Paradox and the A Priori

In T. Gendler & J. Hawthorne, Oxford Studies in Epistemology, Vol. 1 (OUP 2005) 10. Paradox and the A Priori Stephen Schiffer 1. a mckinsey paradox A paradox is a set of apparently mutually incompatible propositions each one of which is apt to seem plausible, at least when considered on its own. A well-known paradox in the literature on privileged access and externalism due to Michael McKinsey (1991) may for present purposes be stated, at least initially, as the set consisting of the following four propositions: (1) John is a priori justified in believing that he believes that if dogs bark, then dogs bark. (2) John is a priori justified in believing that dogs have existed if he—or anyone else—believes that if dogs bark, then dogs bark. (3) For any propositions p, q, if one is a priori justified in believing both p and (q if p), then, ceteris paribus, one is a priori justified in believing q. (4) Even when cetera are paria, one cannot be a priori justified in believing that dogs have existed. Evidently, (1)–(4) are mutually incompatible, and the prima-facie plausibility of each of these propositions may be glossed in the following way. Re (1) The traditional Kantian conception of a priori knowledge is knowledge that is ‘‘independent of experience’’. This alludes to the way in which one is justified in believing the proposition one knows. Whether or not knowledge is a complex state that includes belief,1 knowing p entails 1 See Williamson (2000) for an argument that it is not. 274 | Stephen Schiffer being justified in believing p, and while one’s belief may enjoy being justified in more than one way, there is at least one way of being justified that sustains one’s knowledge. What makes one’s knowing p a priori is that one’s knowing p is sustained by one’s being a priori justified in believing p. The ‘a priori’ in ‘a priori knowledge’ pertains to the way in which one is justified in believing that which one knows. Now, I am aware that some philosophers are reluctant to allow that one can know a priori that one believes any proposition, and these philosophers will deny that anyone is ever a priori justified in believing that he or she believes any given proposition. But if one sticks to the definition of a priori as ‘‘independent of experience’’, then it does seem that John, a normal New Yorker (if there is such a thing), is a priori justified in believing that he believes that if dogs bark, then dogs bark.2 For the way in which he is justified does indeed seem—at least when considered on its own, prior to reflection on the paradox—to be ‘‘independent of experience’’. While John has, and knows that he has, the same evidence we have for believing that he believes that if dogs bark, then dogs bark, he does not believe that he believes that if dogs bark, then dogs bark on the basis of that evidence. His being justified in believing that he believes that if dogs bark, then dogs bark does not seem to consist in his having any reasons for holding that belief, empirical or otherwise; nor does his being justified seem to consist in his having an experience of any particular kind. The idea of one’s being justified in believing a proposition without one’s having any particular kind of perception or sensation or any a posteriori or a priori reason may at first strike one as implausible, but it is actually a familiar phenomenon that is arguably manifested in, e.g., the way you are justified in believing that it is wrong to torture children just for the fun of it, or the way you are justified in believing that if there are numbers, then there are numbers. We may even in these cases speak of a person’s justification for her belief, provided we take this to mean 2 As will presently be apparent, one of my purposes in this paper is to engage the a posteriori/a priori distinction as it is currently understood in epistemology. But apart from that concern, much of this paper would be unchanged if the McKinsey paradox were stated not in terms of a priori justification, but in terms of a stipulated sense of non-evidential justification, where evidential justification would include the way in which one’s perceptual beliefs are justified by one’s sense experiences but would not include the way in which one is justified in believing that, say, one believes that there are prime numbers. Paradox and the A Priori | 275 whatever it is that constitutes her being justified, where this need not consist in any reasons she has for believing what she does. [The notion of justification as whatever constitutes one’s being justified in believing a proposition is vague. I would like to think that the vague notion suffices for my purposes in this paper, but that may be naı̈ve, and even if it is not, it would be nice to have some idea of what an acceptable precisification of the vague notion might look like. Perhaps a few precisifications would suit my purposes in this paper; I offer the following as a stab at one of them. The form ‘J is a justification for x’s believing p’ has more than one use, and some of them imply neither that x believes p, nor, if x does