Necessity and Externality Quassim Cassam Mind, New Series, Vol. 95, No. 380. (Oct., 1986), pp. 446-464. Stable URL: http://links.jstor.org/sici?sici=0026-4423%28198610%292%3A95%3A380%3C446%3ANAE%3E2.0.CO%3B2-5 Mind is currently published by Oxford University Press.
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Necessity and Externality QUASSIM CASSAM In philosophical thinking about modality, it is tempting to suppose that one will ultimately be compelled to choose between two seemingly unattractive options. T h e first would be to embrace a 'Platonist' or 'realist' conception of necessity, according to which necessary truths are to be accounted for not in terms of what is to be found in the natural world, but rather in terms of what is to be found in what is thought of as a non-natural realm. T h e proposal is that necessary or conceptual truths record or reflect relations between abstract entities such as universals, such entities being understood to be non-spatio-temporal. As Strawson puts it, universals, if they exist at all, are objects which are 'incorrigibly abstract7,1and it is of non-natural relations between such incorrigibly abstract entities that we are alleged by the realist conception to be speaking whenever. we speak of 'conceptual' necessities. If realism is found unattractive, then it would seem that the only alternative would be to accept a form of modal scepticism and to regard the practice of modalizing as embodying some form of metaphysical error. According to those whose positions might be described as 'naturalistic' or 'anthropocentric7, the temptation to suppose that realism and scepticism constitute the only two options is one which ought to be resisted, for there is a third option that escapes most of the objections to the other two. T h e naturalist recoils from the realist's picture both because the very idea of an incorrigibly abstract object is one which he finds problematic, and because the appeal to universals is apparently devoid of explanatory force. Instead, the naturalist proposes an account of necessity which makes no appeal to anything outside nature, but insists that his position does not amount to a form of modal scepticism, for a naturalistic conception of necessity is quite compatible with the hardness of the conceptual 'must'. I t is with this last claim that I shall be primarily concerned in this paper. If it can be shown that naturalism does not so much give an account of the hardness of the conceptual 'must' as undermine it, there will be reason to doubt that naturalism constitutes a genuine third option. According to one exaggeratedly reductionist form of naturalism, socalled 'necessary propositions' rest upon nothing more than the way in which we choose to use words or find it natural to use words, so that necessary propositions turn out to mean the same as, or to be equivalent in content to, propositions about the use of words. Even if this view is rejected, as it surely must be, there remain other forms of the doctrine which retain Cf. p. 7 of 'Universals', Midwest Studies in Philosophy, 1979. I am much indebted to this paper.
Necessity and Externality
447
the view that necessary propositions reflect or depend upon our use of words, without holding that they can be reduced to propositions about our use of words. Thus, the modal status of a proposition such as 'justification must be public' might be held to rest upon no more than the fact that we are not prepared to call something a 'justification' unless we are also prepared to call it 'public'. This need not be a matter of explicit decision, and there may indeed be causal-naturalistic explanations for the fact that we use words in this way rather than any other; nevertheless, if we had used words differently, we would not have been guilty of the kind of 'factual' error which the realist would choose to speak of in this situation. For if it is intelligible to speak of necessary propositions as 'true'and such talk may not be unproblematic-their truth does not consist in their successfully mirroring the structure of an independent abstract reality. Rather, they depend for their truth upon what might loosely be described as 'linguistic' conventions. Thus, it would seem that whereas for the realist a counterfactual such as (R) 'If we had found it natural to give the sum of 7 and 5 as 1 3 , 7 5 would still be 12' will be deemed true, since nothing said or believed by human beings can alter objective relations between universals, the naturalist will apparently lack the resources to have (R) and counterfactuals like it come out as true. T h e naturalist who denies that human natural history constitutes the subject-matter of necessary propositions, but who is nevertheless committed to regarding (R)-type counterfactuals as false, might be labelled a 'weak naturalist' or 'weak dependence theorist'. If necessary propositions are said to reflect or to depend upon the use of words, then it would seem that the naturalist could have no basis for insisting that even if we had found it natural to use words differently, things would still 'really' be as stated in the consequents of the (R)-type counterfactuals, for given the limited resources at the naturalist's disposal, it is unclear what the force of such a 'really' could be. I t might be thought that the later Wittgenstein was a weak dependence theorist, or at any rate, that his conception of necessity bore a more or less strong family resemblance to what here has been characterized as 'weak' naturalism. T h e suggestion that necessary propositions reflect the use of words finds its echo in Wittgenstein's claim that so-called necessary propositions are 'grammatical sentence^',^ taken in conjunction with his view that grammar describes the use of words in l a n g ~ a g eWittgenstein's .~ opposition to strong reductionism is evident in his insistence that 'the propositions "Human beings believe that twice two is four" and "Twice two
+
Thus Moore reports Wittgenstein as having held that 'sentences, which would commonly be said to express necessary propositions, are in fact merely expressing rules of grammar.' See 'Wittgenstein's Lectures in 1930-33' in G. E. Moore, PhilosophicalPapers, London, Allen and Unwin, 1959, pp. 267-8. Cf. Wittgenstein, Philosophical Grammar, trans. A. J . Kenny, Oxford, Blackwell, 1975, $8, and Remarks on the Foundations of Mathematics, 3rd edn., trans. G. E. M. Anscombe, Oxford, Blackwell, 1978,1-128. See Wittgenstein, Philosophical Grammar, $23.
