On Some Arguments for the Necessity of Necessity

On Some Arguments for the Necessity of Necessity Bob Hale Mind, New Series, Vol. 108, No. 429. (Jan., 1999), pp. 23-52. Stable URL: http://links.jstor.org/sici?sici=0026-4423%28199901%292%3A108%3A429%3C23%3AOSAFTN%3E2.0.CO%3B2-E Mind is currently published by Oxford University Press.

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On Some Arguments for the Necessity of Necessity BOB HALE

Must we believe in logical necessity? I examine an argument for an affirmative answer given by Ian McFetridge in his posthumously published paper "Logical Necessity: Some Issues", and explain why it fails, as it stands, to establish his conclusion. I contend, however, that McFetridge's argument can be effectively buttressed by drawing upon another argument aimed at establishing that we ought to believe that some propositions are logically necessary, given by Crispin Wright in his paper "Inventing Logical Necessity". My contention is that Wright's argument, whilst it likewise fails, as it stands, to establish the necessity of necessity, establishes enough to close off what appears to me to be the only effective-looking sceptical response to McFetridge's original argument. My paper falls into four principal parts. In the first, I expound McFetridge's argument and draw attention to the possibility of a certain type of sceptical counter to it. In the second, I begin a response to this sceptical move, taking it as far as I can without reliance upon argument of the kind given by Wright. Turning, then, to Wright's argument, I explain to what extent I think it is successful and seek to rebut some objections to the argument which, were they well-taken, would show that the argument cannot enjoy even the partial success I wish to claim for it. Finally, I return to my main theme and try to show, with the assistance of what I take to be solidly established by Wright's argument, that the sceptical response collapses.

Must we believe in logical necessity? An argument for an affirmative answer was given by Ian McFetridge in his posthumously published paper "Logical Necessity: Some Issues" (McFetridge 1990). In this paper, I expound and examine the argument I take McFetridge to have been propounding and explain why it fails, as it stands, to establish his conclusion. I believe, however, that it is possible to re-inforce McFetridge's argument so that it does work. To explain how this can be done, I need to examine another argument aimed at establishing that we ought to believe that some propositions are logically necessary-hence the plural in my title-given by Crispin Wright in his paper "Inventing Logical Necessity" (Wright 1986). My contention is that Wright's argument, whilst it likewise fails, as it stands, to establish the necessity of (belief in) necessity, establishes enough to close off what appears to me to be the only effective-looking sceptical response to McFetridge's original argument. Since my proposed buttressing of McFetridge's argument relies upon my claim that Wright's argument, while not completely successful, does secure a result very much to the purpose, I need to get clear precisely what that argument establishes. This requires a moderately Mind, Vol. 1 0 8 . 4 2 9 . January 1999

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lengthy digression from my main theme, in consequence of which this paper falls into four principal parts. In the first, I expound McFetridge's argument as I understand it and draw attention to the possibility of a certain type of sceptical counter to it. In the second, I begin what I hope will be an effective response to this sceptical move, taking it as far as I can without reliance upon arguments of the kind given by Wright. I turn, in the third part, to Wright's argument, explain to what extent I think it is successful and, in the course of doing so, seek to rebut some objections to the argument which, were they well-taken, would show that the argument cannot enjoy even the partial success I wish to claim for it. Finally, I return to my main theme and try to show, with the assistance of what I take to be solidly established by Wright's argument, that the sceptical response collapses.

1. McFetridge 's argument, and a sceptical counter to it The argument with which I shall be concerned comes at the very end of McFetridge's paper, and occupies little more than half of one page. As with many short but weighty arguments, however, a degree of preparation is needed to set the stage for it. The conclusion of the argument is that we must believe in logical necessity. But what is logical necessity? And what does belief in it amount to? McFetridge has much to say in the body of his paper about these questions, some of it essential to understanding and appreciating the force of his argument. The first question may naturally be taken to split into two by shift of emphasis: firstly, what is logical necessity? and second, what is logical necessity? I am quite sure that McFetridge did not see himself as providing a complete characterisation, much less a dejinition, either of the narrower notion of logical necessity or of the broader one of necessity; as we shall soon see, that does not greatly matter. Part of what he says on the first of these questions is that logical necessity is the strongest kind of necessity, in the sense, approximately, that "if it is logically necessary that p, then it is necessary that p in any other use of the notion of necessity there may be (physically, practically, etc.). But .. . the converse need not be the case. Something could be for example physically necessary without being logically necessary" (McFetridge 1990, p. 137).' This I McFetridgerightly, I think-regards the assumption that logical necessity is the strongest kind of necessity as central to a traditional conception of logical necessity. It is worth emphasising that McFetridge does not simply assume that logical necessity has this feature; he gives a very interesting argument for it (1 990, p. 138). This is one reason why he should not be seen as attempting to

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explanation (that i s o f "strongest") will not quite do as it stands, as McFetridge himself notes, because there are epistemic notions of possibility on which the contradictory of what is logically necessary may be epistemically possible. Thus on one view, one or other o f Goldbach's Conjecture and its negation is logically necessary, but whichever of them it is, the other is epistemically possible (that is roughly, true for all w e presently know).2 The explanation can, I think, readily be adjusted to accommodate this c ~ m p l i c a t i o n O . ~n e obvious reason why--even if there were not other, decisive, reasons against doing so--it would be unsatisfactory simply to deJine logical necessity as the strongest kind of necessity is that this would leave it quite obscure what logical necessity has to d o with logic. McFetridge's second main claim speaks to this concern. He writes: Deductive validity is the central topic of logic. S o if, as Aristotle and others have thought, to think of an argument as valid requires define logical necessity as the strongest kind of necessity. I think this argument,which I shall not go into here, is basically sound, but establishes a somewhat weaker conclusion than McFetridge claims. What the argument shows is not that logical necessity is the strongest kind of necessity-"the highest grade of necessity", as he puts i t - b u t that logical necessity is absolute, in the sense that if it is logically necessary that p, then there is no non-epistemic sense of possibility in which it is possible that not-p. The claim that a kind of necessity is absolute is equivalent to the claim that there is no stronger (non-epistemic) kind of necessity. To establish that logical necessity is the strongest kind of necessity would require showing that there cannot be more than one kind of absolute necessity. It is not easy to see how this might be shown; indeed, it is not clear that it is even true. At any rate there is a significant question that ought not to be foreclosed by simply defining logical necessity to be the strongest kind. See Hale (1996, pp. 93-1 17) for a discussion of an argument for the absoluteness of logical necessity very closely related McFetridge's, and of the philosophical significance of its conclusion. The example is, of course, doubly tendentious. Intuitionists and constructivists generally will not like it. Nor will those who agree that true number-theoretic propositions are necessary, but deny that the necessity can be properly regarded as logical. I leave readers of either persuasion to choose their own examples. Of course, no examples can be given that will commend themselves to those who deny the existence of logical necessity altogether, but that is obviously no cause for legitimate complaint. The matter is not entirely straightforward. It would be easy enough to amend the characterization to: "if it is logically necessary thatp, then it is necessary that p in any other non-epistemic use of the notion of necessity there may be". But such an amendment is in good standing only if we can satisfactorily mark off epistemic notions of necessity. The question is how that should be done. I think that the salient feature of epistemically modal notions is that they involve a relativity to time in one way or another (for example a relativity to our current state of information), and that the best way to frame the needed amendment may thus be to exclude all notions of necessity which involve such relativity.

us to deploy a notion of necessity, then that notion, if any, will deserve the label "logical" necessity. There will be a legitimate notion of "logical" necessity only if there is a notion of necessity which attaches to the claim, concerning a deductively valid argument, that if the premisses are true then so is the conclusion. (McFetridge 1990, p. 136) His thought, clearly-and, in my view, correctly-is that if there is any logical necessity at all, thee-or at least a-fundamental case of it lies in the connection between the premisses and conclusion of a valid argument. Accordingly, it will suffice to establish his main thesis to show that we ought to believe that at least some modes of inference are logically necessarily truth-preserving. That is why it is unnecessary, for his purposes, to provide a fully general characterization, or general definition, either of necessity in general or of logical necessity in particular. What he does need to do is to explain what it is to believe, of a given mode of inference, that it has that character. His explanation (which, in my view, displays something close to philosophical genius in its originality and simplicity) can be seen as the product of two entirely familiar and uncontroversial points, one about valid deductive inference and the other about subjunctive or counterfactual conditionals. The point about deductive inference is, in essence, the very first thing we all learn when we begin to study logic: that we must distinguish the question whether an argument is valid from the question whether its premisses are true, the validity, or otherwise, of the argument being independent of the truth-value(s) of the premiss(es). As McFetridge puts it, . .. the acceptability in an argument of some mode of inference is supposed to be quite independent of whether or not the overall premisses of the argument represent beliefs we have or mere suppositions we are making, as we put it, "for the sake of argument". Deductive inferences, then, are supposed to remain valid when they are applied to mere suppositions, and indeed regardless of what suppositions they are applied to, or are made in the course of the argument. (McFetridge 1990, p. 151) The point about counterfactual conditionals is likewise, at least in essence, simple and familiar enough: our assessment of a conditional "If it were (had been) the case that p, it would be (have been) the case that q" is typically, if not invariably, relative to or dependent upon various background suppositions concerning the truth-values of other statements. When we agree, for example, that if Simpson had not landed on the snow bridge, he would have fallen another 100 feet, probably to his death, we are envisaging Simpson's fall occurring in circumstances very much like those in which he actually fell, perhaps differing from the actual circumstances

