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(2) 2 committed to something's being true according to the fiction just because it would be true were PW true, Hale's objection cannot get off the ground. In any case, Rosen's second rejoinder is that there are uses of the conditional in natural language which show that counter-possible conditionals are not all trivially true, and that on these understandings Hale's objection would fail even if the "were PW to be true, then ..." was adopted (Rosen 1995, pp. 69-70). Hale attempted to counter both of these responses in 1995a. He had two responses to the approach consisting of taking the "According to PW..." operator as primitive. The first appears to be an attempt to argue that an "According to the fiction..." operator which is such that one cannot infer from `If what PW says were true it would be that A' that `According to PW, A' is too restrictive in what it allows is true according to PW. If this is what is supposed to be shown, however, the strategy of argument is a poor one, since it consists of picking one such operator and showing that it is inadequate. Hale's straw dummy is "PW says that...", an operator which holds only for those claims explicitly stated by PW (or "near enough explicitly", to use Hale's expression, whatever that might exactly amount to). Clearly taking what is explicitly said by a fiction to be the only things true according to it will be inadequate for the fictionalist's purposes: but Hale has given us no reason to suppose that there cannot be a halfway house between this and a "According to PW..." operator which when "According to PW, A" holds then for any B which is an entailment of A (or a strict consequence of A), or which meets some other condition such that it is trivial when the fiction makes necessarily false claims. There are problems about what the modal fiction represents, and how much it can represent implicitly, if the modal fictionalist position is offered as a reduction of modality (see Nolan 1997a), but Hale's does not seem to be one of them. Hale's second attempt to show the inadequacy of taking the "According to PW.." operator to be primitive is that it is "a second constraint ... upon any acceptable reading of this prefix that whenever, if PW were true, it would be true that A ..., it must also be true that according to PW, A". Perhaps this is merely a restatement of the conclusion of his first attempt. If it is meant to be independent, it appears to simply beg the question. The modal fictionalist who accepts Hale's reading of counter-.
(3) 3 possible conditionals and who claims PW is necessarily false has no reason to accept this "second constraint". Rosen's other response was to say that counter-possible conditionals need not be taken to be trivial. Hale briefly mentions reasons to think that our discriminatory use of counter-possibles in some contexts can be explained on pragmatic grounds -- though even if successful, this would do little to show that counter-possible conditionals in English were all vacuously true. (I have defended the non-triviality of counterpossible conditionals in Nolan 1997b, though I will not rehearse the arguments in their favour here). Hale also points out that if these counter-possible conditionals are only contrary to some grade of necessity less than that of logical necessity (such as metaphysical necessity), then there remains a sense in which PW is only contingently false -- which would impale it on the other horn of his original dilemma (see below). Hale then claims that making room for non-trivial counter-possible conditionals -- in particular conditionals with logically false antecedents -- Rosen "cannot stop short at tinkering with the logic or semantics of counterfactuals: a thoroughgoing implementation ... requires him to repudiate the standard classical account of logical consequence" (Hale 1995a, p. 78). He also describes the move Rosen would have to make as "some form of relevantist revisionism". I am not sure whether this parade-ofhorrors rhetoric is meant to be taken entirely seriously – in any case it seems false (again, Nolan 1997b is an example of accommodating counter-possible conditionals with little or no mutilation to the classical account of logical consequence). In any case Hale provides no reason here to suppose classical accounts of logical consequence need be repudiated by any who make non-trivial sense of counterpossible or even counter-logical conditionals. So it is far from clear Hale has uncovered a difficulty for modal fictionalism, even if it is granted that the "According to PW..." operator is to be analysed as some form of conditional, or alternatively is the case whenever the corresponding conditional is.. Horn 2: Modal Fictionalism is Contingently False On the other hand, if the story of possible worlds is only contingently false, Hale argues that there is also a problem. It is probably best to quote him in full on this point. (from Hale 1995b, p. 65):.