448 Quassim Cassam
is four" do not mean the same'.4 At the same time, the weak naturalist's insistence that the truth of necessary propositions does not consist in their corresponding to an independent modal reality is paralleled by Wittgenstein's claim that grammar is, in a certain sense, a r b i t r a r ~Consequently .~ what is called 'possible' is what is called 'necessary' is also arbitrary, a point that Wittgenstein makes more than once in his later writing^.^ T h e sense in which grammar is arbitrary is not that the formation of concepts cannot be explained by facts of nature, but rather that grammar cannot be justified by reference to the structure of reality.' One set of grammatical conventions may be more convenient than another, but not 'truer' than another. Indeed, Wittgenstein was frequently tempted by the view that so-called necessary propositions or 'grammatical' sentences are nonsensical or merely pseudopropositions that are incapable of being literally true, and that strictly speaking say n ~ t h i n gWhat, . ~ then, of (R)-type counterfactuals? I t must be confessed that Wittgenstein's position on this matter is by no means unequivocal. This is a point to which I shall return in due course. At present, it will suffice to note, without further comment, the following passage from the second part of the Philosophical Investigations: But what would this mean: 'Even though everybody believed that twice two was five it would still be four'?-For what would it be like for everybody to believe that?-Well, I could imagine, for instance, that people had a different calculus, or a technique which we should not call 'calculating'. But would it be wrong? (Is a coronation wrong? To beings different from ourselves it might look extremely Does the weak dependence theorist provide an adequate account of necessity? Is his view combinable with the 'hardness' of the logical or conceptual 'must'? It is possible to imagine someone objecting as follows: it is required by our concept of necessity that what is genuinely necessary must be so independently of what humans regard as necessary. What is necessary is not, as it were, up to us. T o say this is not merely to say that necessity, properly so-called, cannot be a product of explicit decision on our part, for given certain very general facts of nature, including facts about human nature, we may not have had any choice in the matter. I t is also to say that what is genuinely necessary must be so independently of what we find it natural to say or believe. What such independence involves is well captured by counterfactuals of the form (R); any theory that claims to have done justice to our conception of the hardness of the conceptual 'must' must at the Philosophical Investigations, trans. G. E. M. Anscombe, Oxford, Blackwell, 1978, p. 226. On the arbitrariness of 'grammar', see P. M. S. Hacker, Insight and Illusion, Oxford, Oxford University Press, 1972, chap. 6, and P. M. S. Hacker and G. P. Baker, 'Critical Notice of Wittgenstein's Philosophical Grammar', Mind, 1976. See Philosophical Grammar, for example, $82. Philosophical Investigations, p. 230.
As reported by Moore, 'Wittgenstein's Lectures in 1930-33', p. 268.
Philosophical Investigations, pp. 226-7.
'
Necessity and Externality
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very least have the resources to have such counterfactuals come out as true. I t is precisely because the weak dependence theorist fails to produce this outcome that he cannot be deemed to have proposed a satisfactory account of necessity. T h e objector's sense of disappointment has been splendidly expressed by Stanley Cavell, in connection with what he takes to be Wittgenstein's position: [Wittgenstein's] philosophy provides, one might say, an anthropological . . . view of necessity; and that can be disappointing; as if it is not really necessity which he has given an anthropological view of. . . 'But something can be necessary whatever we happen to take as, or believe to be, necessary'. But that only says that we have a (the) concept of necessity-for it is part of the meaning of that concept that the thing called necessary is beyond our control.1° If Cavell has accurately characterized our conception of necessity, then it will come as no surprise that weak naturalism should sometimes have been regarded as inducing a form of intellectual vertigo, a feeling that the ground has been removed from under our feet. What is more, naturalism begins to look uncomfortably like a form of scepticism. I t is not so much the case that Cavell's Wittgenstein has provided an anthropocentric treatment of necessity as that he has undermined our ordinary conception. I t is because weak dependence theory is apparently unable to meet the Cavellian demand concerning (R)-type counterfactuals that it is legitimately seen as amounting to a form of scepticism about necessity. I t is by no means beyond dispute, however, that the naturalist is in no position to endorse (R)-type counterfactuals. According to what Blackburn has characterized as 'quasi-realism',ll there is a way of registering the desired verdicts on the counterfactuals without incurring what the naturalist would regard as unwelcome ontological commitments, for quasirealism requires no more than a natural world and patterns of reaction to it. T h e quasi-realist begins with an account of the nature of ethical judgement and subsequently invokes elements of the apparatus developed in this context in his account of the nature of modal discourse. T h e point of departure for the quasi-realist's account of ethical judgement is an examination of expressive theories of judgement in general, theories that attempt to explain the practice of judging in a certain way by regarding such judgements as expressive, and contrasting them with judgements that have genuine truth conditions. Expressive theories, thus conceived, will face the task of explaining the fact'that in ethical discourse we appear to be making judgements with genuine truth conditions, and one way of responding to this challenge would be to embrace the Humean notion of projection: thus, 'we project an attitude or habit or other commitment onto the world, when we speak and think as though there were a property of things which our lo
S. Cavell, The Claim of Reason, Oxford, Clarendon Press, 1979, pp. I 18-19.
" For an account of 'quasi-realism', see Blackburn, Spreading the Word, Oxford, Clarendon Press, 1984, chaps. 5-7.