believe p, that x is justified in believing p. As I shall use the form, however, J’s being a justification for x’s believing p entails that x believes p, that x is justified in believing p, and that J is what constitutively makes x justified in believing p. I say ‘a justification’, as opposed to ‘the justification’, to allow for overdetermination with respect to what makes x justified in believing p.3 Yet, as I already confessed, even with these stipulations, the locution is still pretty vague as regards how justifications are to be individuated or what it is for something to belong to, or be part of, one, and I doubt that these questions enjoy determinately correct answers with any helpful degree of precision. So, I shall further stipulate that—at least to a first approximation4—J is a justification for x’s believing p iff J is a maximal sequence of sets of true propositions such that: (i) (ii) (iii) each set constitutes a non-trivial metaphysically sufficient condition for every succeeding member of the sequence; each set constitutes a non-trivial metaphysically sufficient condition for x’s being justified in believing p; and each proposition in each member set is essential to the set’s constituting a metaphysically sufficient condition for x’s being justified in believing p (that is, each such proposition is a necessary part of a sufficient but not necessarily necessary condition for x’s being justified in believing p). 3 I do not feel a need to add that J is an ‘‘epistemic’’ justification for x’s believing p, because I do not think there can be moral or prudential justifications for believing p; such justifications can only be justifications for making it the case that one believes p, say, by taking a drug that one believes will cause one to believe that one is a very lovable person. 4 I would not be shocked to learn that what follows falls short of the mark—that is, of what I need for this paper—in one way or another. 276 | Stephen Schiffer To this I add the following gloss: . To say that a set of propositions s constitutes a metaphysically sufficient condition for a set of propositions s0 is to say that the conjunction of the members of s metaphysically entails the conjunction of the members of s0 . . A set of propositions constitutes a trivial metaphysically sufficient condition for itself, but I shall not attempt any further precisification of what it is to constitute a ‘‘non-trivial’’ metaphysically sufficient condition for a set of propositions. (A consequence of the non-triviality requirements is that the fact that x is justified in believing p is not part of what justifies x in believing p.) . Nor will I attempt to accommodate either degrees of belief or degrees of justification, although the notion of partial belief will make a cameo appearance in what follows. The mere notion of being justified in believing a proposition should suffice for my purposes. . I shall say that a proposition is included in—or is a part or component of—a justification J which x has for believing p if that proposition either (a) is a member of one of J’s member sets or (b) is directly entailed by some conjunction of propositions that are members of one or more of those sets. Entailment here includes metaphysical necessitation, and I will only gesture by example at the intended sense of ‘directly’ in ‘directly entails’. Suppose that the fact that I came to believe q in such-and-such a way entails that I am a posteriori justified in believing q. Then that fact also entails that [(I am a posteriori justified in believing q) and (68 þ 57 ¼ 125)] and that [(I am a posteriori justified in believing q) or (68 þ 57 ¼ 5)]. Here, only the proposition that I am a posteriori justified in believing q is ‘‘directly’’ entailed. The subtle (a)-or-(b) disjunctive condition is intended to enable me to say that x’s being a priori/a posteriori justified in believing a certain proposition q is ‘‘part of’’ one’s justification for believing p, when the proposition that one is a priori/a posteriori justified in believing q is not itself a member of any of J’s member sets. . The reason I do not count each minimally sufficient condition as a distinct justification for x’s believing p—and the reason my definition takes its complex form—is that one sufficient condition for x’s being justified may supervene on another, and in that case we Paradox and the A Priori | 277 should not want to say that x’s being justified in believing p is overdetermined. Such supervenience can happen in one of at least two ways. First, a sufficient condition whose specification requires epistemic notions such as justification may supervene on a condition that is specifiable in non-epistemic terms. Second, a sufficient condition that is specifiable in non-epistemic terms may supervene on a condition that is specifiable in more basic non-epistemic terms, in the way that, say, biological facts supervene on physicalchemical facts. . Roughly speaking, a justification J for x’s believing p is maximal just in case no other justification can be derived from J by ‘‘inserting’’ a new set of true propositions