)), are all logically equivalent(since the conditional is material), the conventionalist may retort that we donot, contrary to appearances, need an infinite sequence of distinct stipulations,but one single stipulation: in stipulating that Urp, we eo ipsostipulate thatUr(Urp), etc., since the contents of each stipulation, and so the stipulationsthemselves, are identical. As against this, it may be observed that the assump-tion that stipulations with logically equivalent contents are identical is scarcelyunproblematic—indeed, in this context, it handsomely begs the question at is-sue: since all logical truths are logically equivalent, it would enable the con-ventionalist to take care of them all with a single stipulation, say ofprp—surely it should not be that easy! But even if the assumption is granted, itdoes not appear, on reflection, that this reply is open to the conventionalist.The biconditionals linking the conditionals in the sequence will themselves benecessary. But their necessity must again be derivative, and thus, in her view,they must be consequences of U. The reply therefore merely re-instates theregress at one remove. The conventionalist may, of course, seek to avoid theregress in a different way, by simply augmenting U with an additional stipu-lation for Urp. But this manoeuvre is equally futile. For one thing, there willbe many other necessities in the same case asp—infinitely many, exemplify-ing different logical forms, so that no finite extension of U could save theday. And in any case, the manoeuvre merely relocates the problem. For theexpanded base class, U1, will now comprise both U and Urp, from which pcan be deduced bymodus ponens. Corresponding to this deduction there isthe necessary truth: Ur((Urp)rp), which belongs neither to U nor, cru-cially, to U1. Its necessity must therefore be put down to its being a logicalconsequence of U1, and ... off we go again.

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This last ploy, ineffective as it is, might suggest a way around theobjection—in essence, Dummett’s—we’ve been reviewing. For it might seemthat the (necessary) truths about logical consequence which we’re strugglingto capture could be brought into reach by conventionalising the means of de-duction along with the ultimate premisses. We are forever being thwarted bysuch facts as this: whenp andprq are both in U, butq is not, we can securethe conventional necessity ofq by appealing to the fact that it is a conse-quence of those other necessities bymodus ponens, but only at the cost ofhighlighting another necessity—in this casepr(( prq)rq)—as yet uncon-ventionalised. So why not cut through the problem by writing in a conventioncorresponding to that rule of inference, and similarly for such other rules aswe may require. Thus we might try to take care of inferences bymodus po-nensby a stipulation to the effect that any statement is to be true which re-sults in a truth when it is substituted forB and a truth is substituted forA inArB.17 But as Quine pointed out, this gets us nowhere, very slowly. For ourconvention corresponding tomodus ponensis, and has to be, general. To ap-ply it, we must make some inferences. In this case, besides observing that atruth results from substitutingq for B and some truthp for A in ArB, we mustinfer from our general convention that if a truth results from puttingq for Bandp for A in ArB, thenq is to be true, and thence infer (bymodus ponensonce again), thatq is to be true. Since these inferences must themselves beaccorded the same or similar treatment, we can never get to first base. In short,any attempt to subvert Dummett’s objection by conventionalising the means ofdeduction merely lands the conventionalist in Quine’s version of the regress.

These objections allow—at least for the sake of argument—that the con-ventionalist strategy can at least get started, by conferring truth by conventionupon sentences in the base class by direct stipulation. But even this much isopen to question. It is called into question by an equally old objection to con-ventionalism which claims that the conventionalist confuses sentences withpropositions—in the sense that she mistakenly treats what makes words or sen-tencesmeanwhat they do (and so renders them apt to express certain proposi-tions) as what makestrue the propositions they are thereby enabled to express.The anti-conventionalist thought is that the conventionalist illicitly runs to-gether determinants of meaning with determinants of truth—it is granted thatwhat words and sentences mean is determined by conventions explicitly adoptedor otherwise entrenched in our linguistic practice, and granted, further, that whatwe say—what propositions we express—by our words is accordingly conven-tionally determined. But that, so the objection runs, is the end of the matter, asfar as conventions go—it does not follow that the truth of the propositions ex-pressed, if indeed they are true, is ever, in any sense, a matter of convention.Nor is it true: conventions merely determine what proposition is expressed by asentence—whether that proposition is true is always afurther question whoseanswer is never settled by our linguistic conventions.

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At first sight, this objection—in sharp contrast with the objections of Quineand Dummett just discussed—charges conventionalism with a mistake about theproper bearers of truth-values, and rests upon the claim that sentences, as dis-tinct from the propositions they may serve to express, cannot discharge that rôle.However, whilst this is suggested by my initial formulation of the objection, andmay have been what some of its early proponents had in mind, it is—or so itseems to me—inessential to the real force of the objection, which need not relyupon any controversial insistence that propositions are the only or primary bear-ers of truth-value, or that sentencescannotbe truth-bearers. All the objectionrequires is that if sentences, rather than propositions, are to be taken as truth-bearers, then it must beinterpretedsentences that are so taken (i.e. sentenceswith a certaincontent, or understood as having associated with them certain def-inite truth-conditions). The objection can then be put: the rôle of convention isrestricted to determining the content of the interpreted sentence—its truth-value,or that of the content (proposition) it expresses, is afurther, separate and inde-pendent matter which is not, and could not be, settled or determined by stipu-lation. So understood, the objection rests upon two claims: first, that only whathas a (more or less) determinate content—in the sense, minimally, that it is as-sociated with some (more or less) definite condition for its truth—can be trueor false; and second, that once something—a declarative sentence, say—is thusassociated with a truth-condition, it is—already, as it were—an objective andindependent matter whether that condition is or is not fulfilled, so that there issimply no room for a stipulation to settle its truth-value.18