450 Quassim Cassam
sayings describe . . .'I2 Quasi-realism may then be defined as the project of establishing the legitimacy of these projections, of demonstrating the propriety of projected predicates. One of the quasi-realist's central concerns is to resist the suggestion that he is committed to some form of mind-dependence thesis. His response to this charge arises naturally out of his response to the 'Frege point', which objects to expressive theories on the grounds that the predicates with which such theories are concerned may figure in sentences that may in turn occur in unasserted contexts, in which no attitude is evinced when the sentence is uttered. Conditional contexts are a case in point, and so it would seem that some account is called for of what is involved -in placing commitments in such contexts. T h e quasi-realist's account of this matter begins with the observation that an important feature of moral sensibilities is the way in which they pair attitudes. We endorse certain pairings but not others. Conditionals, it is claimed, are a device enabling us to endorse certain pairings; it appears, therefore, that conditionals themselves express a moral point of view. T h e next stage in the quasi-realist enterprise concerns the notion of truth. I t might be thought that expressive theories deny moral remarks genuine truth conditions, but if 'it is true that. . .' can also be given a quasi-realist explanation, then given the quasi-realist's account of why it should be natural to treat expressions of attitudes as if they are ordinary judgements, we might simply regard ourselves as having constructed a notion of moral truth. The quasi-realist is now in a position to tackle the mind-dependence thesis, as expressed by conditionals such as (DE) 'if we had different sentiments, it would be right to kick dogs.' T h e quasi-realist's account of conditionals generally gives him a swift way with this. On the quasi-realist reading, (DE) endorses a sensibility which allows information about what people feel to dictate its attitude to kicking dogs, but such a sensibility quite evidently does not merit our endorsement. Indeed, if the quasi-realist has established his right to the notion of truth, (DE) actually comes out as false. Correspondingly, a conditional such as (RE) 'if we had different sentiments, it would still be wrong to kick dogs' comes out as true, for a sensibility which regards the rightness or wrongness of kicking dogs as independent of what people feel is one that does merit our approval. T o speak of moral facts altering or disappearing as a consequence of changes in our sentiments would be to endorse counterfactuals such as (DE), and, as Blackburn has written, 'it will not be part of good moralizing to do that.'13 The quasi-realist's response to the thesis of mind dependence might be challenged. His response rests upon the assumption that an individual who claims that 'if we had different sentiments, it would be right to kick dogs' could only be construed as endorsing a certain kind of moral sensibility, lZ
Spreading the Word, pp. 170- I .
l3
Ibid., p. 219,n. 2 1 .
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45 I
but it might be argued that this is not the only possible view of the matter. An alternative reading of the conditional comes to mind as soon as a distinction is drawn between two kinds of attitude that might be adopted towards ethical discourse and practice. T h e first might variously be described as 'internal' or 'subjective' or 'participant', and the second as 'external' or 'objective' or 'detached'. T h e former perspective takes the existing framework of ethical discussion for granted, and is quite happy to view ethical judgements as true or false in a mind-independent way. This is not, however, the only possible perspective, for in moments of philosophical reflection, one might find oneself stepping back and considering the standing of ethical discourse as a whole. If,-in such reflective moments, one concludes-as the projectivist concludes-that in order to explain the practice of moralizing it is necessary to refer only to the natural properties of things and natural reactions to them, the thought may seem inescapable that values are the 'children of our sentiments' in a sense that the quasirealist is committed to viewing as problematic. If, in speaking as zf there were a property of things that our sayings describe, we are projecting human emotions, sentiments, and attitudes, then, from this detached perspective, the thought will be tempting that had our attitudes been different, moral facts would also have been different. This would be a philosophical thought, and one way of giving expression to such philosophical disquiet would be in terms of counterfactuals such as those formulated and dismissed by the quasi-realist. If such counterfactuals are formulated in this kind of 'externalist', even sceptical, philosophical spirit, the quasi-realist's response will immediately seem misdirected. T h e objection was that such counterfactuals endorse 'defective' sensibilities, but the point of the externalist use of the counterfactuals is not to endorse any particular kind of moral sensibility-the conditional expresses a philosophical rather than an 'internal' moral point of view. T h e difficulty is that, as the quasi-realist would have it, the very same counterfactual may be used either to endorse a certain kind of moral sensibility, or to make the externalist point. Whilst the defectiveness of a conditional such as 'if we had different sentiments, it would be right to kick dogs', understood internally, is all too evident, the very same sentence may be used as a somewhat colourful way of making the externalist point, and if this use is to be dismissed as defective or illegitimate, such a dismissal has yet to be argued for successfully. A feature of the quasi-realist's position that is even more problematic is the suggestion that his treatment of ethical discourse might have some bearing upon the problem of necessary truth, for immediately after outlining his response to the problematic conditionals in the context of ethics, Blackburn adds that 'Similarly, it would have been true that 7 5 = 12, whatever we had thought about it.'14 What the quasi-realist appears to have in mind is the following: it has often been noted that we find it extremely
+
l4
Ibid.
452 Quassim Cassam
difficult to imagine or make sense of alternative arithmetics, but it has seemed unclear what philosophical significance ought to be attached to such imaginative limitations. The quasi-realist's elegant proposal is that we dignzfy truths the contraries of which we cannot imagine as 'necessary'. In so doing, we express our own mental attitude, but may resist the charge that such truths, being reflections of our imaginative limitations, are not "really" necessary, for the quasi-realist will 'deny that anything more can be meant by the real modal status of a proposition, than can be understood by seeing it as a projection of our (best) attitude of comprehension or imagination towards it.'15 AS for conditionals such as (D), 'if we had had different attitudes, it would have been true that 7 5 = 13', these are claimed to be false. Correspondingly, conditionals of the form (R) are claimed to be true. It is far from clear that the quasi-realist has earned the right to adopt such a view of the problematic counterfactuals. It has been noted that the quasirealist sees conditionals with evaluative components as themselves expressing a moral point of view, as endorsing certain kinds of moral sensibility, and it is this which permits him to dismiss as false conditionals such as 'if we had thought otherwise, it would have been permissible to kick dogs', for such conditionals endorse the 'wrong kind of sensibility'. It appears, however, that this view of the matter can be of no help in the mathematical case, for there is a striking disanalogy between the two cases that rules out the possibility of generalizing the quasi-realist's response to the 'ethical' conditionals. For it is surely not being suggested that a conditional such as 'if we had thought differently, twice two would be five' is an expression of a moral point of view, an endorsement of a defective moral sensibility. But in what, in that case, does the defectiveness of the conditional consist? If the conditional is to be dismissed as defective or false, it is surely not on the same grounds as those on which the 'moral' counterfactuals are dismissed as false, for the two cases are quite different. As it stands, the unargued leap from one area to the other seems quite mysterious. Indeed, whilst there is at least a moderately clear sense in which someone who asserted the dependenceexpressing 'moral' conditional might be guilty of bad moralizing, and in which he might therefore be deemed to have said something false, it is much less clear how someone who asserted the corresponding conditional concerning mathematics might be thought to be guilty of bad mathematical practice. It may be far more natural to view such an assertion as attempting to make a philosophical point, parallel to what was earlier characterized as the externalist point about ethics; not a point internal to the practice of mathematics but a point about mathematics, albeit one that practising mathematicians might find it difficult to accept. What is more, it may be insisted that it is a point implied by the quasi-realist's own account. For given the thesis that necessary truths give expression to our own imaginative limitations, it is surely legitimate to suppose that we might have had
+
l5
Spreading the Word, p. 217.