anywhere in J.] Re (2) We may suppose John is an intelligent undergraduate who has had a few philosophy courses. John is familiar with Putnam’s twin earth thought experiments; he has read about unicorns in Naming and Necessity; and he is familiar with the notion of object-dependent concepts and propositions from his reading of Gareth Evans and more recent things in the theory of propositional content. As a result, John has come to accept the philosophical theory according to which it is necessarily the case that: (i) the property of being a dog is the property of belonging to a natural kind to which something belongs if, but only if, it is a dog; (ii) this natural kind is individuated partly in terms of a certain evolutionary lineage that would not exist if dogs had never existed; and (iii) propositions involving our concept dog—that is, propositions to which we may refer using thatclauses containing the word ‘dog’—are individuated partly in terms of the property of being a dog, so that those propositions would not exist if that property did not exist. And from all this, John recognized, it follows that dog-propositions are dog-dependent, which is to say that propositions involving our concept dog would not exist if dogs had never existed. The reasoning that led to John’s philosophical belief—a belief in a proposition that is either necessarily true or necessarily false—was of the kind with which we philosophers are very familiar, and it is apt to seem (at first glance, anyway5) that we would say that it is a priori. 5 In case you are already protesting that John’s reasoning will arguably presuppose that dogs have existed, and that that is not a proposition John can be a priori justified in 278 | Stephen Schiffer Re (3) This closure principle presupposes the more familiar closure principle that if one is justified in believing both p and (q if p), then, ceteris paribus, one is justified in believing q. The more familiar closure principle is really better stated as the principle that if one is justified in believing the conjunction [p & (q if p)], then, ceteris paribus, one is justified in believing q.6 The reason this is a better statement is not that a person who believes two propositions might not put them together so that she believes the conjunction; that contingency is already reasonably taken to be subsumed by the ceteris paribus clause. The reason is that— by my lights, at any rate—believing a proposition is just a matter of believing it to a contextually relevant high degree,7 and it may be that, while both the degree to which a rational person believes p and the degree to which she believes (q if p) pass the relevant threshold for deeming the person to believe both propositions tout court, the degree to which she believes the conjunction [p & (q if p)] is below that threshold. I propose simply to bypass this complication by assuming throughout that, if in the cases at issue one is justified in believing both p and (q if p), then one is also justified in believing the conjunction [p & (q if p)], and, when it simplifies the exposition, I shall write as though the closure principle is formulated in terms of such a conjunction.8 believing, let me counsel patience and remind you that I am at this point not speaking in propria persona, but merely glossing the prima-facie plausibility of (2) and the other members of the set of mutually incompatible propositions. 6 What explains the truth of this closure principle, assuming it is true? That is a very important question, but one I shall not here try to answer. I will, however, venture the thought that it is constitutive of being a rational believer who possesses the concepts of conjunction and the conditional that it is impossible for such a person, when functioning normally, not to believe q when she believes [p & (q if p)]. This sort of claim is a key ingredient both in commonsense functionalist accounts of propositional attitudes, such as those in (Lewis 1983b) and (Loar 1981), and in more recent work on concepts and justification, such as (Peacocke 1992) and (Boghossian 2003). 7 I am aware that there are those who deny this—e.g., Harman (1986: 22–4), Williamson (2000: 99), and Peacocke (2003: 113–15)—but I am unpersuaded by their reasons. 8 But why not replace the (1)–(4) formulation of the McKinsey paradox with the one consisting of the following three mutually incompatible propositions? . John is a priori justified in believing that [(he believes that if dogs bark, then dogs bark) & (dogs have existed if he believes that if dogs bark, then dogs bark)]. . For any propositions p, q, if one is a priori justified in believing [p & (q if p)], then, ceteris paribus, one is a priori justified in believing q. . Even when cetera are paria, one cannot be a priori justified in believing that dogs have existed. Paradox and the A Priori | 279 Anyway, when the closure principle (3) is understood in the now stipulated way, it is apt to seem plausible, and I shall often suppress the ceteris paribus qualification, since it pertains to general considerations of rationality which we may take to be in place. Very