If this objection is sound, conventionalism—at least as an account of thesourceof necessary truth—is fundamentally misconceived. It is not just, as thearguments of Quine and Dummett seem to show, that conventional stipulationcannot possibly provide, directly or otherwise, for the necessity ofall neces-sary truths—it cannot account for that ofany. But is it sound? It may be coun-tered that the objection overlooks a crucial possibility. Why should meaning(or truth-conditions) and truth-value not be fixedtogetherby stipulating thetruth of a suitable sentence? Indeed, is this not precisely what happens whenmeanings are fixed byimplicit definitionconceived, as it standardly is, as pro-ceeding through a stipulation of the truth of a sentence or sentences embeddingthe definiendum. It may thus appear that the objection, if sound, rules out thepractice of implicit definition, so that if that procedure, as standardly con-ceived, is viable and legitimate, theremustbe something wrong in the objection.

It might appear that if a proponent of the original objection is to stay inplay, he must reject altogether the standard, stipulative, conception of implicitdefinition to which this counter to it appeals, perhaps replacing it by the idea—advocated in recent writings by Paul Horwich—that what fixes the meaning ofthe definiendum is not astipulationof truth, but ouracceptingor regarding astrue some sentence(s) containing it.19 I am not myself convinced that switch-ing from stipulation to acceptance in and of itself makes any crucial differenceto the point at issue. In any case, it does not seem that any such shift is needed

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for an effective response to the counter-objection. For it is not clear that theobjection must be in tension with the idea that implicit definition proceedsthrough a stipulation of truth, when that is properly understood. What the ob-jection denies is that we can stipulate the truth of a proposition, or fully inter-preted sentence (i.e. a sentence which is already and independently associatedwith a definite content, or determinate truth-condition). That is, there is roomfor stipulation only in a case where some aspect of meaning (and so, what prop-osition is expressed by a sentence) is yet to be determined—but this is pre-cisely how, according to the standard conception of it, an implicit definitiondoes work. The vehicle of the stipulation is some sentence incorporating thedefiniendum, but otherwise composed of expressions whose meaning is al-ready understood (and so already determined), in a syntactic fashion whosesemantic significance is again already determinate. If we schematically repre-sent this sentence by ‘f(t)’ (where ‘t’ is the definiendum), the import of thestipulation is that ‘t’ is to take on a meaning which ensures, given the meaningsof the expressions in ‘f’, that ‘f(t)’ is true—i.e. expresses a true proposition.Since, independently of the stipulation, ‘f(t)’ has no determinate sense (or truth-condition) as a whole, there need be no attempt at stipulation where there is noroom for it, and no inevitable clash with the idea that what already possesses adefinite truth-condition cannot be made true by stipulation. Indeed, on this ac-count, nothing is, strictly speaking, made true by stipulation. Rather, a sentencewhich—prior to the stipulation—lacks a completely definite meaning comes toexpress a certain truth. There is, therefore, a sense in which it is correct to saythat meaning (or truth-conditions) and truth-value are fixed together by an im-plicit definition—by stipulating that the sentence which is its vehicle is to ex-press a truth, we thereby determine its truth-condition. But in doing so, we donot create a truth by stipulation, rather we create a means of expressing one. Inany interesting case, i.e. any case in which the implicit definition isn’t otiose,there won’t already be an independent way of expressing the truth in question.There being a truth, awaiting the means of expression, as it were, is aprecon-dition of successful implicitly definitional stipulation.

If this is right, the force of the objection to conventionalism we’ve beenreviewing remains undented. The upshot—since it is hard to see how else onemight make good on the idea that any truth might be produced by conventionor stipulation, if not via implicitly definitional stipulation—is that conventionsor stipulations concerning whole sentences aren’t and can’t be the source of thetruth of any propositions.

Explaining necessity—some needed distinctions and the transmissionmodel of explanation

We have already seen some reason to expect that principles plausibly takento govern explanation of contingencies may not generally carry over to expla-nations of necessity. I want now to take up some questions I left aside when

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considering Blackburn’s attempt to skewer a conventionalist explanation on thesecond horn of his dilemma. What kind of explanation may we properly andsensibly demand, when our explanandum is (some) necessity? When we ex-plain a contingency, at least part of what we do is explain why that particularcontingency obtains,rather than not(or rather than some competing alterna-tive). Since there is no possible alternative to a necessity, nothing clearly andstraightforwardly analogous to this carries over to explanations of necessity—sowhat does make for a good or illuminating explanation in this case? I can dolittle more than scratch the surface of these hard questions here. However, it isclear that we need some distinctions. First, and most obviously, we need todistinguish between explainingparticular necessities and explaining necessityin general; but we clearly ought to distinguish also between explaining, in re-gard to any given necessary truth, why it istrue, and explaining why it isnec-essary. Since our concern is principally with explaining necessity in general, itis this idea that is especially in need of clarification; but I think it will be in-structive to look briefly at how the other explanatory tasks may be discharged.