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only in that he unluckily misses the snow bridge 20 feet down into the crevasse and in other respects consequent upon that difference. We are not envisaging a situation in which the crevasse bottoms out at 30 feet, or in which there is no crevasse there at all. Whilst the point itself is simply stated, an explanation of the significance McFetridge finds in it requires a few more words. He begins by reminding us of a familiar crux in the theory of counterfactual^.^ If we try saying that a counterfactual is true if there are suitable truths from which, in conjunction with its antecedent, its consequent may be inferred by means of a natural law, then we confront (as Goodman first pointed out) two problems. How is the class of natural laws to be demarcated? And how are we to circumscribe the class of "suitable" truths from which, together with the antecedent, the consequent is to be inferred? We cannot allow just any true statement to figure as a supplementary premiss, since the negation of the antecedent will be true, and from this together with the antecedent itself, any consequent whatever may be drawn.5 We would like to restrict the admissible supplementary premisses to those co-tenable with the antecedent, where that means: it is not the case that, were the antecedent true, they would be false. But that is hopelessly circular, if our goal is to explain the truth-conditions of counterfactuals. However, as McFetridge observes: ". . . this will not be a difficulty if we change priorities and try rather to understand reasoning from a supposition" (McFetridge 1990, p. 152). His thought, in part at least, is that if we relinquish the aim of explicating the truth-conditions of counterfactuals and raise instead questions about reasoning from suppositions, there will be no objectionable circularity involved in characterising co-tenable suppositions in this way. What specific questions about reasoning from suppositions did he have in mind? Although he does not raise them explicitly, I think it is clear that two of them could be put like this: Given a certain suppositio-that p--what modes of inference can be employed in reasoning under that supposition? and, for a given mode of inference M: Under what range of suppositions may M be employed? Modes of inference, here, need not be thought of as restricted to patterns of inference to which recognition is accorded in formal logic. We may think of (putative) natural laws, or lawlike general statements, a s o r as having associated with t h e w m o d e s of inference. Indeed, we may even view singular statements of various kinds (including, most obviously, "hat follows is my gloss on McFetridge (1990, pp. 151-3).

At least if the logic is classical, or even intuitionistic.

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conditionals) as being employable as such.6 Of course, precisely because such statements involve expressions which tie them to a particular subject matter, their use as principles of inference will be limited in a way that the use of modes of inference such as modusponens and modus tollens is not. But this is no objection to viewing them as employable as modes of inference. Limitations of applicability of the kind just noted are limitations of relevance. The reason why I cannot use, say, the generalization that copper conducts electricity in figuring out what will happen if I dig in lime at the rate of 100 grams per square metre where I plan to plant fritillaries, is not that the generalization cannot be relied upon under this supposition; it is simply that the generalization has no bearing on the question that interests me. Of greater interest here is a different kind of limitation upon the employability of a mode of inference, of which McFetridge reminds us. The range of suppositions under which a natural law, for example, may be employed as a principle of inference may be very large, but not so large that there is no supposition under which it may not properly be so used. In very many contexts, there is no objection to reasoning in accordance with the inverse square law, say, assuming that it can be brought to bear upon the matters under consideration. But if we are trying to work out the observational consequences of a rival physical theory in which gravitational attraction is governed by an inverse cube law, say, then obviously we ought not to make inferences employing the usual square law. Somewhat differently, and equally familiarly, it may be that there are known boundary conditions on the law, satisfaction of which can often be taken for granted; but under suppositions where their satisfaction is in question, so too is use of the law as a principle of inference. There may, then, be suppositions that can be entertained, in reasoning from or under which a mode of inference is not properly relied upon. We are now ready for McFetridge's answer to the question about the content of a belief in logical necessity, or more exactly the content of the belief that a certain mode of inference is logically necessarily truth-preserving (so that the corresponding conditional is true as a matter of logical necessity): I ... suggest that we treat as the manifestation of the belief that a mode of inference is logically necessarily truth-preserving, the preparedness to employ that mode of inference in reasoning from any set of suppositions whatsoever. Such a preparedness evinces Thinking of statements, whether lawlike or not, as usable as principles of inference need not, of course, involve any commitment to Ryle's notorious attempt to make out that they are merely "inference tickets" and not genuine true or false statements at all.

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the belief that, no matter what else was the case, the inferences would preserve truth. (McFetridge 1990, p. 153)7 To draw out, more explicitly than McFetridge himself does, the contrast he is implicitly making between natural and logical laws, we might-with a small, but so far as I can see, unobjectionable extension of Goodman's use of the term "co-tenable3'--call the range of suppositions under which the use of a mode of inference Mis not questionablifor the sorts of reason touched upon its co-tenability range. Part of McFetridge's thought is then that natural laws, employed as modes of inference, have typically a large, but not unrestricted, co-tenability range. And his earlier claim that logical necessity is the strongest kind of necessity can now be seen to require that there be no restrictions upon the co-tenability range of logical laws; the corresponding modes of inference would, as he puts it, preserve truth, no matter what else was the case, and so may legitimately be employed in reasoning from any set of suppositions whatsoever.$ That completes the stage-setting. We are ready for the argument itself. On McFetridge's account, to believe that a particular rule of inference R is logically necessarily truth-preserving is to believe that no matter what supposition s we may make, R is truth-preserving in reasoning under s . If we agree with him that the fundamental case of logical necessity, if there is such a thing at all, is that involved in valid infeience, belief in logical necessity centrally involves-though its content may not be exhausted Fairly clearly, McFetridge is not suggesting that the content of a belief in logical necessity can be explicated in wholly non-modal terms. He is, rather, proposing that it can be explained in terms of acceptance of a kind of generalized counterfactual. In a little more detail, and going somewhat beyond anything he says in his paper, the idea can be put like this. To believe that an inference p, so q" is necessarily truth-preserving is to believe the corresponding conditional "Ifp, then q" to be logically necessary, i.e. to believe that (p + q). If we write r~ for the counterfactual conditional, McFetridge's thought is that the content of this belief can be given by: Vs(s B O,-+9)). On any standard semantics for counterfactuals, he is clearly right, at least in the sense that the (logically) necessitated conditional and the corresponding generalized counterfactual are equivalent. If (p + q) is true, then p +q is true at all possible worlds, and hence at all nearests-worlds, whatever s may be, so that Vs(s m O,+ q)) is true. Conversely, if Vs(s rn (p + q)) is true, then p + q is true at all nearests-worlds, however s is chosen. But since s can be chosen any way we like, thismeans wemust havep +q trueat all worlds, that is (p + q ) . 06vio;sly the idea can be easily tdcover arbitrary beliefs in logical necessity, say by. explaining the belief that necessarily. .p as the belief that Vs(s m p). . A Quinean sceptic about necessity may baulk at the characterisation of logical laws as having a completely unrestricted co-tenability range. Such a thinker may agree that what are usually called logical laws have a more extensive co-tenability range than what are taken to be laws of nature, however hndamental. So much is merely an alternative expression of the view (to which he, with Quine, subscribes) that logical laws are more deeply entrenched in our overall system of beliefs than any others. But no statements (or principles of inference) are, he may protest, so deeply entrenched as to be unbudgeable (absolutely entrenched). No questions are here begged against this position. It is true enough that McFetridge's