few philosophers would deny that if one is justified in believing [p & (q if p)], then, ceteris paribus, one is justified in believing q, and it is apt to seem hard to see how we can get a false principle by putting ‘a priori’ before ‘justified’. After all, the fact that you are justified in believing q cannot require anything that is not entailed by the fact that you are justified in believing [p & (q if p)]. Given that, how can your justification for believing q depend on experience when your justification for believing [p & (q if p)] is independent of experience? Re (4) It may be hard to find anyone willing to deny this.9 Paul Boghossian (1998: 275) expressed a very widely held view when he wrote that the proposition that water exists is ‘‘clearly not knowable a priori’’, and this conviction, I suspect, extends to the thought that one might be a priori justified in believing that dogs have existed. If we could be a priori justified in believing that there are, or have been, dogs, then it may seem that we could in principle be a priori justified in believing any empirical fact, and that is apt to seem preposterous. So much for the prima-facie plausibility of the mutually incompatible propositions comprising the paradox set. What has to give? 2. a sharpening of the issues The traditional Kantian conception of a priori knowledge is knowledge that is ‘‘independent of experience’’, and thus knowledge sustained by one’s being justified ‘‘independently of experience’’ in believing that which one knows. I think it is fair to construe the intended sense of ‘independent of experience’ as meaning that, when one is a priori justified in believing p, then one’s being justified in the way in which one is I could; but, as will presently be clear, it is important that the paradox be stated in a way that makes it easy separately to address John’s justification for believing that he believes that if dogs bark, then dogs bark and his justification for believing dogs have existed if he believes that if dogs bark, then dogs bark. 9 An exception is Sawyer (1998). 280 | Stephen Schiffer justified—one’s justification or entitlement or warrant (in this paper I use these notions interchangeably) for believing p—does not itself entail one’s being a posteriori justified in believing any other proposition. That may sound circular, but it is not; it merely means that however we precisify the vague notion of being independent of experience, an experience-independent way of being justified in believing a proposition cannot itself entail one’s being justified in believing some other proposition in an experience-dependent way. Thus, according to the traditional Kantian conception of the a priori, you are not a priori justified in believing a proposition if you are justified in believing that proposition in a way that entails being a posteriori justified in believing some other proposition. There is something puzzling about this conception of the a priori. The a priori/a posteriori distinction is supposed to be mutually exclusive and jointly exhaustive of ways of knowing and ways of being justified, and no one balks at the idea that one may be a posteriori justified in believing a proposition even though the way in which one is justified requires being a priori justified in believing a certain other proposition. For example, my a posteriori justification for believing that Jane and Anthony are second cousins may essentially involve my being a priori justified in believing that two people are second cousins if a parent of one is a first cousin of a parent of the other. Considerations of symmetry therefore suggest (but by no means entail) that our conception of the a priori might allow one to be a priori justified in believing a proposition even though the way in which one is justified entails being a posteriori justified in believing a certain other proposition. There are in fact examples which give some support to this symmetric conception of the a priori. Here are three such examples. (i) Most philosophers who work on the problem of vagueness believe that a proposition is knowable only if it is determinately true. If, for example, it is indeterminate whether Harold is bald, then these philosophers would agree that one cannot know either that Harold is bald or that he is not bald. I take it that, whether or not this widely held belief counts as knowledge (or is even true), it is a belief that is justified, and that the justification philosophers have for believing it is one they regard as a priori. It is the result of the sort of armchair conceptual analysis and theorizing that characterize analytical philosophy. At the same time, part of the justification these philosophers have for believing that proposition about vagueness is the empirical proposition that they have neither heard nor themselves been able to think of any counter- Paradox and the A Priori | 281 examples to it. Thus, if I am right that this justification counts as a priori as philosophers use that expression of art, then one’s justification for believing a proposition may count as a priori even if that