Consider the particular necessity that the sum of the firstn positive inte-gers isn21n/2, i.e. n(n11)/2. someone who wishes to know why this is somay be told—“Well, consider what you get when you add the firstn positiveintegers to themselves in reverse order. Then you have a sum of 2n terms: (1121... .1(n21)1n) 1 (n1(n21)1 ... .1211). Since addition commutes and asso-ciates, this sum of 2n terms is equal to a sum ofn terms, each of which is asum of two terms: (11n)1(21(n21))1 ... 1((n21)12)1(n11). Notice thatas the left hand terms increase by 1, the right hand terms decrease by 1. Obvi-ously, then, each of thesen terms is equal ton11. So the total isn(n11). Justlook at the diagram:

1 2 3 ... .. n1 1 1 ... . . 1n n21 n22 ... . . 1

J 5 n(n11)

n11 n11 n11 ... . . n11

So the sum of the firstn positive integers is just half of that:n(n11)/2”

Whilst not every proof is explanatory, this one (which could, of course, be re-placed by a more rigorous inductive proof ) has a good claim to be so. It ex-plains why the sum of the firstn positive integers isn(n11)/2. Does it explainwhy that isnecessarilyso? No, not as it stands. It perhaps suggests an expla-nation, but it does not give one. The facts cited in the explanation—its startingpoints—such as that twice the sum of the firstn positive integers is, or can beexpressed as: (1121 ... .1(n21)1n) 1 (n1(n21)1 ... .1211), and that addi-tion is commutative and associative—are themselves necessary, and the transi-tions are necessarily truth-preserving. So we can easily get an explanation why

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it is necessarythat the sum of the firstn positive integers isn(n11)/2 by point-ing out that each of the undischarged premisses in the explanation why the sumof the firstn positive integers isn(n11)/2 is itself necessary, and appealing tothe principle that what follows from necessities is itself necessary (i.e. to themodal logical law: (▫p ∧ ▫( prq)) r ▫q). Of course, we haven’t explainedwhy the undischarged premissesare necessary (or, for that matter, why the gov-erning modal logical law is so)—but that is no reason to suppose that we haven’treally explained why it is necessary that the sum of the firstn positive integersis n(n11)/2—to think otherwise is to commit the ‘fallacy of many questions’.

Whilst our little example suggests a model—thetransmission-model—forthe explanation of a quite wide range of particular necessities, it offers no pros-pect of an explanation of necessity in general. Although I do not suppose thatanyone will be much tempted to think otherwise, it is worth being clear pre-cisely why this is so. An explanation of necessity in general need neither be,nor provide for, an explanation of each and every particular necessity. What isrequired, rather, is to explain why there is any necessity at all—we may, and Ishall, take this to amount to the requirement to explain why, assuming it to beso, it is true that there is at least one necessary truth, i.e. why∃p▫p.20 Natu-rally, this requirement cannot be met by any explanation which makes essentialappeal to the necessity, as distinct from the truth simply, of its explanans. It isfor this reason that the transmission-model, whilst providing for the explana-tion of many particular necessities, cannot possibly support an explanation ofnecessity in general.

It looks to be the transmission-model that Blackburn has in mind when heurges, on the first horn of his dilemma, that any explanation why▫p whichappeals to another necessity,q, cannot discharge but must merely postponethe explanatory task. Certainly if no other style of explanation of any neces-sity is possible—i.e. other than one conforming to the transmission-model—wecan be sure that no explanation of necessity in general is to be got by appealto necessities. The fact that we can, in accordance with the model, explainsome particular necessities in terms of others indicates that some necessitiesare more fundamental—explanatorily more fundamental, anyway—than oth-ers. It would be consistent with acknowledgement of that point to hold thatsome necessities are not merely more fundamental than others, but fundamen-tal, not just in the sense that they do not admit of explanation in terms of thetransmission-model, but in the strong sense that they do not admit of explana-tion at all.21 Given such a base class of fundamental necessities, all othernecessities might be explained, transmissively, in terms of it. But on the as-sumption that only transmissive explanation is possible, it remains the casethat there can be no explanation of necessity in general. The assumption thatthere must be a base class of fundamental, inexplicable, necessities is inessen-tial to the point. Someone who holds that necessities may be explained onlyin terms of the transmission-model might, without inconsistency, hold that ev-ery necessity is so explicable, so that there just is no base class. Of course,

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if every necessity is to be explicable, without circularity, in terms of thetransmission-model, then there must be an infinite regress of ever more fun-damental necessities. This may be thought—and in my view is—implausible,but I have not been able to see that the regress is actually vicious. But it isworth being clear why, even if non-vicious, the regress is inevitable. In anytransmission explanation of a particular necessity, appeal is made not simplyto the truth of at least one further necessary truth, but to itsnecessity—this iswhat makes it atransmissionexplanation—and, if circularity is to be avoided,the explanans must be anew necessity which, if every necessity admits of atransmission explanation, calls for explanation in its turn in terms of afurthernecessity, and so on. It follows thatif transmission is theonly model for ex-plaining necessity, there can be no explanation of necessity in general—i.e. ofwhy there are any necessities at all. We cannot infer outright that there can beno explanation of necessity in general, since we lack any ground to assert therequisite minor premiss—that any explanation of necessity must be a trans-mission explanation. Indeed, although we have as yet no concrete alternativemodel, we have just observed that transmission explanations exhibit a feature—their essential play with the (transmitted)necessityof their premisses—whichit is not obvious that every candidate explanation of necessity must share. Noth-ing established so far shows that there cannot be explanations of the shape:▫p becauseq, where—while it may be necessary thatq—the necessity thatq,as distinct from its truth, does no distinctive explanatory work. In the absenceof reason to foreclose on the possibility of such alternative non-transmissiveexplanations of necessity, we cannot—without further argument—conclude thatno explanation of necessity in general is possible (even if it is granted thatthere can be no satisfactory explanation of necessity which appeals only tocontingencies22).