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by-belief that there is at least one such rule. Accordingly, to deny that a particular rule R is logically necessarily truth-preserving is to hold that there is some suppositions such that, with s in play, we may not safely reason in accordance with R. And to disbelieve in the existence of logical necessity is to hold that for every rule R, there is some suppositions under which we may not safely employ R. McFetridge does not argue, concerning any particular rule, that it is logically necessarily truth-preserving. The argument he gives is designed to show, rather, that we must believe that some rules have this character. "To abandon the belief in logical necessity", he writes, "would be to believe that for every acceptable mode of inference M there is at least one proposition r (it might be a very long disjunction) such that it is illegitimate to employ M in an argument which makes the supposition that r" (McFetridge 1990, p. 53). McFetridge argues that this sceptical position is incoherent. Before we turn to details, we should pause briefly to note a point about the scope of his argument which is implicit in the remark last quoted. McFetridge equates "abandoning the belief in logical necessity" with believing the negation of what, on his proposal, is the content of the belief that at least some rules are logically necessarily truth-preserving, that is that for every rule, R, there is some supposition s such that, if it were the case that s, applications of R would not always preserve truth. The equation might be challenged. In particular, a sceptic about necessity might think he can decline to accept that there are any rules which would preserve truth no matter what else was the case, but decline also to endorse the contradictory belief that for any rule, there are or could be circumstances in which it would not preserve truth. This kind of sceptic might aptly be called an agnostic about necessity. On my construal of his argument-which seems clearly correct, given his gloss on what it is to abandon belief in logical necessity-McFetridge's target is the kind of sceptic who commits himself to the belief that there are no rules applications of which would be truth-preserving no matter what else was the case. This characterization pre-empts the use of what a thinker of this persuasion might othenvise view as a perfectly serviceable piece of vocabulary: there is, the Quinean may hold, no objection to describing logical laws as (logically) necessary, any more than there is to describing those of physics as (physically) necessary; provided that we do not fall into the error (as he supposes) of thinking that the necessity attaching to logical laws is any different in kind from that belonging to the laws of physics, or to any other statements deeply entrenched in our overall theory of nature. But whilst the Quinean may deplore the proposed usage, it begs no question against him: in particular, it is still open to him, for all that has been said thus far, to voice his doubt as the doubt that there are any logically necessarily truth-preserving modes of inference, in the sense proposed.

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kind of sceptic might, by contrast, be called an atheist about necessity. Thus if agnosticism is a tenable position, it would seem that McFetridge's argument, at least as I construe it, suffers from a serious limitation. Perhaps there is an alternative construal of his argument on which it does not suffer from this limitation, but if there is, I have not managed to get it into clear focus. In any case, given my construal of McFetridge's argument, the question must obviously be confronted: What should be said to the would-be agnostic about necessity? The answer, I think, depends on what kind of agnostic he would be. The crucial question concerns the source of his unwillingness to be committed either to the belief that some rules are necessarily truth-preserving or to the belief that no rules are. He may be unwilling because, whilst he takes himself fully to understand the altematives, he simply cannot see how to determine which should be accepted. This is straightforward agnosticism. But he may be unwilling because he doubts the coherence or intelligibility of the terms in which the alternatives are put, perhaps because, like Quine, he regards all modal talk as somehow defective and philosophically disreputable. The straightforward agnostic may, I think, be answered quite swiftly. This agnostic accepts the disjunction: Either for every rule R, there is some supposition s such that if it were the case that s, applications of R would not always preserve truth or there is at least one rule R which would preserve truth no matter what else were the case. If McFetridge's argument is good, it shows that the first disjunct must be rejected. So unless she can find fault with that argument, the straightforward agnostic should come off the fence and accept the other disjunct. Evidently a good answer to the more radical agnostic calls for many more words; more, certainly than I can spare here, where I can do no more than indicate the lines along which I think it should run. An answer might begin by pointing out that blanket rejection of the counterfactual conditional as simply unintelligible is not only desperate but clearly in tension with the plain fact that nearly everyone seems to understand it well e n ~ u g h so , ~that this agnostic had better have some very convincing reasons for thinking that our apparent understanding is illusory. If the agnostic is Quine himself, it would be in point to observe that, official professions to the contrary notwithstanding, he appears in practice to have no difficulty in making sense of talk of statements holding true "come what may" (note "may", not "does"), and that it does not appear possible to formulate the central theses of "Two dogmas .. ." (Quine 195 1) without using some modal word. But a fully satisfying answer would have to go Well enough; I do not claim, and do not need to claim, that we are in possession of unquestionably correct answers to all the hard questions which a philosopher might raise about the meaning, analysis or truth-conditions of counterfactual conditionals.

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deeper than such sniping and challenge the eminently questionable assumptions about the constraints on intelligibility on which this kind of scepticism (about modal and intensional notions in general) feeds.1° On my reading, then, McFetridge's target is the sceptic who commits himself to the belief that there are no rules applications of which would be truth-preserving no matter what else were the case. His argument to the incoherence of this runs as follows: Either (a) for some R, the sceptic holds that we know (and so can fully state) a suitable s or (b) he holds that whilst there is, for every R, such an s, in no case do we know it (and so in no case are we able fully to state it). (a) collapses: let R be a rule for which we can fully state the relevant supposition, which we shall denote s*. Then, where R is "From X infer A", let R* be the rule "From X, i s * infer A". By hypothesis, s* is a full statement of the circumstances in which R (allegedly) fails to preserve truth, so that R* is a counter-example to the sceptic's claim. So he must opt for (b). (b), however, is no good either, according to McFetridge, because its effect is to render (all) our rules of inference unusable. Let R be one of our rules, and let p be some supposition. To know whether we can rely upon R under the supposition that p, we have to ask: if it were the case that p, would R be truth-preserving? But answering this question will involve some reasoning, on the supposition thatp. What rules shall we use, in carrying out that piece of reasoning? Not R itself, obviously, since its reliability in the case in question is sub judice. But no other rule either. For to determine whether we can rely upon another rule, R', we have again to answer the question: were it the case that p , would R' be reliable? So we are stuck, or off on an infinite regress. As McFetridge has it ". .. the same problem will break out again, on the view that no rule is co-tenable with the universal range of suppositions" (McFetridge 1990, p. 154). Hence we must accept that there are some rules which are unrestrictedly reliable, in the sense that there are no suppositions under which they may fail to preserve truth. To this argument as it stands there is, it seems to me, a fairly obvious counter. Why can't the sceptic retort along these lines: Why do you assume that if I am to use a rule R in reasoning under the supposition thatp, I must first be able to ascertain whether R is, under that supposition, reliable? I don't have to do that. It is enough that I have no positive reason to doubt that R will fail under the supposition that p . l o Many of the essential points are made by H. P. Grice and P. F. Strawson (1956), succinctly and forcefully reiterated by Crispin Wright (1986, see especially pp. 18S90).

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This sceptic is claiming that it is not required, if we are to be entitled to employ a rule of inference R under the supposition that p , that we assure ourselves that, were it to be the case that p, rule R would (still) be truthpreserving. His attitude is that in employing R in reasoning under a supposition, we make a defeasible assumption to that effect-so long as that assumption remains undefeated, we have all the justification we need, and all the justification of which the case admits, for employing the rule. He believes in British justice: a rule is innocent until proven guilty.

2. A response to the sceptic begun The sceptic's reply is plausible, but is it cogent? I think it is fair to say that the position he seeks to occupy will constitute no genuine alternative (i.e. to the belief that there must be some absolutely or unrestrictedly valid rules) unless we can take his "falsificationist" methodology seriously. I shall try to show that we cannot do so. If the sceptic's professed falsificationist attitude towards rules of inference is not to be empty, it requires us to think that, for any one of our rules R which has thus far survived all attempts to envisage its failure, it is nevertheless conceivable that some circumstances p should obtain, in which R would recognisably fail to be reliable. Falsificationism without the possibility of recognisable falsification is not worthy of serious consideration. So let us consider, schematically, how this allegedly conceivable "falsification" of a rule could come about. For definiteness, and without loss of generality, let us suppose R to be the rule of Conjunction Elimination (&E). What is alleged to be conceivable is that circumstances p might obtain, of which we could recognise that, if they did obtain, this rule would fail to preserve truth. Here '3"will have to be a description of circumstances in which some particular conjunctive statement-which we may represent as "A and B"-would be true, and yet one of its conjunct* "B" say-would be false. The claim would be that since, by the rule in question, "B" can be inferred from "A and B", we can see that, were it to be the case thatp, this rule would fail. In performing this marvellous feat of recognition, we must accomplish several things which it will be worthwhile to list separately, obvious though they may be: (i) we have to recognise that, were it to be the case thatp, "A and B" would be true (ii) we have to recognise that, were it to be the case thatp, "B" would not be true