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different imaginative limitations, and to suppose that in these circumstances the modal facts would have been different. T h e controversial conditional (D) may simply be a striking way of making this point, and if this is so, the quasi-realist's abrupt dismissal ofit seems unwarranted. T h e position at which we have arrived, then, is this: it was demanded earlier that any plausible theory of necessity should result in the truth of (R)-type counterfactuals, for our concept of necessity demands that what is called 'necessary' should be 'beyond our control', and without (R)-counterfactuals coming out as true, it would appear that this Cavellian demand is not met. T h e quasi-realist's attempts at providing the naturalist with a way of registering the desired verdicts on the -problematic conditionals have yet to be shown to be convincing, and so nothing has yet been done to diminish the feeling of disappointment or vertigo to which the anthropocentric conception gives rise. T h e feeling remains that the ground has been removed from under our feet. This might, however, prompt the following rejoinder: it is an error, it might be suggested, to view the weak dependence theorist's position as a form of scepticism about necessity, for this kind of naturalist does not regard himself as denying anything to which clear sense can be attached. Even if, prior to philosophical reflection, we find ourselves tempted by what the realist says, the point of the naturalist's discussion is to suggest that closer scrutiny reveals the realist view as unintelligible, and thus not a genuine rival. T h e cure for our vertigo is to have this pointed out to us; we will be less disappointed with what Cave11 calls the 'anthropological' view of necessity if we can be persuaded that realism is unintelligible. I t is no objection to a philosophical position that it fails to match up to an incoherent standard. But what reason is there to believe that the realist position is one of which no sense can be made? At this point the naturalist might borrow the following line of thought from a paper of McDowell's: according to this line of thought, the realist or Platonist view is closely associated with the notions of 'externality' or 'independence'. T h e idea of necessary truths transcending the reactions and responses of participants in our practices is just the idea that the relation of our mathematical thought and language to the reality it characterizes can be contemplated . . . from sideways on-from a standpoint independent of all the human activities and reactions that locate those practices in our 'whirl of organism'; and that it would be recognizable from the sideways perspective that a given move is correct at a given point in the practice.16
Given the connection between realism and this notion of an independent perspective, it would seem that the way to discredit the former is to discredit the latter; if the idea of a 'sideways on' perspective can be shown to be dubious, the credibility of realism will be threatened. As for the dubiousness l6 McDowell, 'Non-Cognitivism and Rule-Following', in S. Holtzman and C. Leich, eds., Wittgenstein: to Follow a Rule, London: Routledge & Kegan Paul, 1981,p. 150.
454 Quassim Cassam
of the notion of externality, this, apparently, is easily demonstrated, for the perspective envisaged by realism is one that we cannot occupy, and 'it is only because we confusedly think that we can that we think we can make any sense of it.'17 Freed from this misconception, the hardness of the logical 'must' no longer seems threatened by anthropocentrism. T h e logical 'must' is indeed hard; it is simply a matter of our not misidentifying the perspective from which the necessity is discernible. T h e necessity is indeed only discernible from within the midst of our logical and mathematical practices, and is in this sense dependent upon our 'whirl of organism'. Any feeling of having been short-changed by this ought to be dispelled by the realization that the demand that necessity also be discernible from the 'sideways' perspective is an unintelligible one, for the simple reason that the very idea of such a perspective is not one of which we can make any sense. T h e realist will not be satisfied by this. T h e difficulty, it will be recalled, was that it was demanded that necessity, properly so-called, should not be dependent upon what we say or believe. One way of expressing this demand would be to present it as the demand that any plausible account of necessity should be in a position to have (R)-type counterfactuals come out as true. T h e response to the realist was then to attempt to show that these are not demands to which sense can be attached. T h e naturalist, following McDowell, concerned himself with the notion of externality, but it is not altogether clear what the connection is between the discussion of externality and realism as here characterized. Is it really plausible to suggest that the demand that (R)-counterfactuals come out as true is literally unintelligible? And if this is the claim, how does the attack upon the notion of externality help establish it? Perhaps what the weak dependence theorist has in mind is the following: the point is not to suggest that the Cavellian conception of necessity is incoherent, or that the demand that (R)-counterfactuals come out as true is illegitimate. T h e point may be to suggest that this is a demand that can be met on the naturalist's perspective, and it is only tempting to suppose that he is committed to denying this on the assumption of some notion of an external perspective. Consider the situation in which we are immersed in our practices. From the internal, participant standpoint, there is no temptation to suppose that the truth of '7 + 5 = 12'is in any way within human control. Practising mathematicians do not doubt that in carrying out proofs it is compulsory to proceed in a certain manner and they may well show no hesitation in endorsing (R)-counterfactuals. From an internal standpoint, then, everything seems to be in order; the realist's demands are apparently met, so whence his dissatisfaction? Presumably, he has formed some conception of an external perspective, from which his demands appear not to be met; from this supposed point of view, he will claim, zf what the naturalist says is true, then mathematics would turn out to be dependent upon us, and the realist will claim that this would represent the ultimate l7
McDowell, op. cit., p. 150.