Non-transmissive explanations

Let us take stock. The upshot of my examination of Blackburn’sdilemma—if I am right—is that neither horn presents its would-be takers witha conclusive objection. The argument on the contingency horn suffers fromtwo weaknesses. First, it cannot run without the assumption that what is nec-essary is necessarily necessary, which effectively begs the question against aproponent of explanations of necessity in terms of conventions which mightnot have been adopted. It is true enough that there are other, more effective,objections to a conventionalist account of the source of necessity—those ofDummett and Quine appear to show that convention cannot be the mother ofall necessities, and another plausibly shows that it cannot give birth toany.But, second, even if directed against one who (seeks to explain necessities byreference to contingencies but who), unlike the conventionalist, accepts the S4principle, it requires the further assumption that she not only holds that▫pbecauseq, but is committed to the ‘would’-counterfactual:¬q ▫r ¬▫p, or at

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least to the ‘might’-counterfactual:¬qLr ¬▫p. But as we saw, even if somesuch assumption is defensible in regard to explanations of contingencies, thereare good reasons to deny that it holds for explanations of necessities. The ar-gument on the necessity horn appears effective only on the assumption thatany explanation ‘▫p becauseq’, where it is necessary thatq, must be atransmission-explanation.

Although I have not been able to see how to refurbish the second horn ofBlackburn’s dilemma, I have to confess that I am also quite unable to see howplausible, non-conventionalist, explanations of necessities, or of necessity ingeneral, in terms of contingencies might go. I shall therefore confine attention,in the remainder of this paper, to further exploration of the alternative ap-proach, which looks for an explanation of necessity whose explanans com-prises only propositions which are themselves necessarily true. As we have seen,it may be thought that no such explanation can possibly succeed, because itmust be either viciously circular or regressive. But I have suggested that thisfirst horn of his dilemma may be less sharp than it first appears—that whileany explanation of necessity on the transmission-model seems bound to leaveus with a “bad residual ‘must’ ”, as Blackburn puts it, it is at least not obviousthat every explanation of necessity must be of that kind. I want now to try toconsolidate that suggestion. At least some necessities, I shall claim, admit ofnon-transmissiveexplanations of the form ‘▫p becauseq’—explanations inwhich the explanans,q, is indeed necessary (at least if it is true, as it must be ifwe are to have an explanation at all), but in which what explains the necessityof the explanandum is notq’s necessity, but its truth simpliciter. If this claimcan be made good, it leads to a very simple and straightforward explanation ofnecessity in general—that is, why there are some necessarily true propositions:Suppose that▫p becauseq. Then▫p. Hence∃p▫p. Provided our explanationwhy ▫p is non-transmissive, there is no residual ‘must’.

The best way to see how some necessities might be explained non-transmissively is by examples. Here are two. Consider the propositions:

(1) Vixens are female foxes(2) The conjunction of two propositionsA andB is true only if A is true

andB is true

I take it that these propositions are not only true, but necessarily so. That is:

(3) ▫ Vixens are female foxes(4) ▫ The conjunction of two propositionsA andB is true only ifA is true

andB is true

are both true. Why is that? According to the conventionalist answer discussedearlier, the truth of (2) and, perhaps less directly, that of (1)—and thence thatof (3) and (4)—is secured by conventions which fix the meanings of their keyingredient words. In an earlier section, I upheld a version of an old and simple

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objection to the conventionalist theory, that it mistakes determinants of mean-ing for determinants of truth: conventions at best determine the content or truth-conditions of a (partially interpreted) sentence—even if they do so by stipulatingthat the sentence is to express a true proposition, the truth of that proposition isnot itself a matter for stipulation. I think that this objection not only highlightswhat is fundamentally wrong with conventionalism, but also helps point us inthe right direction. For if what makes (1) and (2) true, and necessarily so, isn’tfacts about our linguistic conventions—because these determine meaning ratherthan the truth of what is meant—what can do so, if not facts about what thesepropositions are about, i.e. a certain kind of animal and a certain function ofpropositions? This suggests some very simple answers to our questions about(3) and (4):

(5) ▫(Vixens are female foxes) because being a vixen justis, or consistsin, being a female fox.

(6) ▫(The conjunction of two propositionsA andB is true only ifA is trueandB is true) because conjunction justis that binary function of prop-ositions which is true iff both its arguments are true.