justification includes one’s being a posteriori justified in believing a certain empirical proposition. If in such a case what one is a priori justified in believing is also something one knows, then there are instances of one’s knowing a proposition a priori where one’s justification for accepting the proposition is not wholly independent of the character of one’s experience. (ii) A student taking her first logic course is given a homework assignment in which she is asked to determine whether a certain formula is a theorem of propositional logic. She proves that it is a theorem, but not having complete confidence in her newly acquired skills, does not fully believe that it is. When she then speaks to her friend Bob, whom she knows to be good at logic, and he tells her that he came up with the same proof, she then fully believes that the formula is a theorem. I believe many philosophers would be content to class the student’s justification as a priori, even though part of that justification is her being a posteriori justified in believing a certain empirical proposition, that is, that her friend came up with the same proof. There is a better way to gloss this example. We need again to advert to the fact that beliefs come in degrees:10 one can believe a proposition more or less firmly, to a greater or lesser degree, and to believe a proposition tout court is just to believe it to a contextually relevant high degree. Let us pretend that degrees of belief can be measured in the interval [0, 1], 0 representing complete disbelief, 1 complete belief.11 Then we may suppose that before she spoke with her friend, the student believed to, say, degree .8 that the formula was a theorem. At that time, her justification for believing that proposition to degree .8 was entirely a priori; it was just her a priori confidence in the proof she constructed. But when she learns that her friend Bob came up with the same proof, she comes to believe to, let us suppose, degree .95 that the formula is a theorem. At that point, her justification for believing to degree .95 that the formula is a theorem includes her a posteriori justified belief that 10 See p. 278 above. The issue of partial belief is very complex, and there is more than one way in which I am presently indulging in simplification. See e.g. Schiffer (2003: ch. 5). But I think the simplifications are benign in the context of this paper, since the points I am using them to make would be unaffected by a replacement of the simplifications with the considerably more complex real McCoy. 11 282 | Stephen Schiffer Bob came up with the same proof of the formula, yet, notwithstanding this, there is, I believe, some inclination to say that her justification for believing that the formula is a theorem is a priori.12 Whether or not this is the best way to speak—a question I shall presently address—we should notice that this is not a case of overdetermination. The student would not believe to degree .95 that the formula was a theorem just on the basis of believing that her friend thought he proved that it was. Her single justification for believing to degree .95—and thus, in context, for believing tout court—that the formula is a theorem is constituted by the purely a priori reasons she had for believing to degree .8 that her proof was sound together with the extent to which she was able to take the fact that Bob came up with the same proof to be empirical evidence of the proof’s soundness. An actual example of this sort is provided by Andrew Wiles’s justification for believing that his proof of Fermat’s Last Theorem is sound. Wiles worked out his proof in private and did not show it to other mathematicians until he felt he had it right. No doubt his degree of belief in the soundness of his proof went up when his work was confirmed by other mathematicians, so that when he finally fully believed he had proved the theorem, his justification for believing it had this ineliminable a posteriori element. (iii) Accepting as you do the law of excluded middle, you believe that Giuseppe Verdi did or did not write the song ‘‘I’m Too Sexy for My Shirt’’. But you know that that instance of excluded middle entails that Verdi existed, and you are not justified in believing that Verdi did or did not write the song unless you are justified in believing that he existed. But even though your justification for believing that Verdi existed is a posteriori, I think that many philosophers would say you are a priori justified in believing the logical truth that Verdi did or did not write ‘‘I’m Too Sexy for My Shirt’’. 