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(iii) we have to recognise that our rule of &E cannot be truth-preserving unless, were "A and B" to be true, "B" would be true also. There may be more,l but this will do to be going on with. Now, save in the case (which I suppose we may discount)12 where "p" is some description of an allegedly possible circumstance which expressly states that "A and B" is true, discharging subtask (i) will involve some reasoning. And the same goes, of course, for subtask (ii). And-though this point needs rather careful handling13-it goes for subtask (iii) as well. Let us, again without loss of generality, take the first case. Some reasoning has to go on here-to the conclusion, in this case, that were it the case thatp, "A and B" would be true-and any reasoning proceeds, either explicitly or implicitly, in accordance with some rule(s). But which rule(s)? Not &E. Of course, we cannot now argue, as McFetridge did, that that rule can't be employed because it is (still) subjudice; for according to the position we are now discussing, all rules are always to be regarded as innocent until proven guilty. They may, if you wish, be said to be, in that sense, sub judice, but they are not so in any way which renders their use objectionable. But we can rule out the use of &E none the less. First, we can see that it could not, in any case, be the only rule employed. For if ' I There surely is more. In particular, we should have to recognise, given the contents of the acts of recognition (iHiii), that were it to be the case thatp, &E would fail to preserve truth. This clearly involves an inference, from the contents of those acts as premisses. So even if it could be maintaine&as I do not believe it can b e t h a t no reasoning need be involved in (iHiii), it remains that the envisaged recognition of the failure, in the circumstance that p , of &E to preserve truth must involve some reasoning. I conjecture that this point holds quite generally: that whatever rule we are concerned with, and whatever the circumstances in which it allegedly fails to do its stuff, some reasoning will be required for the recognition that the rule would fail in those circumstances. l 2 I suppose we may discount this case because the bald supposition that "A&Bn is true but "B" false is, prima facie, incoherent. What is needed is a specification of some state of affairs which (a) appears to express a genuine possibility and (b) is such that we can be brought to see that, were it to obtain, "A & B" would be true but "B" false, or at least that it would be reasonable to accept the former but deny the latter. I 3 The need for care derives from the fact that it is crucial to avoid claiming that applying the rule of &E itself involves some further reasoning. What we are concerned with here is not an actual application of the rule but what is required if, in certain envisaged circumstances, the rule is to be truth-preserving. This is reasoning about the rule, not reasoning by it. Since the rule is general, and the claim that it is truth-preserving equally general-it is the claim that whenever a conjunction is true, so must be each of its conjuncts separately-a definite step is involved in appreciating that if the rule is truth-preserving, then if, in the circumstance that p, "A and B" would be true, then, in the circumstance thatp, " B would likewise be true. This seems to involve a step of Universal Quantifier Elimination at least, and surely also a step of modus ponens. Acknowledgment of this point does not commit us to the disastrous view that any application of &E has to be mediated by steps of Universal Quantifier Elimination, modus ponens, etc.

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it were to be the only rule employed, "p" would have to incorporate some statement of the form "'A and B' is true and C". This just takes us back to the case where "p" explicitly states that "A and B" is true (or as good as does so), and I think we can discount that at this stage: if we were prepared to swallow this as part of a description of circumstances in which &E would fail, it is quite unclear why we should baulk at a description which just ran "Suppose it were the case that 'A and B' is true but 'B' not true .. .". Second, and more importantly, there appears, in any case, to be a fatal instability involved in supposing that we might reason, under the supposition that p, by &E to the conclusion that &E would fail under that supposition; if we believed that the argument succeeded, we ought not to believe it. If this second claim is correct, then it follows, of course-given that some reasoning by some rule is requirebthat some rule other than &E must be used.I4 It might be objected that this second claim just overlooks the possibility that the reasoning in question could proceed by reductio ad absurdum, or something like it; that is, that we could, assuming for the sake of argument that &E is reliable in reasoning under the supposition that p , argue, by applying that rule under that supposition, to the conclusion that it isn't reliable in reasoning under that supposition, and then, appealing to the principle: A + -.A i- -.A, conclude that it is not reliable under that supposition. More generally, if we can show, by reasoning employing a proposed rule R, that R is not guaranteed to preserve truth, why shouldn't we conclude that R is not guaranteed truth-preserving? On the supposition that R is reliable, we can show that it is not; so it isn't. This objection, it seems to me, misses a crucial difference between regular applications of reductio ad absurdum (or the closely related principle that A + -.A t -.A) and the case with which we are concerned. When we argue by reductio to a conclusion -.A, what entitles us to our conclusion is that we have a valid argument from the supposition that A to a contradiction. Our (continuing) entitlement to the conclusion depends upon our continuing endorsement of that deduction of the contradiction from the initial supposition. Any well-founded doubt about the validity of that deduction would deprive us of our ground for accepting the conclusion. But this condition is precisely not met, in the present case. If our reasoning really did show that rule R is not reliable in reasoning under the supposition thatp, it would show-since we reasoned by R under the supposition that p--that that very piece of reasoning cannot be relied upon, thereby l 4 There are two separate points here. The first is that at any rate &E can't be the only rule involved, the second that it had better not be involved at all. Actually, it is the first point--that the reasoning must make use of some other r u l e ( s t t h a t is more important for the argument I am giving at the moment. But the second point (or, more accurately, a generalisation of it) will be important later.

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depriving us of our warrant for the conclusion that R is not reliable in reasoning under the supposition that p . Likewise with the conclusion -.A reached by an application ofA -+-.A t. -.A: our entitlement to the conclusion depends on our entitlement to the premiss A + -.A. Accepting -.A deprives us, in the present case (though not, of course, in general) of our ground for accepting A + 1A, and thereby removes our ground for accepting -.A.I5 We may take it, then, that some rule R other than &E is deployed in the reasoning of case (i). There is no need to speculate about what rule this could be; assuming the enterprise is coherent, that will clearly depend upon the exact character of the supposition thatp. But it does not matter, for our purposes, what rule R is. Nor can it be properly objected that, before our falsificationist may deploy R, he must first determine whether its use is good under the supposition that p; for his claim was precisely that we quite justifiably treat rules as good until they are revealed as bad. So provided that we have no positive reason to mistrust R, we can use it. But there's the rub. Granting, for argument's sake, that we have so far failed to locate any definite supposition under which R cannot be relied upon to preserve truth, what reason can the falsificationist have, in the present case, for taking it that it is &E, rather than R, that fails under the supposition that p? This looks like a fair question, since someone presented with an appearance that &E fails under the supposition thatp might elect to stand by &E, declare that something must have gone wrong, and point the finger of suspicion at R. So long as that is an option, we have no determinate falsification of &E (or of R, of course). Since it always will be an option, the whole idea that all rules of inference have merely default l 5 To guard against a possible misunderstanding, I should emphasize that the claim I make here does not mean that a rule of inference cannot be, in a certain sense, self-undermining. Consider, for example, the Crazy Rule: From X, infer A, which allows us to infer any conclusion we choose from any given set of premisses, including the null set. Since the Crazy Rule allows us to draw any conclusion we wish, we could apply it to obtain, in particular, the conclusion that the Crazy Rule is not truth-preserving. Thus if the Crazy Rule were truth-preserving, it would not be; so it is not. There is nothing wrong with this argument, which is a perfectly good reductio of the supposition that the Crazy Rule is truth-preserving. But this in no way conflicts with the claim made in the text about the impossibility of showing, by a reductio which uses R under the supposition thatp, that R cannot be relied upon if used under the supposition thatp. There is no conflict, because our reductio of the supposition that the Crazy Rule is sound does not use the Crazy Rule. What it relies upon is not an actual application of the Crazy Rule, but a claim-the correctness of which can be appreciated without reasoning by the Crazy Rule itself-about what, if the Crazy Rule were accepted, we could infer by its means. Someone who rejects the Crazy Rule need have no more difficulty is seeing that this claim is correct than an intuitionist logician has in seeing the correctness of claims about what inferences can be made by means of Double Negation Elimination.

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acceptability--can be treated as innocent until proven guilty-is a sham, because there is no such thing as proving a rule guilty. To this, it may be retorted: "That will indeed be a problem, if you suppose that hypotheses in general, and hypotheses about which rules are truth-preserving in particular, ought to be determinately falsifiable independently of any appeal to pragmatic considerations. But why should we not just agree that there will be various options open, and let pragmatic criteria decide which one to go for? So long as such considerations could favour the verdict that &E fails under the supposition that p, that is enough." Must McFetridge's bold venture bog down, short of its destination, in the swamps of holistic-pragmatic methodology? I do not believe so. To explain why not, I need to take a small digression, through the other argument for the necessity of necessity mentioned at the outset. If all goes well, we shall see that, whilst that argument (i.e. Wright's) does not, as it stands, establish that any statements must be accepted as necessarily true, it does provide the resources needed to break the present impasse.