I claim that (5) and (6) do provide explanations of necessity, that in each casethe explanans is itself not just true but necessarily true, but that in neither casedoes the explanation given appeal to or otherwise presuppose their necessity inorder to explain that of the explananda (i.e. they are non-transmissive). I shalltry to say a little in defence of the last part of this claim shortly; first, I want tomake three preliminary, and mainly clarificatory, remarks.

(i) An explanation of this kind works—explains why it is necessary thatp—by claiming thatp’s truth is a consequence of, or is ensured by, the natureor identity-conditions of something involved that truth (e.g. what it is to be anobject 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-conditionsof things are necessary, in a strong or absolute sense. I think this is right, but Iam not clear what could be said to persuade anyone not already disposed toaccept it, beyond saying that if something has a certain nature, or such andsuch identity conditions,it—i.e. that very thing—could not not have that na-ture or identity-conditions. But—crucially—it seems to me that the claim thatexplanations like (5) and (6) succeed as explanations of necessity does not de-pend upon the correctness of this further claim.

(ii) The explanandum, in an explanation of the kind illustrated by (5) and(6), is why it is necessarythat p, not just why it is true. What allows us toregard what’s explained as the necessity ofp is that fact that the truth ofp isexplained is a special way, in terms of some fact about what it is to be ..., where[being] ... is integral to the proposition thatp. In this respect, our explanationsarestructurallyparallel to those offered by conventionalists, who likewise main-tain that it is necessary thatp whenp’s truth is explained in a special way—thecrucial difference being that whereas the conventionalist claims thatp’s truth is

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ensured by meaning-determining conventions, our explanations take it to beensured by the nature or identity-conditions of the thingsp is about.

(iii) My initial examples are naturally regarded as examples of conceptualor analytic necessities—but on the suggestion I am making, what does the ex-plaining is a fact about the nature or identity of a non-conceptual entity—aproperty, or a relation, or a function, rather than a concept—something belong-ing, in Fregean terms, to the realm of reference, rather than the realm of sense.One might think that in examples like these, the explanation could, and per-haps even should, take a different form—that they should run:

It is necessary that vixens are female foxes because theconcept vixenjustis theconcept female foxIt is necessary that the conjunction of two propositionsA and B is trueonly if A is true andB is true because theconceptof conjunctionjust is theconceptof a (or that) binary function of propositions which is true iff bothits arguments are true.

I don’t want to suggest that putting the explanations this way would be wrong.But I think it is preferable to cast them in the form I’ve chosen—or at leastthat it is desirable to notice the possibility of casting them in that form—for acouple of related reasons. One is that putting them in my preferred style en-ables us more readily to see how explanations of necessity of the same kindmay be given in cases in which it would be either obviously wrong or at leastquite implausible to attempt to see the necessity as having its source in (factsabout) the identity or nature ofconcepts—examples of what are sometimescalled metaphysical necessities, concerning natural kinds, individuals and iden-tity, like: Water is H2O, Gold is an element, George W. Bush is a man, Hes-perus is Phosphorus, etc. There is no plausibility in the suggestion that truthslike these owe their necessity to facts about concepts. The second is that evenin cases where it is (relatively) plausible to cast the explanation in terms offacts about the nature or identity of concepts, doing so—besides tending toobscure what may otherwise be seen as the underlying unity of a wide classof absolutely necessary truths—risks conflating considerations to do with thesourceof necessity with considerations concerning ourknowledgeof it. I donot want to deny that the conceptvixen, say, is no other than the conceptfe-male fox, or that the conceptconjunction is no other than the concept of acertain function. But it seems to me that such identity-relations among con-cepts have more to do with explaining how we know that vixens are femalefoxes, etc., than with explaining why it is necessary, and, more generally, withexplaining why some necessities are knowablea priori, while others are know-able onlya posteriori.

My proposed route past Blackburn’s dilemma claims that it overlooks aspecies of explanation in which necessities are explained by appeal to factsabout the nature or identity (-conditions) of the things they concern (what it is

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to be an object of a certain kind, or to be a certain property or relation or func-tion, etc.). It is plausible that these facts are themselves necessary, but—or so Iam claiming—the explanation does not exploit or rely on their necessity. Theflaw, on the first horn of the dilemma, lies with the assumption that if one ex-plains ‘▫p becauseq’, where it is necessary thatq, this must collapse into atransmissive explanation ‘▫p because▫q’. The key claim here, clearly, is thatin giving a non-transmissive explanation, the necessity of the explanans is notin any relevant way presupposed. It may be objected that, provided the secondhorn of the dilemma is sharp, we cannot avoid presupposing the necessity ofour explanans. For if the argument of the second horn is sound, there can be noexplanation of a necessity via a contingency, so that we cannot explain the ne-cessity that vixens are female foxes, say, by claiming that being a vixen just isbeing a female fox without presupposing that the latter too is a matter ofnecessity.

There is, as I have argued, reason to doubt that the argument of Black-burn’s second hornis sound, and I, at least, am not clear how it can be madesecure. But even granting that that could be done, it does not seem to me thatthe objection is good. For even if (one agrees that) an explanation ‘▫p becauseq’ of the kind suggested cannot be correct unless (one thinks that)q is itselfnecessary—so that the necessity of the explanans is in a sense presupposed—itdoes not follow that it is presupposed in a relevant way, i.e. in a way that com-promises the explanation. It would do so if the explanation worked by trans-mitting the necessity of the explanans to the explanandum, but that it does notdo. The objection simply misses this distinction or assumes that it marks nosignificant difference.