(4) 4 If, instead, he opts for the view that PW, though false, is no worse than contingently so, he must hold that PW might be (or might have been) true. But how is this modal claim -- the claim that possibly PW is true -- to be understood? If we apply the usual fictionalist recipe, what we get is: "According to PW, there is a possible world at which PW is true", which is equivalent to the conditional "If PW were true, there would be a world at which PW is true". Since what the antecedent hypothesizes is PW's truth at the actual world @, this conditional is an immediate consequence of "If PW were true at @, PW would be true at @". But this conditional is merely an instance of the schema "If A were true at @, A would be true at @", which holds whatever proposition A may be -- even an impossible one. In particular, "If PW were true at @, PW would be true at @" -- and hence its consequence "According to PW, there is a possible world at which PW is true" -- would be true, even if PW were impossible. Thus the official fictionalist paraphrase certainly cannot adequately capture the content of the claim that possibly PW is true. In this writer's opinion, this horn of the dilemma is badly constructed. In the first place, it is clearly not the case that the antecedent "If PW were true..." is equivalent to "If PW were true at @...". Even for modal realists, in general "p" and "p is true at @" do not mean the same thing, and typically have different intensions. "Pigs fly" is true at many possible worlds (though not at the actual one): however "pigs fly at @" is true at no world. Conversely, "Julius Caesar crossed the Rubicon at @" is true in all worlds, but "Julius Caesar crossed the Rubicon" is false at many other possible worlds. Standard antecedents hypothesise the truth of the antecedent - but it is by no means a widespread view that antecedents of counterfactual conditionals hypothesise that the antecedent holds at @. (For all that is standardly said, one might suppose that they hypothesise that we inhabit some world in which the antecedent is true, and leave entirely open the question of whether that world is @ or not). I suspect that most theorists have not paid particular attention to whether or not the hypothesis introduced by antecedents of counterfactuals introduces the hypothesis that the antecedent is true at the actual world, but there is a reason to suppose that this is not the case, besides the fact that in general "p" and "at @, p" do not mean the same thing..
(5) 5 Antecedents which explicitly distinguish the hypothetical case from the actual case make sense in ordinary English counterfactuals. "If I had more money than I actually do, I could buy a yacht", or "I would finish that report for you, if I only had more time than I actually do", both make perfect sense. The hypothetical situation in which I have more money than I actually do seems perfectly coherent. However, the hypothetical situation in which I actually have more money than I actually do is an incoherent one, and the counterfactual "If I actually had more money than I actually do, I could buy a yacht" does not sound as if it makes a very coherent supposition, at least to my ear. So "counter-actuals" provide another, compelling, reason to suppose that a counterfactual about what would happen if p were the case is not equivalent, or even in general the same in truth value, as a counterfactual about what would happen if p were actually the case. In the second place, it is difficult to see exactly what the problem is supposed to be here, even if Hale retreats from treating "If p then q" and "if p at @ then q" as equivalent. The essence of the charge seems to be that "If PW were true, at some world PW would be true" is going to be true whether or not PW might have been true, since it would also be true if PW were necessarily false, and so is not an adequate way of capturing the claim that PW might have been true. However, if this is a problem, it does not seem to be a problem specifically for modal fictionalism. It is a problem for the combination of S5 and Hale's view of the trivial truth of counter-possible conditionals. For take any way of capturing the claim that a given claim is possibly true (even something as straightforward as "q is possibly true"). If some such claim is true, then that claim, by Hale's lights, would still be true even if q were necessarily false. For if q is possibly true, then by S5, it is necessary that it be possibly true, and so (by the standard interdefinition of necessity and possibility). So if it were necessarily false, all hell would break loose, by Hale's lights: any conditional of the form "if q was necessarily false, then p" will be true when it is necessary that q is not necessarily false. So in particular, "`According to PW, there is a possible world at which PW is true' - would be true, even if PW were impossible" is trivially true, given that PW is possible and S5 holds, according to Hale's treatment of the conditional contained in that sentence..