3. Interlude- Wright 's anti-Quine argument 3.1 The argument

Wright's argument (1986, pp. 1 9 2 4 ) is directed against the radical form of empiricism advocated by Quine, according to which all statements whatever are subject to revision in response to recalcitrant experience, with revision in any particular case being a holistic affair essentially involving the application of broadly pragmatic considerations. It runs as follows. Let 8 be some theory we are putting to the test and L our underlying logic. We derive from 8, using L, various conditional statements whose antecedents describe observationally checkable initial conditions, and whose consequents specify observable predicted outcomes. Let I - + P be any such. A series of observations E will be recalcitrant (more fully, recalcitrant with respect to 8 + L) if it provides, or appears to provide, grounds to accept I but reject P, Quine accepts that faced with E, we should make some adjustment, but holds that we have many options open. These include: (1) Replacing 8 by some 8* differing from 8 by omission of one or more of the statements which figure as premisses in the L-derivation of I + P

(2) Rejecting one or more of the L-axioms or rules required for derivation of I + P from 8 (3) Denying that E does, after all, warrant acceptance of I and denial of P. Since, however, E's recalcitrance depends upon the conditional I + P being derivable, using L, from 8 , Quine must-given his claim that all statements have the status of no more than hypotheses, revisable in the face of recalcitrant experience-recognise a fourth option, viz. that of denying that E is, after all, recalcitrant (with respect to our currently accepted package of theory + logic), even if it warrants denial of I + P, by way of denying that this conditional is a consequence of that package, that is, to deny the statement which Wright labels:

8 i-,I+P In other words, that E is recalcitrant must be regarded by Quine as no more than a hypothesis, no less subject than any other hypotheses involved to assessment and possible rejection via the proper application of his pragmatic methodology. Wright's argument focuses on the question: under what circumstances will it be reasonable, by Quine's lights, to retain As in the case of other available responses, pragmatic considerations should be allowed to determine whether this is a good move. But how, Wright asks, is that to be determined? (W)

The decisive consideration ought to be, presumably, the degree of further recalcitrance with which the various alternative courses tend to be beset. But once the recalcitrance of experience becomes . . . a hypothetical matter, the question is transformed into: how often are the various alternative courses beset by sequences of experience which, according to the best hypothesis, are recalcitrant? And now, in order to decide whether recalcitrance is the best hypothesis, we have to consider how it tends to fare in pragmatic competition with the alternativesand the beckoning regress is evident. So the official Quinean answer to the question, when is it reasonable to believe a statement like W, is no answer. (Wright 1986, p. 193) Wright's thought, as I read it, may be elaborated as follows: Provided that it is not a merely hypothetical matter what the consequences (and in particular, the observationally checkable consequences) of a given combination of theory and logic 8 + L are, and provided that it is similarly not hypothetical what the consequences of alternatives 8* + L* are (where 8* and/or L* are variants on 8 and L), we may make comparative assessments of 8 + L and 8* + L* in regard to overall simplicity, explanatory power and whatever else we take to be included among the broadly pragmatic parameters against which we think competing theories should be evaluated. In particular-though the notion doubtless calls for further elucidation and

On Some A ~ g u m e n t s , f othe ~ ATecessip of H e c e s s i ~ 39

refinement-we can make some comparative assessment of the degrees of recalcitrance attaching to them; that is, roughly, the extent to which each clashes with observationally attested phenomena by yielding conditional predictions whose antecedents appear to be fulfilled, but whose consequents do not. That one of the competitors suffers from a higher degree of recalcitrance than the others will be a strong (though not necessarily decisive) consideration against it. But decisive or not, relative degree of recalcitrance will clearly be an essential consideration in pragmatically guided theory choice. Now suppose that we treat Wand its kin as mere hypotheses. The irnmediate effect, of course, is that any assessment of the relative merits of competitors 0 + L and 0* + L* which we may have made along the foregoing lines now takes on a provisional character, conditional upon certain claims like W which we are now viewing as hypotheses. Under different hypotheses about their observational consequences, a comparative assessment might go quite differently. Further, since E's recalcitrance with respect to our currently accepted combination 0 + L is contingent upon acceptance of we are confronted with the further option of retaining that combination by rejecting Wand thereby dissolving the appearance that E is after all recalcitrant. To make progress, we need to determine whether we should retain or jettison JX To do this, we must assess, inter alia, the relative degrees of recalcitrance involved in combinations respectively retaining and rejecting W. But any comparative assessment we may make will again be merely conditional, upon hypotheses about the consequences of the options under consideration. Since all such hypotheses are in the pragmatic melting pot along with all other statements, we have no progress-only regress. 3.2 Some doubts about the argurnent answered

As with any regress argument, doubts about the cogency of Wright's argument will focus on one or other of two questions: Do we really have a regress? and, if so: Is it vicious? Obviously I cannot anticipate and respond to every way in which a doubt of one kind or the other might be raised against Wright's argument. I shall therefore confine myself to what seem to me to be the most promising counter moves. Someone might concede that there is a regress, but deny that it is vicious on something like the following grounds: The regress would indeed be vicious, if the possibility of constructing it showed that Quine's pragmatic methodology [QPM] cannot be applied to determine what choice to make in any particular situation of prima facie recalcitrance. It would show this if it were true that, in order to decide what to do in any given case, Quine would have to resolve each of an infinite sequence of ques-

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tions of the form: Is such-and-such a hypothesis beset with a higher or lower degree of overall recalcitrance than the other options available? But QPM does not require us, when confronted with recalcitrant experiences, to consider all the possible options which are, in some sense, theoretically open. Given any particular theory 0, apparently confuted by an E which inclines us to accept I but reject P, where I -+P is derivable in L from 0, there will be very many ways of adjusting 0 to some 0* which does not have this consequence. Most of them, we simply won't have thought of. QPM doesn't require us to think out all these 0 * ~ v e ifn it were possible for us to do so (as it surely isn't)--and assess their relative degrees of recalcitrance. It is, rather, a methodology for deciding among already given options, viz. the ones which have actually occurred to us. If further, previously unthought of, variants on 0 are subsequently suggested, we should evaluate them (in comparison with options already considered), as and when they are proposed for consideration. The same applies to other options, such as adjusting our logic (whilst leaving 0 as it is), so that I -+ P is no longer derivable from 0, and equally-the crucial point here-to the option of leaving both 0 and our logic L in place, but rejecting W. One point should, I think, be conceded to the above: it would be quite unreasonable to require the Quinean, when faced with an apparently recalcitrant train of experience E, to review all possible adjustments to his currently accepted belief-system which would lead to an accommodation of E. Rather, as the objector says, QPM is a methodology for choosing from among some given (typically small, and necessarily finite) collection of actually proposed options. But this concession does not dispose of the difficulty. It is true that, once the concession is made, it cannot simply be assumed that the option of denying recalcitrance by denying some consequence hypothesis such as Wmust be among the range of options actually up for evaluation. But this does not matter. To see why it does not matter, suppose that Quine, who has hitherto subscribed to 0, but has just had recalcitrant experience E, is actually considering a few options of the type: adjust 0 to e*. And suppose that, after assessing the pros and cons, he plumps for one of them. In so doing, he implicitly claims that it is reasonable to move from 0 to this alternative. Since this would not be reasonable, if E were not recalcitrant with respect to 0, and that is so only upon the assumption he is taking it that acceptance of TV is reasonable. That is, his actual pragmatically guided choice of adjustment is really conditional upon Ws acceptance. The point here is not that there may be a further option in addition to those Quine actually considered, such that, if he had included it for consideration along with the others, he might have come to a different decil6

Something like this response was suggested by my colleague Philip Percival.