The concession that an explanation of the suggested kind cannot be cor-rect unless the explanans is itself necessary would by itself be fatal—the lastpoint notwithstanding—if the aim were to furnish areductiveexplanation, i.e.a general account of the source of necessity, or of how there can be such athing as necessity at all, which draws only upon premisses which are not them-selves true as a matter of necessity. But that was not the aim, and it is notclear how the demand for a reductive explanation could be justified. Reduc-tive explanation is, necessarily, a very special case. Puzzled over the existenceof truths or facts of a certain general kind—B-facts—we furnish an account oranalysis of key concepts involved in terms ofA-concepts, in the light of whichB-facts are reducible toA-facts, i.e. can be exhibited as logical consequencesof A-facts. Such an explanation shows that the initial appearance of a specialclass of (puzzling) facts is misleading—there areno B-facts over and aboveA-facts, or, if you like, thereare B-facts, but they are justA-facts presented ina novel guise. It is obvious that not every kind of fact can admit of reductiveexplanation, and that—unless irreducibility is simply equated with inexplica-bility or unintelligibility—reductive explanation cannot be an adequate modelof explanation in general. Any sensible would-be reductionist about facts, oralleged facts, of some given kind must concede the first point, even if she isdisposed to resist the second, and so must justify her insistence that facts of

314 / Bob Hale

that kind be somehow reduced to facts of some other kind, rather than justaccepted as irreducible. Quite apart from the specific points I’ve made againstBlackburn’s dilemma, it is hard to see how it can avoid relying on the assump-tion that modal facts—if there are such facts and if their existence is not tobe simply unintelligible—must be reductively explicable. That assumptioncannot be justified merely by adverting to the undisputed facts that we findnecessity puzzling and are hard pressed to explain its source or basis (in Black-burn’s words, “think there must ... be something whichmakesthem so, butwe cannot quite imagine or understand what this is”)—since so much is con-sistent with there being anon-reductive explanation. To the extent that theproposed dilemma rests upon the unargued premiss that only a reductive ex-planation could serve to render the existence of modal facts really intelligible,it is hard to see that it has any real force.

To be sure, philosophical puzzlement about a kind of fact need not be fu-eled by narrowly reductionist prejudices. A (somewhat) more liberal concep-tion might grant that facts of a given kind may be rendered intelligible withoutbenefit of reductive explanation, perhaps by charting relations of superveniencebetween them and facts of some other, arguably less problematic, kind. And—since we may seem no better placed to explain how modal facts might super-vene on the non-modal than we are to reduce the former to the latter—thismight seem to offer Blackburn a way to run his dilemma without reliance uponany specifically reductionist assumption. But it seems to me that so far fromenabling a re-instatement of the dilemma, any such move towards a more lib-eral conception of explanation—one which finds space for explanation basedupon supervenience relations—actually has quite the opposite tendency. Per-haps we can, in certain cases, alleviate puzzlement about the existence ofB-factsby observing that they supervene uponA-facts—that is, that, whileB-facts don’treduce toA-facts, there can be no variations inB-facts without matching vari-ations inA-facts. Precisely because facts about supervenience are themselves aspecies of modal facts—facts about necessary co-variation—there can be nogeneral explanation of modal facts in terms of supervenience. But the swordcuts both ways. Precisely because supervenience-explanations work through factsabout supervenience, there can be no such (correct) explanations unless thereare such facts.23 But the purpose of the dilemma was to wean us off a truth-conditional—i.e. fact stating—conception of judgements of necessity.

The account of the source of necessity I have proposed is, of course, di-ametrically opposed to the view—endorsed, albeit with tongue somewhat incheek, by Quine24—that necessity resides not in the things we talk about, butin our ways of talking about them. I am rejecting this view, even in regard tothe cases for which it is most plausible, i.e. those where we can express thetruth held to be necessary by means of a sentence which would be classifiedas analytic (at least by anyone prepared to employ that notion). In claimingthat certain necessities can be non-transmissively explained by appeal to factsabout what it is to be an object of a certain kind, or a certain property or

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relation or function, I am not only embracing a form of the essentialism whichQuine so vigorously opposed, but am also siding with those who view factsabout the essential natures of things as fundamental, in the sense that theyunderlie and explainde re necessities, rather than the other way about.25 Forthe purposes of my suggested explanation of necessity in general, it is enoughthat some necessities can be explained in this way. It is not necessary to claimthat all necessities can be so explained.26 I can afford to leave that questionopen, and will do so. On one view—consistent, so far as I can see, with ev-erything I have claimed here—there is a fundamental or base class of neces-sities which directly reflect and are to be explained by reference to the naturesof the things they concern, and a much larger class of necessities members ofwhich are to be explained, ultimately by reference to necessities in the baseclass, in accordance with the transmission model. This view would see theclass of necessities as a whole as structured in a way which leaves room fortransmissive explanations to play an indispensable role in accounting for non-basic necessities. Of course, there is a temptation to say that just because thenecessity of non-basic necessities is explained, ultimately, by reference to ne-cessities in the base class, with those necessities themselves being explainedin terms of facts about essences, all necessities have their source in such facts.This suggests an alternative view, on which there is, from anontological ormetaphysicalpoint of view, no distinction to be drawn between more or lessfundamental necessities—the class of necessities as a whole is flat and un-structured, and explanations of necessity in accordance with the transmissionmodel reflect no relations of dependence of some necessities on other morebasic ones, only theepistemologicaldependence of our recognition of somenecessities on that of others. Whilst each of these rival views has its attrac-tions, my own inclination is towards the former, partly because I suspect thatthe latter destabilises if taken as a wholly general account of necessity,27 andpartly because I think the fact—as it would be, if the former view is correct—that only alimited class of necessities admits ofnon-transmissiveexplanationmakes it easier to sustain the view that certain necessities asymmetrically de-pend upon facts about essences or natures and that the non-transmissive char-acter of such explanations is not undermined by the fact that truths aboutessences or natures are themselves necessary. But the development of thosethoughts, and the needed further defence of the proposal I have canvassedhere, must be left to another occasion.28