12 Christopher Peacocke (2004: 28) correctly observes that, ‘‘there is a distinction between what gives us access to the entitling conditions for a priori knowledge, and the entitling conditions themselves’’. But I believe he makes an overstatement when he adds that ‘‘possession of what the thinker knows to be a proof (a tree-structure of contents) provides an a priori entitlement to accept a logical or arithmetical proposition’’ (2004: 28). Whether someone in possession of what he knows to be a proof has a priori knowledge that the proof is a proof depends on whether he is a priori justified in believing that the proof is sound. A person may have only an a posteriori justification for believing that a proof is sound, and the student example suggests that a person may have an a priori justification with an a posteriori component for believing that a proof is sound. Paradox and the A Priori | 283 Well, do these examples show that one may be a priori justified in believing a proposition even though one’s justification includes the fact that one is a posteriori justified in believing a certain other proposition? I doubt that the current use of ‘a priori justified belief’ among philosophers is such that it could deliver a determinate verdict. Fortunately, a determinate verdict is not required; it is possible to resolve the McKinsey paradox without getting embroiled in verbal disputes generated by a tendentious use of the labels ‘a priori’ and ‘a posteriori’. Notwithstanding this, however, there is a distinction implicit in the examples already before us to which we should attend before attempting a resolution. Certain indisputably a priori justifications are wholly a priori, in that one’s a priori justification for believing a certain proposition does not contain an a posteriori justification for believing any proposition, and certain indisputably a posteriori justifications are wholly a posteriori, in that one’s a posteriori justification for believing a certain proposition does not contain an a priori justification for believing any proposition. Then there are mixed justifications, justifications that have both a priori and a posteriori components, and here we find an interesting division. In certain of these cases we would say that the justification as a whole is indisputably and determinately a posteriori, notwithstanding its a priori component. My justified belief that Jane and Anthony are second cousins is such an example: we would say that I am a posteriori justified in believing that they are second cousins, but an essential part of my justification is my being a priori justified in believing that two people are second cousins if each has a parent that is a first cousin of a parent of the other. In certain other cases, such as the examples (i)–(iii), philosophers’ intuitions appear to be mixed. None of these examples, I believe, is such that nearly all philosophers would judge them to be examples of indisputably, or determinately, a posteriori justifications. But philosophers evidently fall into four groups as regards any one of the examples (i)–(iii). Some will say the justification is a posteriori; some will say that it is a priori; some will say that it is neither a priori nor a posteriori, but rather a justification that is partly a priori and partly a posteriori; and some will not know what to say. As I said in the preceding paragraph, it may be that none of these responses is determinately wrong; and, as I also said, such indeterminacy does not preclude a determinate resolution of the McKinsey paradox. Still, we have an interesting distinction that demands an explanation. 284 | Stephen Schiffer The interesting distinction is between the mixed justifications that are indisputably a posteriori, such as my a posteriori justification for believing that Jane and Anthony are second cousins, and those, such as (i)–(iii), which are arguably neither determinately a posteriori nor determinately a priori. I believe there is a principled basis for this distinction.13 To a first approximation, a mixed justification for x’s believing p is determinately a posteriori when, and only when, two conditions are satisfied: first, the a priori component by itself does not justify x in believing p to any degree; and second, what the a priori component does do is enable x to take the a posteriori component to be evidence that p is true (that is, all other things being equal, the a posteriori component does not justify x in believing p to any degree in the absence of the a priori component, but given the a priori component, x is justified in taking the a posteriori component to be evidence that p is true). In the second cousin example, my evidence for believing that Jane and Anthony are second cousins is whatever evidence I have for thinking that each has a parent who is a first cousin of a parent of the other, but I would not be able to take that evidence as evidence that Jane and Anthony are second cousins if I did not know that two people are second cousins if a parent of one is a first cousin of a parent of the other. At the same time, my being a priori justified in believing that two people are second cousins if each has a parent who is a first cousin of a parent of the other by itself gives me no reason to believe to any degree that Jane and Anthony are second cousins. In the mixed cases that are arguably neither determinately a priori nor determinately a posteriori, the a priori component does not serve merely to enable the a posteriori component to be taken to be evidence that p is true. In some of these cases, the a priori component in itself justifies x in believing p