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sion. Nor is it that Quine cannot make his choice of adjustment without Jirst determining whether or not acceptance of W is reasonable. Of course, he cannot show that that choice is reasonable without doing that, but that is a further issue. Nothing stops him just assunzing that acceptance of W is reasonable. The crucial question concerns, rather, what it is for the assumption to be reasonable, by Quine's lights. Once claims about the consequences of a given combination of theory+logic (and hence statements about its attendant degree of overall recalcitrance) are treated as mere hypotheses, in the pragmatic melting pot along with the rest, there can no longer be any determinate truth about what degree of recalcitrance attaches to any theory+logic combination, with the upshot that there is no target for the pragmatist to aim at.' So whilst the argument, if it succeeds, does show that QPM is infeasible, this is not because applying it demands carrying through an infinite process (to the bitter non-end, as it were), but because it proves to be completely illusory that there is a determinate conception of what a successful adjustment of a belief-system would be, by pragmatic lights. Since the point is crucial, it is worth re-stating more fully. Let 0, be the option of keeping 0 + L and accommodating E by denying W, and let O,, . .. , 0,be the other options up for consideration. Then acceptance of W will be reasonable, ceteris paribus, provided that the degree of recalcitrance attaching to 0, exceeds that of at least one of the 0,.But what degree of recalcitrance attaches to 0 ,depends upon what its consequences are. This is not determined merely by the rejection of T.f/: O,(i.e. 8 + L + -, W)no more has determinate consequences on its own than does any of the other combinations of theory+logic under consideration. Its consequences have to be settled by appeal to some further statement which, for Quine, can only be a further hypothesis. But which hypothesis? Since, for different choices of H, we shall get different assessments of the degree of recalcitrance attaching to O,, + H, we should, presumably, take that H which minimizes recalcitrance. But the claim that some particular H (perhaps one among a small range of alternatives actually considered) minimizes recalcitrance is itself a further hypothesis again, which we may call H'. H' has its own range of competitors, viz. rival hypotheses about which of the hypotheses co-ordinate with H minimizes the degree of recalcitrance besetting 0,; Once again, we should, presumably (and as always, ceteris paribus), select that one among H' and its rivals which is l7

This, I take it, is the thought in or underlying Wright's remark: The moral is that it cannot be a correct account of tlze basis of our confidence in statements like Wthat belief-systems in which they figure enjoy relative success; if that were the right account of the matter, there could be no explaining the ~equisitenotion of 'success'.(Wright 1986, p. 193, emphasis mine)

42 Bob Hale

attended by the lowest degree of recalcitrance. But that in turn is a hypothetical matter, the relevant hypotheses being H and its competitors . . . . So long as the degree of recalcitrance attaching to hypotheses about consequence is itself held to be a further, hypothetical matter-as it must be, for Quine-there can be no stepping out of the regress. But unless we can step out, no determinate degree of recalcitrance attaches to any hypothesis, and in consequence of that, no definite content attaches to the assumption that it is (or isn't) reasonable to retain R18 So none attaches, either, to the supposition that some one among the original, limited range of options actually considered (i.e. O,, .. . ,Oh)is "pragmatically best". So the regress is vicious. It may be conceded that the crucial question concerns what it is for the assumption W to be reasonable, by Quine's lights, but denied that he need answer it in a way that generates the threatened regress. The contrary appearance, it may be claimed, results from giving a question-begging, non-pragmatic answer. The Quinean answer should be: any continued acceptance of any statement historically accepted is, by default, reasonable, provided adjustments have been made somewhere so as to defuse what was perceived as recalcitrance. The Quinean background to this answer is that the pragmatist starts from the status quo: a question of what it is reasonable to believe only arises for some specified array of options against the background of an extant web of belief. So judgements of reasonableness are always doubly relative: relative to a background of assumptions and relative to the options under consideration. The background of assumptions, being inherited from an earlier stage, is reasonable by default. So it is false that acceptance of W will be reasonable only if the degree of recalcitrance attaching to 0, exceeds that of at least one of the 0,.This answer would be correct only if rejecting W were among the options being explicitly considered. But if W belongs to the web of beliefs not considered for revision on this occasion, then its continued acceptance is reasonable by default.' This defence rests upon three claims:

(A) The question of what is reasonably believed only arises in regard to an explicitly mooted set of options concerning what adjustment (if any) we should make to our total belief-system, faced with some ostensibly recalcitrant experience, and then arises only against a background of historically accepted assumptions

(B) The background assumptions are themselves reasonable b,v default I s Hence Wright's remark (1986. p. 194) that the Quinean injunction (roughly: adjust so as to minimize recalcitrance) is "hopelessly impredicative". l 9 This line of defence was proposed by my colleague Jim Edwards.

On Some Argun~e~zts for the Necessity ofLVecessity 43

(C) There is no reason why H'should not be one of these background assumptions. It would suffice, to undercut the defence, to reject any one of them. I shall, however, argue against all three. First, a preliminary point.There is an obvious prinza facie inconsistency between (A) and (B). (A) seems to imply that no question can arise as to the reasonableness of background beliefs, while (B) declares those beliefs to be reasonable, which they can hardly be if the question of their reasonableness cannot even arise. I take it that this apparent inconsistency is to be resolved by drawing a distinction, in effect, between the way or sense in which the background beliefs are reasonable, on the one hand, and the reasonableness that is in question in relation to the options actually up for assessment in any given case. The former are default reasonable, and default reasonableness is not a matter of being what is best believed, where that is to be assessed by pragmatic criteria. But the preferred option. among those actually up for evaluation, is precisely the one which, among those options, comes out tops by pragapparent inconsistency is to be avoided by reading matic ~riteria.~"The (A) as claiming "The question of what is reasonably believed by pragnzatic criteria only arises in regard to an explicitly mooted set of options . . . and .. . only against a background of historically accepted assumptions". So, the proponent of this defence is not refusing my question: "What is it for the assumption of W to be reasonable, by Quine's lights?". Rather, he is answering it: "It is for it to be default reasonable (as glossed above)", with the aim of blocking the regress by denying that the correct answer to the question turns on what would be the result of applying pragmatic criteria. I begin with (B). Quine's defender sees that it will not do just to say, without qualification, that any continued acceptance ofjust any statement historically accepted is, by default, reasonable. Hence the qualification: ". . . provided adjustments have been made somewhere so as to defuse what was perceived as recalcitrance". But I do not see how even with the qualification, this can possibly be right, as it stands. Can it really be the case that retention of a previously accepted hypothesis is default reasonable, provided sonze adjustmentsno matter ~vhich-have been made to defuse what was perceived as recalcitrance? Suppose, in some previous situation of our being confronted with recalcitrance, we made a bad choice-bad, by Quinean pragmatic guidelines, I mean. (Nothing guarantees that we never misapply QPM.) We considered options involving rejecting some l o This assumes, but only for convenience, that pragmatic criteria will determine a unique best option. If there isn't (i.e. if there are two or more options between which pragmatic criteria do not decide), then we are free to choose from among the pragmatically best options, and whichever we choose will be reasonable.

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statement S, but plumped for some other option and retained S. In fact, we miscalculated; perhaps we over-estimated the overall degree of recalcitrance attaching to the former options, or under-estimated that attaching to the option we went for, or perhaps both. We should have dumped S, but we didn't. But we did make an adjustment somewhere so as to defuse what was perceived as recalcitrance, so the proviso is met. Does that make our retention of historically accepted S reasonable by default? How can the mere fact of historical acceptance make it default reasonable to continue to accept a statement which we should have previously rejected, and would have rejected, had we not misapplied Quine's pragmatic directives? In real life, we have to live with our mistakes, no doubt (at least to the extent that we cannot undo them), but this does not make them any less mistaken. In one way, indeed, the comparison with practical affairs is unduly favourable, for there we are often justified in saying: "We've gone down that road now, it's too late to turn back and we must just stick to it and make the best of a bad job"-but we are never, so far as I can see, justified in saying anything really analogous to this when it comes to theory. The incorrectness of (A) is a straightforward corollary of the objection to (B). Ifthe argument against (B) is sound, then there can be cases in which the continued acceptance of at least some of our historically accepted background beliefs is reasonable, if at all, not by default but only because, when the option of rejecting them was previously entertained, they were-by the proper application of pragmatic criteria-reasonably retained. So the argument against (B) shows that there can be cases in which at least some of our historically accepted background beliefs are subject to assessment as reasonable or not bypragmatic criteria. So, even when (A) is qualified as I have said it should be, it is false, because it implies that the question of reasonableness, by pragmatic criteria, can arise only for options explicitly up for assessment, and not for any background beliefs. It is true, I think, that this argument only gets us the limited conclusion that the question of reasonableness-by-pragmatic-criteria (briefly, p-reasonableness) can arise for certain of our background beliefs, those for which the option of rejection has been previously considered. That is, it does not follow that the question ofp-reasonableness must arise for all background beliefs. So someone might, for all that I have argued thus far, insist on the minimum concession, and say: "Very well, I admit that the question ofp-reasonableness is properly raised in relation to those of our background beliefs for which the option of rejection has, as a matter of historical fact, been actually entertained. But as for the rest of our background beliefs, the question ofp-reasonableness (as distinct from reasonableness simplicter) is out of order and they are simply default reasonable". This cannot but appear a pretty desperate move, if only