Notes

1. Dummett (1959), p.1692. The qualification is obviously needed, since without it, there would be no room for

unknown absolute necessities. For further explanation and some remarks on the en-suing complications, see Hale (1999), pp.24–5.

3. Or at least, not by any philosophy of necessity that accepts that there aretruthsabout what is necessary and what is not.

316 / Bob Hale

4. Blackburn (1986), p.119.5. op.cit. pp.120–16. loc.cit. p1217. As I think Blackburn must be assuming—it could, of course, be argued that the

best way to view conventionalism is precisely as a deflationary account, aimed lessat explaining necessity than at explaining it away.

8. The supposition is somewhat problematic, since it is at least open to question whetherendorsing an explanation ‘B becauseA’ invariably commits one to the correspond-ing counterfactual:¬A ▫r ¬B. I shall return to this point.

9. via the principle—sound on standard semantical accounts of counterfactuals—thatLA, A▫rB £ LB. FromL¬q and¬q ▫r ¬▫p, inferL¬▫p, i.e. ¬▫▫p.

10. I am not sure, but I suspect I may owe this point to Crispin Wright. Somethingvery close to it certainly came up in a discussion with him. It is independentlylikely that he should be credited with it, since he makes essentially the same pointin a very careful critical assessment, in Wright (1985), with which I have beenlong familiar, of Casimir Lewy’s arguments against the conventionalism advocatedby John Wisdom.

It is also worth remarking that the S4 principle is hardly one that Blackburnhimself can insist upon, since his own projectivist construal of judgements ofnecessity—lacking, as it does, the resources to make good sense of iterated modaloperators—almost certainly requires him to reject it. See Hale (1984) and also Wright(1987)

11. Quite apart from this point, there is bound, anyway, to be room to challenge theapplicability of the principle, when the explanation of necessities is in question—given that when▫B, A ▫rB will be vacuously true, no matter whatA may be, and¬A ▫r ¬B can be at best vacuously true (when¬A is impossible), otherwise false.

12. It was suggested to me, by Richard Gaskin, in discussion of an earlier version ofthis paper.

13. DefiningA Lr B, with David Lewis ((1973), p.2), as¬(A ▫r ¬B), the truth of¬A Lr ¬B requires that¬¬B be false, and so that¬B be true, at at least one ofthe nearest¬A worlds, so if there are any¬A worlds at all (i.e. ifL¬A), some ofthem will be¬B worlds (so thatL¬B).

14. Even that much is not obviously true, but I can, fortunately, set this tricky questionaside here.

15. U need not be finite, since among our finitely many stipulations, there may be stip-ulations guaranteeing the truth of infinitely many instances of some given form.But there is bound to be such ap, because there are infinitely many forms whoseinstances are necessary truths, and only finitely many of these can figure in ourstipulations.

16. The assumption is justified by the consideration given in the preceding note.17. As in Quine (1936), p.92.18. There are, of course, statements—most obviously, but not only, statements concern-

ing our own future actions—which we can make true, or indeed false, by acting orreacting in various ways, and whose truth-values are not independent of us. Butthat is perfectly consistent with the second claim. We may make them true (or false)by acting or reacting in ways required (or proscribed) by their already determinatetruth-conditions—we cannot make them true just by stipulating them to be so.

19. See Horwich (1997) or (1998), ch.6. Horwich’s proposal is to replace what he callsthe standard account, according to which, where “f ” is the definiens and “#f ” some

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sentence embedding it, we stipulate that the meaning of “f ” is to be the meaning“ f ” would need to have in order that “#f ” be true, by the view that the meaning “f ”has is the meaning constituted byregarding“#f ” as true (see (1998), p.138)—notethat ‘true’ as applied to sentences, for Horwich, means: ‘expresses a true proposi-tion’ (see (1998), p.133, fn.3). For some critical discussion of Horwich’s view, anddefence of a version of the standard account, see Hale and Wright (2000).

20. Equivalently, we may take it as the requirement to explain why∃p(▫p ∨ ▫¬p). Itis worth noting that no distinctively classical principles are required to establish theequivalence.

21. Of course, anyone who thinks that any explanation of a necessity must be a trans-mission explanation will deny that there is any such difference in strength—unavailability of a transmission explanation will, for him, entail inexplicability toutcourt.