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truth of the matter, whatever we may be inclined to say whilst immersed in the practice of mathematics. I t should now be clear what the significance is of the attack upon the notion of an independent perspective, for from the internal standpoint there is no temptation to deny any of the realist's demands. I t is only from the supposed external standpoint that doubts arise, and so a swift way of removing such doubts would be to demonstrate the unintelligibility of the perspective in which they originate. I t is by no means beyond dispute, however, that the coherent formulation of the realist's anxiety presupposes a deeply problematic conception of externality. What is required is something relatively modest, which may be characterized as follows: it is true, it will be-conceded, that there is much that we take for granted whilst immersed in our ordinary practices. In carrying out proofs we find it overwhelmingly natural to proceed in a certain manner, and these dispositions are generally reinforced by training. T h e result is that from a participant standpoint, the logical 'must' will seem as hard as one could possibly wish; we do not doubt that it is compulsory to proceed in a certain manner, independently of what human beings say or believe. Nevertheless, we are also given to periods of philosophical reflection, during which the attempt is made to stand back from our practices and view them with a certain coolness and detachment. T o be sure, there are limits to this process of detachment, but it would be a mistake to conclude from this that it makes no sense to suppose that any degree of detachment is possible, for this would be to deny the possibility of philosophical reflection, including the kind of philosophical reflection that the weak dependence theorist appears to be engaged in. This last point lies at the very heart of the matter. T h e foregoing response to the charge that naturalism undermines the hardness of the conceptual 'must' turned on an alleged difficulty with the notion of an external standpoint, but the naturalist's attempt to demonstrate the incoherence of the notion of externality that is responsible for the generation of the realist's anxiety seems to be self-defeating. For what the realist requires is no more and no less than that very degree of aloofness or detachment that the weak dependence theorist himself requires in order to assert that necessity and possibility are products of our 'grammar', or that no concepts are absolutely the correct ones. Or consider the claim that provable correctness in mathematics is dependent upon our partially shared 'whirl of organism'. What are we to make of this? I t is evidently not a statement internal to the practice of mathematics; it is, in an obvious sense, an 'external' claim about mathematics, and if we are prepared to grant ourselves the luxury of detaching ourselves far enough from our practices in order to be able to assert the dependence of logic and mathematics upon our 'whirl of organism', then we cannot in the very same breath deny to the realist the very same degree of detachment, without appearing guilty of bad faith. And if we can detach ourselves far enough to be able to say what the weak
dependence theorist says about mathematics and logic, how can it be denied that from this relatively detached perspective, (R)-counterfactuals do not appear to be true? Turning finally to the quasi-realist's defence of (R)counterfactuals, it cannot be claimed that no sense can be made of the standpoint from which such counterfactuals are anything other than true, for it must be the very same standpoint as that from which the quasi-realist does his philosophizing, and manages to claim that in dignifying a truth as necessary, we are expressing our own mental attitude. T o summarize, if necessity and possibility are wholly dependent upon our grammar, our 'whirl of organism', or our imaginative limitatio-ns, then it cannot be truefrom the perspective that these claims are made-that necessity and possibility are in any obvious sense 'beyond our control'. Thus far, then, each attempt to undermine the charge that weak dependence theory amounts to a form of scepticism about necessity appears to have been a failure. T h e latest attempt acknowledged that our concept of necessity requires what is genuinely necessary to be independent of what human beings think; it acknowledged, in other words, the demand that (R)-counterfactuals come out as true. I t insisted that the anthropocentric conception gives us all of this, for the temptation to suppose otherwise only arises on the assumption of an illegitimate, incoherent, 'sideways-on' perspective. I t is now clear, however, that this supposedly unintelligible standpoint is simply the standpoint of philosophical reflection, including the standpoint of the naturalist's own reflections, and the conclusion seems inescapable that what we ordinarily call 'necessary truths' are not necessary in the way that we believe that they are, whilst immersed in our practices. This has all the makings of a sceptical conclusion, a scepticism about necessity. T o put it more explicitly, if Cavell's characterization captures something of the flavour of our ordinary concept of necessity, then if it is a philosophical truth that what are called 'necessary truths' are products of our grammar, the upshot is that there are no necessary truths. Paraphrasing Cavell, if the a priori turns out to have a history, then it cannot really have been the a priori that was in question. All of this might, however, prompt the following paradoxical thought: it has been objected that the realist's standpoint cannot, in all consistency, be deemed to be illegitimate without calling into question the naturalist's own reflections on logic and mathematics. Surprisingly, the illegitimacy of his own remarks may be something that the dependence theorist would be prepared to accept. As Bernard Williams has written in connection with the later Wittgenstein's remarks on necessity, one result of our decisions may be that 'The dependence of mathematics on our decisions . . . is something which shows itself in what we are and are not prepared to regard as sense and is not to be stated in remarks about decisions.'18 Thus, it may be conceded l8 Williams, 'Wittgenstein and Idealism', in G. Vesey, ed., Understanding Wittgenstein, London, Macmillan, 1974, p. 95.