to some degree, the a posteriori component being that in the justification which justifies x in believing p to the higher degree to which x in fact believes p. This is what is going on in examples (i) and (ii). In other cases, such as the Verdi example (iii), the a posteriori component (e.g. your evidence that Verdi existed) is needed just to secure that there is a proposition which is an instance of a propositional schema (in this case the schema p or not-p, which represents the law of excluded middle) that one is a priori entitled 13 This explanation was inspired by remarks made by Celia Teixeira during the discussion of an earlier draft of this paper at the 2003 European Summer School in Analytical Philosophy. Paradox and the A Priori | 285 to believe has only true instances. Presently we will see that there is still another way in which a mixed justification may fall on the notclearly-a-posteriori side. I formulated the McKinsey paradox as the set consisting of the following four mutually incompatible propositions: (1) John is a priori justified in believing that he believes that if dogs bark, then dogs bark. (2) John is a priori justified in believing that dogs have existed if he believes that if dogs bark, then dogs bark. (3) For any propositions p, q, if one is a priori justified in believing both p and (q if p), then, ceteris paribus, one is a priori justified in believing q. (4) Even when cetera are paria, one cannot be a priori justified in believing that dogs have existed. But in view of the somewhat equivocal nature of a priori justification that has come to light, let me now offer these two stipulative definitions: A person is purely a priori justified in believing p, and thus has a pure a priori justification for believing p, just in case her justification for believing p—or one of her justifications for believing p, should it be overdetermined that she is justified in believing p— does not include her being a posteriori justified in believing some other proposition. A person is impurely a priori justified in believing p, and thus has an impure a priori justification for believing p, just in case (a) her justification for believing p—or one of her justifications for believing p—is not determinately a posteriori but (b) does include her being a posteriori justified in believing some other proposition. Then our initial paradox set, (1)–(4), may give way to these two precisifications:14 14 Other precisifications are possible involving mixed cases—e.g. ones which would require the (obviously false) closure principle that if one is purely a priori justified in believing one of the propositions p and (q if p) and impurely a priori justified in believing the other, then, ceteris paribus, one is impurely a priori justified in believing q—but these add nothing of relevance to what is already covered by the two displayed. 286 | Stephen Schiffer (1p) (2p) (3p) (4p) (1i) (2i) (3i) (4i) John is purely a priori justified in believing that he believes that if dogs bark, then dogs bark. John is purely a priori justified in believing that dogs have existed if he believes that if dogs bark, then dogs bark. For any propositions p, q, if one is purely a priori justified in believing both p and (q if p), then, ceteris paribus, one is purely a priori justified in believing q. Even when cetera are paria, one cannot be purely a priori justified in believing that dogs have existed. John is impurely a priori justified in believing that he believes that if dogs bark, then dogs bark. John is impurely a priori justified in believing that dogs have existed if he believes that if dogs bark, then dogs bark. For any propositions p, q, if one is impurely a priori justified in believing both p and (q if p), then, ceteris paribus, one is impurely a priori justified in believing q. Even when cetera are paria, one cannot be impurely a priori justified in believing that dogs have existed. At this point, the following possible resolution, which I shall call Resolution A, is apt to suggest itself. (As will presently be clear, I am not putting Resolution A forward as the resolution I accept.) As regards (1p)–(4p), Resolution A holds, (3p) and (4p) are true, but (1p) and (2p) are false. (4p) is true, because the only justification a belief that dogs have existed can enjoy is an a posteriori justification. (3p) is true for the following reason. We are supposing that if one believes both p and (q if p) and cetera are paria, then one believes the conjunction [p & (q if p)], and it is conceptually impossible for a normal person to be justified in believing [p & (q if p)] but not to be justified in believing q (this is in part because it is impossible for a normal person to believe [p & (q if p)] and not to believe q). Now suppose that one is justified in believing q only if one believes q on the basis of justification J. Since being justified in believing [p & (q if p)] entails being justified in believing q, it follows that one’s justification for believing [p & (q if p)] must entail J. If J is either an a posteriori or impure a priori justification, then it follows that