(6) 6 Now, Hale need not accept S5 himself. (On p. 65, in footnote 4, he even says it might be a cause for concern if modal fictionalism required S5. Oddly he says "this is not, so far as I can see, in prospect". This is odd because the simple formulation of Rosen's he is addressing makes no mention of accessibility restrictions, and is committed to S5, except insofar as counterpart theory interferes.) Perhaps he may even think that the argument given above means that his view of counter-possibles, and his criterion of what would be a satisfactory way of saying that something was possibly true, together force the rejection of S5. A natural response to this, however, is to conclude that since his criterion, together with his account of counter-possibles, makes it incoherent to accept S5, the fault lies rather with his criterion than with S5, or with his approach to counter-possibles (dubious though that approach may be in its own right). We should not require that a statement that something is possible would not be true if that thing were impossible: or at least there is not yet any evidence that this requirement must be respected by the modal fictionalist. So for all Hale has said, the modal fictionalist can rest perfectly easily on this horn of his dilemma too, if the fictionalist chooses. Hale may have some other reason for thinking that there is a problem for the "contingency" horn, but so far as I can discern he does not make this problem explicit. He sums up his objection as being that "the crucial possibility claim ought not to be a consequence of a proposition which would be true even if PW were necessarily false" (p. 65, footnote 4), but nowhere in (1995a) or (1995b) does he explain further why he thinks this might be a problem. Since it is not plausible as a general principle that a claim C ought not to follow from the claim that it is necessarily false that C, Hale has not demonstrated that the modal fictionalist who takes his "contingent" horn need feel any discomfort.. Rosen's Third Way In Rosen 1995, which is a response to Hale's objection, Rosen raises a third possibility for the modal fictionalist, one which would enable him or her to avoid Hale's dilemma. Hale's dilemma relies crucially on PW being false: and at first blush this is eminently fair, since the point of modal fictionalism is to reject its truth. (Or perhaps at least stay agnostic, and thus putatively allow at least for the doxastic possibility that it is false). However, Rosen points out that the modal fictionalist could.
(7) 7 take PW (or a relative, PW*) to lack a truth-value altogether, and to use this truthvalueless fiction as the modal fiction (Rosen 1995, p. 72). The thought is that the fiction might employ a predicate with no literal application, e.g. the technical predicate "... is a world-mate of ...". Sentences containing uses of this predicate and its cognates might be thought to have no literal truthvalue, despite being true according to the fiction, which holds that this predicate does correspond with a genuine relation. (Rosen compares it with the nonsense verb "gimble" in Lewis Carroll's Jabberwocky. This is also, as Rosen points out, analogous to the treatment of fictional names employed by Frege (Rosen 1995, p. 72).) While this is an approach that some might take to predicates which arise in fictions, it does face some shortcomings. The things which are true or false according to fictions are often thought to be propositions: but people often balk at thinking there are truthvalueless propositions. It is also not clear that predicates such as "world-mate" would really not make literal sense. Enough is said about the "world-mate" relation to make it plausible -- even, by the modal fictionalist's lights, very plausible, that no actual relation has the features ascribed to it, or even could have. There are other reasons to dislike the "truthvalueless" approach to claims involving fictive predicates and names too, but Rosen was pointing out an option rather than providing a defence of it, and it is an option which has still not, so far as I know, been shown to be completely untenable for a modal fictionalist seeking to avoid Hale's dilemma.. Conclusion Hale's dilemma fails to seriously damage the modal fictionalist programme: as far as I can tell, there is no serious cost in embracing either horn of his dilemma, and it is possible to avoid the dilemma, though the desirability of the "third way" is still dubious. There remains the tricky problem of what to say about the "According to PW..." operator, and whether or not a modal fictionalist is able to avoid commitment to unreduced modality through the device of the modal fiction. But these problems are not problems which arise from Hale's dilemma -- they had already been identified by Rosen 1990, and the various proposed solutions do not seem to have much connection with the specific challenge Hale raises. If modal fictionalism is in trouble, the source of these difficulties lie elsewhere..
(8) 8. References Hale, Bob. 1995a. "A Desperate Fix". Analysis. 55/2: 74-81 Hale, Bob. 1995b. "Modal Fictionalism: A Simple Dilemma". Analysis. 55/2: 63-67 Nolan, Daniel. 1997a. "Three Problems for ‘Strong’ Modal Fictionalism". Philosophical Studies. 87/3: 259-275 Nolan, Daniel. 1997b. "Impossible Worlds: A Modest Approach". Notre Dame Journal of Formal Logic. 38/4: 535-572 Rosen, Gideon. 1990. "Modal Fictionalism". Mind. 99/395: 327-354 Rosen, Gideon. 1995. "Modal Fictionalism Fixed". Analysis. 55/2: 67-73. Daniel Nolan Departments of Philosophy University of St Andrews St Andrews, Fife, Scotland KY16 9AL United Kingdom This article © Daniel Nolan 2005.
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