Necessity and Externality 457 that what the dependence theorist says is, strictly speaking, nonsensical, although it manages, as it were, to gesture at something of great importance. Unfortunately, none of this is immediately illuminating, for surely some defence is required of the claim that the dependence of mathematics upon our decisions cannot be stated; after all, why should it have been a result of our decisions that attempts to express the anthropocentric nature of mathematics must result in nonsense? It is true that in the Tractatus, Wittgenstein claimed that there are things that cannot be put into words,lg and regarded the propositions of the Tractatus as themselves constituting illegitimate attempts to put into words what can only be shown. Nevertheless, it is important to recall that Wittgenstein's dismissal of philosophical propositions in the early philosophy arose naturally out of the specific conception of language sketched in the Tractatus; given that Wittgenstein subsequently repudiated this conception of language, the appeal to the Tractatus doctrine of showing as part of a defence of the later philosophy is quite inappropriate. T h e suggestion is that language lacks the resources to express certain philosophical truths, but there is the paradox here-familiar to readers of the Tractatus-that in the very process of denying the possibility of expressing those truths, one is quite liable to end up stating them. There is, however, a better response open to the dependence theorist. T h e point of departure for this rejoinder will be the following line of thought: it was argued earlier that it would be unfortunate if the naturalist were to question the intelligibility of the perspective from which the realist raises his doubts, since this is the very same perspective as that from which the naturalist's own dependence claims are registered. But why should this claim be accepted? Why should it be assumed that the standpoint required by the dependence theorist is a standpoint from which (R)-counterfactuals come out as anything other than true? I t may be granted, in other words, that the formulation of the weak dependence theorist's claims about necessity requires a certain degree of independence or detachment, but it may nevertheless be denied that to arrive at the relatively detached standpoint from which one speaks of the dependence of necessity and possibility upon our grammar or 'whirl of organism' or imaginative limitations is necessarily to arrive at a standpoint from which (R)-counterfactuals appear to be false. T o this objection it may be replied that the reason for supposing that the naturalist's perspective is not one from which the conditionals come out as true is that if one is to speak of the dependence of necessary truths upon our use of words or imaginative limitations, the most natural way of expressing this relationship of dependence would be in terms of various counterfactual conditionals. What, after all, would be the point of speaking of the dependence of necessary truths upon our use of words if it remains true that if we l9 Tractatus Logicus-Philosophicus, trans. D. Pears and B. McGuinness, London, Routledge & Kegan Paul, 1961, 6. 522.
458 Quassim Cassam
had given the sum of 7 and 5 as 13, 7 + 7 would still be I Z ? But now the dependence theorist will claim that to argue in this way is to misunderstand his position. T h e last argument assumed that whatever it is that necessity is claimed to be dependent upon could have been otherwise; the assumption is that it is merely contingent that we happen to use words this way rather than any other, and given this assumption, it is hardly surprising that the anthropocentric position should appear so threatening. What the dependence theorist might say, however, is that it is not that we just happen to use words or to calculate in the way that we do; his point is that it could not have been otherwise. Thus, the correct response to a counterfactual such as 'if we had given the sum of 7 and 5 as 13,7 + 5 would still be 12' is to point out that it has an impossible antecedent, the pleasing upshot of which is that the conditional comes out as true, albeit trivially. T h e quasi-realist might respond in similar terms: it is true, he will concede, that it would be selfdefeating to suppose that necessary propositions give expression to contingent, naturalistically explicable imaginative limitations which are such that we can render intelligible to ourselves the thought that we might not have been subject to these particular limitations. But there are certain kinds of limitation that we cannot view in this light. There is a sense of 'unimaginable' or 'inconceivable' that is such that when we say that we cannot imagine how something could be otherwise, we cannot view this inability as a merely contingent fact about ourselves, as one which we just happen to be subject to. I t is only when the contrary of a proposition is unimaginable in this sense that we speak, and that we are entitled to speak, of that proposition as "necessary". So, when the quasi-realist is asked to comment upon a counterfactual such as 'if our imaginative limitations had been different, 7 5 would still be IZ', his comment may be that it is impossible that our imaginative limitations, in his strict sense, should have been different. There would therefore be no need for him to quarrel with the claim that the conditional is true. In view of this strategy, it would seem that the dependence theorist was quite right to protest when it was earlier assumed that he was committed to dissenting from (R)-type counterfactuals. 20 I t is not difficult to predict the realist's response to this latest line of thought. When the dependence theorist set out to give an account of necessity in terms of human imaginative limitations or grammar, it was objected that such an account had the effect of undermining the hardness of the conceptual "must". T o this the dependence theorist responded that there is no such undermining effect, since that upon which necessity was claimed to be dependent is not to be conceived of as something contingent, something which could have been otherwise; the (R)-type counterfactuals have impossible antecedents. But now what of these modal claims? What
+
20 This line of thought was suggested to me by a reading of Blackburn's 'Morals and Modals', forthcoming in Fact, Science and Morality, eds. Graham Macdonald and Crispin Wright, Blackwells, 1987.
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account does the dependence theorist propose to give of the claim that these things could not have been otherwise? What was hoped for was an explanatory account of necessity, but what we are presented with is the far from illuminating claim that there is no threat to the hardness of the conceptual "must" in what the dependence theorist says because the "must" is a reflection of or dependent upon something which is itself necessary. At this point, the account seems to have come full circle. T h e dependence theorist may defend his claim that the (R)-counterfactuals have impossible antecedents by saying that we cannot imagine them being true, that we cannot render this intelligible to ourselves. If, however, the dependence theorist attempts to comment upon the significance of the last claims, he is left with two unpromising options: it may be that we cannot conceive of the truth of the antecedents because they are impossible, in which case no progress has been made, or the suggestion may be that what it is for them to be impossible is that we cannot imagine them being true, in which case the question appears once again to have been begged. Indeed, it is far from clear that what the dependence theorist has just characterized as unintelligible or unimaginable is really so. Is it really the case that the suggestion that given different facts of nature we might have used words differently is literally unintelligible? This would seem a difficult view to maintain if one also wishes to maintain, with Wittgenstein, that it is nature which lies at 'the basis of grammar'.21 At this point, the dependence theorist will once again protest that he has been misunderstood. Consider once again Wittgenstein's response to the claim that 'Even though everybody believed that twice two was five it would still be four'; his initial reaction is to ask what it would be like for everybody to believe that. His comment is 'Well, I could imagine, for instance, that people had a different calculus, or a technique which we should not call It is striking that Wittgenstein does not directly challenge "~alculating"'.~~ the supposition that everybody might have believed that twice two is five. What he does challenge is the supposition that people who believe this could be said to be engaged in the practice of calculating. I t is this supposition which is contradictory, for answering '5' in response to '2 x 2' simply would not count as "calculating". T h e sceptic wishes to know whether, if we had calculated differently and found it natural to give the answer to '2 x 2' as ' 5 ' , twice two would still be four, but the correct response to this is to point out that on the sceptic's supposition we could not be said to have been engaged in the practice of mathematics at all. T h e point may now be generalized: consider a proposition N, which is deemed to be a necessary proposition. T h e sceptic wishes to know what the status of N would be or would have been if we had all believed N to be false. But now it may be held that recognizing the status of N is (partially) constitutive of 'thinking'; this 21
Philosophical Investigations, p. 230. Ibid., pp. 226-7.