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because it seems just plain wrong to make the admissibility of a question turn on whether that question has, as it happens, been previously asked. The argument against (B) shows that a question as to thep-reasonableness of some statement can be in good order even when none of the options explicitly proposed explicitly raises that question. What justifies putting so much weight on the sheer contingency whether the question of a statement's p-reasonableness has previously been raised? Even this desperate move will, in any case, be futile unless we accept claim (C), that W may be counted among the background assumptions. As against this, I think that in any reasonable sense of "historically accepted background assumption", (C) should be rejected. Wis, recall, a quite specific statement about one particular (putative) consequence of 8 + L-the statement I -+ P. Prior to the occurrence of the putatively recalcitrant E, we need never have considered V! So if the force of the claim that Wis one of our historically accepted assumptions is that we have previously explicitly endorsed that very statement, it will be an entirely contingent matter whether it holds true. I do not need to deny that cases are possible in which the claim, so understood, does in fact hold, since I am free to stipulate that I am concerned with cases in which it does not. If the claim is rather that, while Wmay not be among those statements we have previously explicitly considered and endorsed, it is nevertheless to be reckoned among our background assumptions because it is implied by others which have been explicitly endorsed, then it is regressive. Its effect is to shift attention to the further consequence claim-"W is a consequence of such-and-such explicitly endorsed background assumptions"-which gives rise, at one remove, to difficulties precisely analogous to those afflicting V! 3.3 What does Wright's argument establish?

The immediate, negative, conclusion Wright draws from his argument is: the reasonableness, or otherwise, of judgements of recalcitrance must be exempted from appraisal via the Quinean methodology. And that must go for the ingredients in such judgements, including statements like W . . . . If we are supremely certain of the truth of at least some such statements, the source of this certainty simply cannot be accounted for by Quine's generalized holistic model. The very coherence of the model requires an account of a different sort. (Wright 1986, p. 194) I think that Wright's argument entitles him to this conclusion, but I shall not, here anyway, attempt to furnish further support for that claim, beyond

'

what I have tried to provide in the preceding sub-section.* Wright himself makes three further claims. First, he goes on, more positively, to claim: The right account is ... the obvious one: such statements, or at least an important subclass of them, admit of totally convincing prooJ We must, I suggest, take seriously the idea of proof, as a theoretically uncontaminated source of rational belief, (Wright 1986, p. 194) By this last phrase, Wright pretty clearly means that the capacity of a suitable proof to warrant belief is independent of any claim that is properly subjected to empirical appraisal. Thus his first further claim is tantamount to the thesis that suitable proofs can yield a priori knowledge, or at least a priori warranted belief.22A little later, Wright makes it plain that he thinks the argument entitles him to claim: First, . . . that we do possess some sort of concept of logical necessity. Second, the correct account of the basis for the majority of judgements of logical necessity which we are prepared to make must make reference to the utterly convincing, self-contained character of suitable proofs. (Wright 1986, p. 195) However, as McFetridge observed (1990, p. 149) and as Wright now accepts, there is a step here-from the immediate negative conclusion and the first further claim Wright makes to the claims just quoted-which appears quite unwarranted. It is one thing to accept that we have to regard a proof as establishing a statement (such as a JV)in a way that is not subject to holistic appraisal, and quite another to hold that a statement thus established is necessary. What the argument given shows, at best, is that we have to accept such statements as established, by suitable proofs, as true; nothing in the argument demands their acceptance as necessarily There is also, it should be observed, a g a p t h o u g h , in my view, a much smaller one-between Wright's immediate conclusion and his first hrther claim. The immediate conclusion, as first enunciated, is that "the reasonableness, or otherwise, of judgements of recalcitrance must be exempted 2 1 McFetridge, though dissatisfied with Wright's argument as an argument for necessify, agrees that it establishes at least this much (cf. McFetridge 1990, pp. 148-9). Indeed, he thinks it establishes Wright's first further claim. 2 2 That this is a fair gloss on Wright's actual words seems clear from, inter alia, his critical remarks about "the incoherence of Quine's attempt to 'Duhemise' the traditional realm of the a priori" (cf. Wright 1986, p. 194). 2 3 I think it is possible to bridge the gap-in effect, between a priority and necessity-which McFetridge identifies in Wright's argument. But to go into that here would make too great a distraction from present concerns, so I shall leave the matter for another occasion. McFetridge diagnosed the gap as resulting from "an inadequacy in Wright's account of what it is to regard a statement as logically necessa~y",and that his own argument for the necessity of necessity takes its start from what he regards as a better account of it (cf. McFetridge 1990, p. 150).

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from appraisal via the Quinean methodology. And that must go for the ingredients in such judgements, including statements like W' (Wright 1986, p. 194). If we read the antecedent of the conditional which comes soon after (viz. "If we are supremely certain of the truth of at least some such statements, the source of this certainty simply cannot be accounted for by Quine's generalised holistic model") as hypothesising rational (as distinct from merely unshakeable, but perhaps dogmatic) conviction, then the conditional itself, even if not quite a mere restatement in other words of the immediate conclusion, is at least a corollary of it. The first further claim, viz. "The right account is .. . the obvious one: such statements, or at least an important subclass of them, admit of totally convincing proof' (Wright 1986, p. 194), evidently presupposes that we are rationally warranted in accepting judgements of recalcitrance (along with such statements as W, on which they depend). I think there can be little doubt that Wright intended his intermediate claim-"The very coherence of the model requires an account of a different sort"-to imply that that presupposition is fulfilled. But that begs the question whether the coherence of the model requires such an account at all. What if some recalcitrant Quinean agrees that statements of the kind in question must be exempted from appraisal via the Quinean methodology but denies that their acceptance can be rationally justified in any other way? What should we say to him? The first thing that should be said is that this would represent a very significant concession, no hint of which is to be found in "Two dogmas . . .". Not only does it involve abandoning any aspiration that the Quinean methodology might be quite generally applicable; it is directly inconsistent with one of the most prominent, and most controversial, claims of that article: viz. that every statement whatever is subject to revision in face of recalcitrant experience. Further, once it is conceded that certain kinds of statement must be exempted from the scope of that claim, and from assessment in the only terms Quine allows, an explanation is called for. Clearly it would be insufficient explanation for the Quinean to retort that such statements must be exempted from holistic empirical appraisal, because the attempt so to appraise them causes that methodology to crash. So much is obvious enough, but not to the purpose. What is wanted is an explanation of the principle on which exceptions are to be recognised. It is quite unclear that, much less how, the Quinean can provide one without giving the game away, and unclear. too, how he could fight his corner against an opponent whose less straight-jacketed conception of the various means by which statements of different kinds may be rationally supported enables her to explain both why holistic empirical appraisal is appropriate to a large but limited range of statements and why it is not

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Bob Hale

properly applied to others (including many whose acceptance can be warranted a priori by deductive reasoning). It would be rash to hope that these brief remarks might do more than indicate one direction in which opposition to Quinean epistemological holism might be developed. Important as the issue is, I shall not pursue it further here. Instead, I want to return to McFetridge7sargument and, with some assistance from the argument of this section, complete my response to the sceptical challenge we left it facing. As will soon appear, the use to which I mean to put Wright's argument does not depend upon making good Wright's positive thesis that statements of logical consequence (and, in particular, statements like W)can be warranted a priori.