22. That is, if the contingency horn of Blackburn’s would-be dilemma can be madesharp.

23. I rely here on the factive character of explanatory statements—i.e. that ‘q becausep’ can’t be true unless it is true thatp. Blackburn has argued—for example, in his(1984), p.182ff—that the existence of supervenience relations, such as are oftenthought to hold between matters of value and matters of natural fact, defies expla-nation if one takes a realist view of the supervening ‘facts’, but is more readilyexplicable on a non-realist or quasi-realist view. Although I’m sceptical about thisargument, I’m not directly concerned to dispute it here. My point concerns not theexplanation of supervenience relations, but the explanation of other facts in termsof such relations. It is simply that if one is to explain how there come to beB-factsby pointing out that they supervene onA-facts, one must accept that there are factsabout supervenience. If this is right, then it is not open to one who holds, as Black-burn does, that modal ‘facts’ are really no more than ‘projections’ of our attitudesor imaginative (in)capacities, to assign any explanatory role to superveniencerelations.

24. Cf. Quine (1953), where he writes: “Being necessarily or possibly thus and so is ingeneral not a trait of the object concerned, but depends on the manner of referringto the object” (p.148), and “Necessarygreaterness than 7 makes no sense as appliedto a number x; necessity attaches only to the connection between ‘x . 7’ and theparticular method ... of specifyingx.” (p.149).

25. I am thinking here, mainly, of David Wiggins and Kit Fine—see, especially, Wig-gins (1980) and Fine (1994). The position I defend here has obvious and consider-able affinities with that developed in Fine (1994). The main differences, perhaps,are (i) that whereas Fine operates with a broad distinction between conceptual andnon-conceptual necessities, with logical necessities as a subclass of the former, I donot treat any necessities as having their source, strictly speaking, in concepts (asdistinct from the things—including relations and functions—the relevant conceptsare concepts of ), and (ii) the class of necessities is probably more structured—witha limited subclass of fundamental necessities directly owed to the nature or identityof relevant objects, properties, etc., and others being indirectly, and dependently,necessary—on my view than on Fine’s. I discuss Fine’s view in Hale (1996), sec-tions 5–7; however, I am probably closer to his view than some remarks in thatdiscussion suggest.

26. —or even that all necessities can be explained.

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27. For some discussion of the kind of difficulty I have in mind here, see the article byme cited in note 25, and especially pp.102–14.

28. I thank Joseph Almog, John Benson, Jim Edwards, Richard Gaskin, Gary Kemp,Philp Percival, Adam Rieger, Peter Sullivan, Crispin Wright, audiences in Liver-pool and Delhi, and a group of Glasgow postgraduates including Ross Cameron,Paul McCallion, and Andrew McGonigal for helpful critical reactions to earlier ver-sions of this paper.

References

Simon Blackburn (1986) “Morals and Modals” in Graham Mcdonald & Crispin Wright, eds.Fact,Science & Morality: Essays on A.J.Ayer’s Language, Truth & LogicOxford: Blackwell,pp.119–41.

Michael Dummett (1959) “Wittgenstein’s Philosophy of Mathematics”, originally published inThePhilosophical ReviewVol.LXVIII (1959), pp.324–48 and reprinted in Dummett’sTruthand other enigmasLondon: Duckworth (1978), pp.166–85. Page references are to thisreprint.

Kit Fine (1994) “Essence and Modality” in James Tomberlin, ed.Philosophical Perspectives8,pp.1–16

Bob Hale (1984) “The Compleat Projectivist”Philosophical Quarterlyvol. 36, no.142, pp.65–84— (1996) “Absolute Necessities” in James Tomberlin, ed.Philosophical Perspectives10, pp.93–117— (1999) “On Some Arguments for the Necessity of Necessity”Mind vol.108, no. 429, pp.23–52Crispin Wright (2000) “Implicit Definition and the A Priori” in Paul Boghossian & Christopher

Peacocke, eds.New Essays on the A PrioriOxford: Clarendon Press (2000), pp.286–319,reprinted in Hale and Wright (2001), pp.117–50

— (2001)The Reason’s Proper Study: Essays towards a Neo-Fregean Philosophy of MathematicsOxford: Clarendon Press

Paul Horwich (1997) “Implicit Definition, Analytic Truth, and Apriori Knowledge”Nous 31,pp.423–40

— (1998)MeaningOxford: Clarendon PressDavid Lewis (1973)CounterfactualsOxford: Basil BlackwellW.V.Quine (1936) “Truth by Convention” in O.H.Lee, ed.Philosophical Essays for A.N.Whitehead

New York: Longmans; reprinted in Quine’sThe Ways of ParadoxRevised and enlargededn. Cambridge MA: Harvard University Press (1976). Page references are to this reprint.

— (1953) “Reference and Modality” inFrom a Logical Point of View(Second Edn, revised) NewYork and Evanston: Harper & Row (1963)

David Wiggins (1980)Sameness and SubstanceOxford: Basil Blackwell.Crispin Wright (1985) “In Defence of the Conventional Wisdom” in Ian Hacking, ed.Exercises in

analysis: essays by students of Casimir LewyCambridge : Cambridge University Press,pp.171–97

— (1987) “Realism, Anti-Realism, Irrealism and Quasi-Realism”Midwest Studies in Philosophy12 Minneapolis: University of Minnesota Press, pp.29–47

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