460 Quassim Cassam would be reminiscent of Wittgenstein's suggestion in the Remarks on the Foundation of Mathematics that the laws of logic can be said to show 'how human beings think, and also what human beings call "thinking"'.23 In other words, it would be an error to ascribe thoughts or beliefs to a creature unless that creature is conceived of as having a grasp of the status of N and propositions like it. So the conditional examined by Wittgenstein does after all have an impossible antecedent; the difficulty with the idea of creatures thinking or believing that twice two is five is the difficulty with the idea of such creatures having thoughts or beliefs at all. This line of thought calls for a number of comments; firstly, it is doubtful whether it represents Wittgenstein's considered view of the matter. It is doubtful whether Wittgenstein would have endorsed the view that there is only one way of calculating, any more than he wished to endorse the view that there is, for example, only one kind of practice which may be called the practice of measuring. Consider Wittgenstein's example of people whose footrules are made of soft rubber instead of wood or steel. T o the objection that such people could not be said to be engaged in the practice of measuring at all, Wittgenstein replies: It is similar to our measuring and capable, in certain circumstances, of fulfilling 'practical purposes' . . . It can be said: what is here called 'measuring' and 'length' and 'equal length', is something different from what we call those things. The use of these words is different from ours; but it is akin to it: and we too use these words in a variety of ways.24 It may be objected that Wittgenstein's examples are not fully intelligible when subjected to closer scrutiny, but, as Stroud once suggested,25the point of the examples may have been to render intelligible to us the possibility of alternative ways of proceeding, without rendering those alternatives intelligible to us in detail. By imagining different facts of nature, it may become intelligible to us that people might have engaged in practices different from the usual ones, without those practices themselves becoming fully intelligible to us. Indeed, quite apart from questions of exegesis, it would seem that the dependence theorist would be ill-advised to insist upon the 'transcendental argument' of the last paragraph since, like all transcendental arguments, it has essentialist overtones which it might be in his interests to avoid at this stage. For to speak of a 'constitutive' connection between one idea and another is presumably to speak of an analytic or conceptual connection between the two ideas. T h e transcendental argument traded upon some conception of the necessary conditions of thinking or believing, of what it is to have thoughts or beliefs, but this only serves to illustrate why that argument is not unproblematically available at this stage, for what is Remarks on the Foundations of Mathematics, 1-13' Ibid., 1-5. 25 In 'Wittgenstein and Logical Necessity' in G. Pitcher, ed., Wittgenstein: the Philosophical Investigations, London, Macmillan, 1968. 23
Necessity and Externality
46 I
presently at issue is precisely the question of whether the dependence theorist has provided an adequate account of necessity. Appealing to the transcendental argument simply pushes the difficulty a stage further back, for the theorist's right to speak of necessary conditions may still be in dispute. T o this, the naturalist's final rejoinder may be that there is a simpler way of showing that the counterfactuals do not constitute a decisive difficulty for his position than the preceding remarks suggest. There may be certain forms of naturalism that are vulnerable to the objections developed thus far, but the quasi-realist will insist that to regard his position as a victim of the preceding objections would be to manifest a failure to pay sufficient attention to a crucial feature of that position. Earlier, it was argued that the falsity of (R)-counterfactuals was a consequence of the thesis that necessary propositions depend upon human imaginative limitations, but the quasirealist will deny that he is committed to accepting such a consequence. T h e falsity of (R)-counterfactuals would be a consequence of a position which appealed to imaginative limitations as part of an account of what necessity consists in, but an important feature of quasi-realism is precisely that it does not aim to provide a constitutive account of necessity. T h e quasi-realist may well avoid speaking of necessary propositions 'depending' upon imaginative limitations, given the constitutive overtones of the way of putting things. The quasi-realist's own talk of necessary propositions being expressions of imaginative limitations is much less liable to be misunderstood and is therefore to be preferred. Given his repudiation of constitutive or truthconditional approaches to morality or modality, the quasi-realist might argue that there is no reason to suppose that he is compelled to allow an 'external' reading of the counterfactuals, the reading on which they are alleged to come out as false. All of this renders intelligible the following characterization of what Blackburn regards as a central quasi-realistic tactic in the context of ethics: what seems like a thought which embodies a particular second-order metaphysic of morals is seen instead as a kind of thought which expresses a first-order attitude or need. Perhaps the nicest example comes from counterfactuals which seem to assert an anti-projectivist mind-independence of moral facts: 'even if we had approved of it or enjoyed it or desired to do it, bear-baiting would still have been wrong' can sound like a second-order, realist commitment directly in opposition to projectivism. But in fact, on the construal of indirect contexts which I offer, it comes out as a perfectly sensible first-order commitment to the effect that it is not our enjoyments or approvals which you should look to in discovering whether bearbaiting is wrong . . .'.26 There is more than one way of applying this to the modal case. If the suggestion is that the quasi-realist's treatment simply disallows a second-order 26 'Errors and the Phenomenology of Value', in T. Honderich, ed., Morality and Objectivity, London, Routledge & Kegan Paul, 1985, p. 6.