4. The i-esponse to the sceptic completed The sceptic with whom we were grappling in 52 sought to brush aside the objection that his professed falsificationism about rules of inference was fraudulent-because he could give no content to the idea of determinate falsification of any such rule-by recourse to the idea that he need not be committed to holding that there can be any such thing as determinate falsification indeperjdently of broadlypragmatic considerations. Once such considerations are allowed a role in the decision whether to regard a rule as falsified, he claims, his position can be seen to be a perfectly workable one. It should be clear that this move takes us into what is by now familiar territory. To continue with the example of a supposed falsification of &E, the suggestion is that in the choice between the options before u s - o f holding that &E fails under the supposition thatp, and of holding that it is not &E but R which then f a i l s w e should be guided by consideration of which option does best across a range of pragmatic desiderata such as simplicity, economy, overall theoretical unity, etc. Whatever other desiderata are to be considered here, one of them will certainly, and crucially, be minimization of avoidable recalcitrance. Thus whatever other desiderata are to be taken into account, and however they are to be weighted together, one question we shall certainly face concerns the relative degrees of recalcitrance besetting the options before us. Answering this question will require us to carry out some reasoning, to ascertain the consequences, respectively, of taking &E to be unreliable under the supposition that p, and of taking R to be unreliable. There arises, accordingly, a question about what rules of inference are to be employed in this reasoning. And now, it seems clear, the sceptic faces a fresh dilemma. Either this

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reasoning will involve the application of rules other than &E and R, or it won't. Either way, the sceptic is in trouble. Suppose, first, that it does, and let R l , . . . ,R,,,be the other rules involved. Then there will be open to us, in addition to the options of concluding that &E isn't invariably truth-preserving, and of concluding that R isn't, the further options of drawing the conclusion that R , is not invariably truthpreserving (and in particular, fails under the supposition thatp). or that R, isn't, or .. . or that R, isn't. If we ask: "Why should we stand by these other rules, and see the shortcoming as lying with one of &E and R?", the answer, in general terns, has to be that pragmatic considerations favour this course. But that answer will once again rest upon an assessment of the degrees of recalcitrance besetting these various options, including the options of modifying or scrapping one or more of the R,. This assessment will involve some reasoning .. . . We are at the start of a familiar regress. Suppose instead that only &E and R are involved in the deduction of the consequences of rejecting &E. There are three cases to consider, according as (a) both &E and R are employed, (b) only &E is used, or (c) only R is used. Cases (a) and (b) can be dismissed right away; for the reason already given. the case for rejecting &E will be fatally unstable if it relies on reasoning in which &E itself is essentially involved. This leaves just case (c). But this is no good; if R is used, it will always remain an option to deny that the alleged consequences of rejecting &E really are so, by way of rejecting R. I conclude that the proposed falsificationist methodology, if applied to rules of inference quite generally (including those we might othenvise view as necessarily truth-preserving), cannot be sustained. It collapses because it fails to give real content to the idea that rules can be selectively falsified. The attempt to mitigate that failure by appealing to the idea that pragmatic considerations might guide selective retention and rejection of rules breaks down because it leads into a vicious infinite regress of essentially the same character as that disclosed by Wright's argument. That completes the main argument of this paper. To close, I would like to return to a limitation on the argument noted earlier and venture a suggestion about how it might be lifted. The limitation is that the argument at best establishes a general conclusion: we must believe that some rules of inference are logically necessarily truth-preserving. In and of itself, the argument does not tell us, concerning any particular rules, that we must believe them to be necessarily truth-preserving. Is there a way in which we might advance to some conclusions of that stronger fosm? I think there may be, a way that makes another connection with Wright's argument, or more precisely, with the first of the further claims Wright makes, to the effect that some statements must be reckoned not only to lie beyond the

scope of holistic empirical appraisal but to be capable of being warrantedly believed a priori. If, as I think we should, we accept Wright's second claim, then there is clearly a good deal more to be said about what the range of a priori warrantable statements comprises. Wright's argument singles out a particular kind of statement as thus assertible, namely: statements about logical consequence. As Wright is careful to point out, our entitlement to assert such statements of consequence does not depend upon acceptance of the specific underlying logic L to which they refer. The point may be simply illustrated by reference to a classical derivation o f p from ? ~ p : ?--P assn (1) P 1, DNE 1 (2) An intuitionist, or other logician who rejects DNE, is not thereby prevented from recognising that this is a classically correct derivation, establishing that l i p t ,p. One might be tempted to infer from this that a priori recognition of the correctness of consequence statements is entirely independent of acceptance of any logical principles whatever. But this temptation should be resisted, as can quickly be seen by considering how, even if we are intuitionists, we might convince ourselves of the correctness of the foregoing consequence claim on the basis of the short derivation above. In recognizing its sole ingredient step as classically correct, we reason as follows: 1

the correIn classical logic, if a statement is of the form "-A", sponding statement A may be inferred from it as sole premiss, with the conclusion depending upon whatever assumptions the premiss depends upon. The statement "lip" is of the form "11A", and depends upon assumption 1. So, classically, the statement p may be inferred from that premiss, depending upon the same assumption. This inference is, of course, entirely neutral with respect to acceptance1 rejection of the principle of double negation elimination. But it is an inference, by modusponens, and it would seem to follow that to the extent that i- ,p, we must be warwe can be warranted, a priori, in asserting that ranted a priori in our acceptance of that principle of inference. This raises an obvious, and obviously interesting question, namely: just what logical principles are included in the minimal kit, as it were, needed for (a priori) appreciation of the correctness of claims about logical consequence (i.e. claims about what follows from what, relative to a pre-assigned underlying logic)? I think it is clear that this minimal kit will include at least (some form of) modus ponens (or some principle equivalent to it, at least in the presence of other minimal principles), and that it will also include some principle(s) of quantificational inference (such as YE). What else it

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may include is a question I must leave for another occasion.24Meanwhile, I offer a tempting, albeit tentative, conclusion: whatever the exact contents of the collection of rules of inference we should believe to be logically necessarily truth-preserving, it will include, at least, modusponens and universal quantifier elimination (or their equivalents), together, of course, with any other rules indirectly justifiable by their use.25

Department of Philosophy The University of Glasgow Glasgow GI2 8QQ Scotland email: [email protected]. uk

BOB HALE

REFERENCES Grice, H. P. and Strawson, P. F. 1956: "In Defense of a Dogma". The Philosophical Review, 65, pp. 141-58. Hale, Bob 1996: "Absolute Necessities", in James Tomberlin (ed.) Philosophical Perspectives, 10, Metaphysics, pp. 93-1 17. McFetridge, I. G. 1990: "Logical Necessity: Some Issues", in John Haldane and Roger Scruton (eds.) Logical Necessity & Other Essays Aristotelian Society Series, vol. 11, pp. 135-541 Quine, W. V. 0 . 1951: "Two Dogmas of Empiricism" in his From a Logical Point of View, Harvard: Harvard University Press, 1953. Originally published in The Philosophical Review 60, pp. 2 M 3 . 2 4 An interesting question is whether the minimal kit will include some princip l e ( ~ )governing negation, and if so, which. It seems to me that, even if no negation principles are needed for the ratification of consequence claims of the kind we're concerned with, acceptance of the principle of non-contradiction may be integral to operation with the idea that recalcitrance obliges us to make some revision in our overall corpus of accepted statements. This will carry with it acceptance of some form of the principle of ren'llctio ad absurdurn-at least a weak, non-classical version, i.e. from X, A i- B, togethre with I: A 17B, infer X, Y t 4 - a n d therewith, in the presence of modusponens, acceptance of the principle of modus tollens, i.e. from X k A+B, together with Yk 7B, infer X , Y t -4. 2 5 Earlier versions of this paper, or parts of it, were presented at a conference on Modality held in Bled, Slovenia, at a seminar in Cambridge and at the XXth World Congress of Philosophy in Boston. I am grateful to my audiences on these occasions, as I am to my colleagues Jim Edwards, Philip Percival and Adam Rieger. I am particularly indebted to Crispin Wright for many hours of helpful discussion and much constructive criticism. I should also like to give special thanks to an anonymous referee for Mind, whose patient, careful and perceptive comments have helped me to write a paper which, though appreciably longer than the one originally submitted, is at least in other respects greatly improved. Much of the work was carried out during my tenure of a British Academy Research Readership; I am grateful to the Academy for its generous support.

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Wright, Crispin 1986: "Inventing Logical Necessity" in Jeremy Butterfield (ed.) Latzguage, Mind and Logic. Cambridge: Cambridge University Press 1986, pp. 187-209.

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In Defense of a Dogma H. P. Grice; P. F. Strawson The Philosophical Review, Vol. 65, No. 2. (Apr., 1956), pp. 141-158. Stable URL: http://links.jstor.org/sici?sici=0031-8108%28195604%2965%3A2%3C141%3AIDOAD%3E2.0.CO%3B2-E

References In Defense of a Dogma H. P. Grice; P. F. Strawson The Philosophical Review, Vol. 65, No. 2. (Apr., 1956), pp. 141-158. Stable URL: http://links.jstor.org/sici?sici=0031-8108%28195604%2965%3A2%3C141%3AIDOAD%3E2.0.CO%3B2-E

Main Trends in Recent Philosophy: Two Dogmas of Empiricism W. V. Quine The Philosophical Review, Vol. 60, No. 1. (Jan., 1951), pp. 20-43. Stable URL: http://links.jstor.org/sici?sici=0031-8108%28195101%2960%3A1%3C20%3AMTIRPT%3E2.0.CO%3B2-P

NOTE: The reference numbering from the original has been maintained in this citation list.