462 Quassim Cassam
or 'externalist' reading of the counterfactuals, then this might be thought to be so much the worse for the quasi-realist treatment of indirect contexts. It seems difficult to deny that we do sometimes intend and understand such counterfactuals in the second-order sense, and this is a fact which must be provided for. As already argued, there is little force in attempts to demonstrate the illegitimacy of an 'externalist' reading of the conditionals by calling into question the coherence of the very idea of an external standpoint on our practices. Indeed, having renounced the pursuit of truth conditions in the context of morals and modals, it is the quasi-realist himself who stresses the importance of investigating how we actually use utterances of the problematic kinds, what we actually intend by them. One would expect similarly careful attention to be paid to what we intend by counterfactuals of the form (R) and (RE), and for the quasi-realist to disallow a second-order reading of the conditionals would be to display an uncharacteristic insensitivity to a certain aspect of their actual use. Perhaps, in that case, the point is not to disallow a second-order reading of the counterfactuals, but rather to insist that there is nothing in the quasirealist's account that requires him to say that the counterfactuals are anything other than true on such a reading. Earlier, it was suggested that in claiming that necessary propositions are expressions of our own mental attitude, one has automatically placed oneself in a position in which (R)counterfactuals cannot come out as true (on the 'external' reading). I t was argued that the attempt to counter the objection by calling into question the idea of an 'external' perspective is ill-conceived, but now it might be suggested that there is no need for the quasi-realist to deny this last point. He may allow a second-order reading of (R)-counterfactuals, but insist that given the non-constitutive nature of his account, he is not committed to viewing the counterfactuals as false on such a reading. This response certainly shows that the earlier argument was too quick, but questions still remain. There is still the question of whether the quasi-realist has the resources to have the conditionals come out as true on the 'external' reading. It would not be to the point in this context to remark that such conditionals are capable of being used to express perfectly sensible first-order commitments. Indeed, it is quite unclear what the quasi-realist could point to as entitling him to view the (R)-counterfactuals as true on the 'external' reading, which is what would be required to do justice to our sense of the hardness of the conceptual 'must'. Perhaps this explains the quasi-realist's insistence on always taking the conditionals 'internally', but, as already noted, this strategy is, though heroic, somewhat implausible. There remains another way of pressing quasi-realism that does not rely upon the counterfactuals. T h e quasi-realist responded to the counterfactual-based attack upon his position by emphasizing the distinction between truth-conditional and expressive theories of modal discourse. His view is not that necessary propositions depend upon our imaginative
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limitations (in a constitutive sense), but rather that modal terminology is a way of giving expression to imaginative limitations. I t may be objected that even if this is true, there remains a Kantian 'question of right' to be answered, namely, what entitles us to take our imaginative limitations as a guide to modal truth? There is, prima facie, a gap between the two, and we are owed an account of what justifies us in crossing it. Now, one quick way with this challenge would simply be to deny that there really is any such gap. T h e formulation of the question of right presupposes that we have some conception of there being a contrast, at least in principle, between the idea of modal reality and the idea of our imaginative limitations, so that there is a substantive question to be asked concerning the basis upon which we take the latter to be a guide to the former. But the point of quasi-realism was precisely to deny that we have any conception of what could be meant by the 'real' modal status of a proposition other than in terms of the proposition being a projection of our imaginative limitations. We lack the independent grip upon the notion of the 'real' modal status of a proposition that would be required for the question of right to arise. If our conception of modality is as the quasi-realist describes it, then what appeared to be a gap between two distinct kinds of fact is really no gap at all, and the question of whether or not the crossing is justified is defused. This cannot, however, be a satisfactory view of the matter, for, as observed earlier, the reflective quasi-realist does not claim that there are no restrictions on which imaginative limitations may gain expression in our modalizing. We only modalize on the basis of imaginative limitations that we cannot regard as naturalistically explicable, contingent limitations, what might be called limitations in the strict sense. I t would be a mistake to take naturalistically explicable, contingent limitations as a guide to necessity and possibility, but if it is asked what entitles us to modalize on the basis of imaginative limitations in the strict sense, the answer will be that no sense can be attached to a notion of necessity that contrasts with or transcends the idea of our being unable to imagine, in this sense, how things could be otherwise. As Wittgenstein once put it, there is a use of the sentence 'I couldn't imagine the opposite of that' in which its point is not to indicate a lack of imaginative power, but rather to suggest that 'I can't even try to imagine it; it makes no sense to say "I imagine it"'.27 T h e quasi-realist might argue that the idea that imaginative limitations in the strict sense legitimately gain expression in our modal talk is quite unproblematic. T h e step, if it is a step at all, is a wholly innocent one. In arguing in this way, however, the quasi-realist is in danger of depriving his position of its initial force. One who aims to establish that there can be no adequate naturalistic conception of necessity will have no reason to be displeased with the quasi-realist's latest concession. T h e earlier objections to naturalistic conceptions of necessity were dismissed on the grounds that 27
Philosophical Grammar, I , 983.
464 Quassim Cassam
they assumed that these conceptions are engaged in the enterprise of providing an account of what necessity 'consists in', but now it transpires that the shift in emphasis recommended by the quasi-realist still leaves the naturalist having to concede the inadequacy of purely naturalistic conceptions, constitutive or expressivist. I t is hardly surprising that we should only view ourselves as being entitled to give expression in modal terminology to limitations that we regard as non-natural and non-contingent, but this lends weight to, rather than detracts from, the dichotomy with which this paper began. What was hoped for was an account of necessity in purely naturalistic terms that does not have as a consequence the undermining of the hardness of the conceptual 'must', but it now appears that no such account is available. Given this concession, we are left with the original options of either conceding that there is more to the world than the natural world, or, at any rate, than what is naturalistically explicable, or alternatively, if one is a sufficiently determined naturalist, of regarding the practice of modalizing as metaphysically erroneous.28 Wadham College, Oxford.
QUASSIM CASSAM
For helpful comments on earlier versions of this paper, I am much indebted to Simon Blackburn, John Campbell, David Charles, Richard Gaskin, Bob Hargrave, Sir Peter Strawson, Richard Swinburne, David Wiggins, and Stephen Williams.