one’s justification for believing [p & (q if p)] cannot be a pure a priori justification, since in either event it means that part of what makes one justified in believing Paradox and the A Priori | 287 [p & (q if p)] is that one is a posteriori justified in believing a certain proposition. Neither (1p) nor (2p) is true for the following reason. Since John accepts the philosophical theory according to which dog-propositions are dog-dependent, and since he knows that both the proposition that he believes that if dogs bark, then dogs bark and the proposition that dogs have existed if he believes that if dogs bark, then dogs bark are dogpropositions, he will not be justified in believing either proposition unless he is justified in believing that dogs have existed. But the only justification anyone can have for believing that dogs have existed is an a posteriori justification. As regards (1i)–(4i), Resolution A holds, (1i), (2i), and (4i) are true, but (3i) is false. (1i) and (2i) are true because, while John’s being a posteriori justified in believing that dogs have existed is part of what makes him justified in believing both that he believes that if dogs bark, then dogs bark and that dogs have existed if he believes that if dogs bark, then dogs bark, the a priori components of those latter two justifications do not function to enable John to take the fact that dogs have existed as evidence for the truth of either belief, and this, as noted above, precludes those justifications from being determinately a posteriori. (4i) is true for the same reason that (4p) is true: the only justification a belief that dogs have existed can enjoy is an a posteriori justification. And finally, the closure principle (3i) is obviously false, since it is obvious that it is compatible with one’s being impurely a priori justified in believing [p & (q if p)] that one is either a posteriori justified or purely a priori justified in believing q. For example, by the above displayed stipulative definition of impure a priori justification, one is impurely a priori justified in believing that [Verdi did or did not write ‘‘I’m Too Sexy for My Shirt’’ & (Verdi existed if he did or did not write that song)], but one is only a posteriori justified in believing that Verdi existed. So much for Resolution A. I agree with some of its claims, but disagree with others. I agree with Resolution A that (3p) is true (relative to the stipulated understanding of it) and that (3i) is false. I disagree with Resolution A that (4p) and (4i) are true; I believe that both are false. Resolution A claims that it is impossible for anyone to be either purely or impurely a priori justified in believing that dogs have 288 | Stephen Schiffer existed, and this because it supposes that the only justification a belief that dogs have existed can enjoy is an a posteriori justification. But, as I will presently try to show, it is possible—albeit unlikely—for someone to be purely a priori justified in believing that dogs have existed, and since that is possible, it is also possible for someone’s justification for that belief to be an impure a priori justification by virtue of containing an a posteriori justification for some proposition other than that dogs have existed (perhaps the a posteriori element pertains to the proposition that no one has been able to think of a counter-example to a certain theoretical component of the total justification). Subject to an important qualification, I agree with Resolution A that (2p) is false and that (2i) is true. The important qualification is this. Given Resolution A’s claim that it is impossible for anyone to be purely a priori justified in believing that dogs have existed, it is committed to saying that it is impossible for (2p) to be true and that, therefore, (2i) cannot be false by virtue of John’s being purely a priori justified in believing that dogs have existed if he believes that if dogs bark, then dogs bark. I, however, want to say that, as John has been described (i.e. as a normal, well-educated person living in New York as we know it), (2p) is false and (2i) is true, but that he might have been such that (2p) was true and (2i) was false, and this, as I said in the preceding paragraph, because John might have been such that he was purely a priori justified in believing that dogs had existed. I do not agree with Resolution A that (1p) is false and (1i) is true. My description of John leaves open whether he is purely or impurely a priori justified in believing that he believes that if dogs bark, then dogs bark. Given that, as things are, John’s justification for believing that dogs have existed can only be a posteriori, that a posteriori justification must be part of either his justification for believing [a] that he believes that if dogs bark, then dogs bark or his justification for believing [b] that dogs have existed if he believes that if dogs bark, then dogs bark. It must be part of his justification for believing [b], but it need not be part of his justification for believing [a]. It must be part of John’s justification for believing [b], because it is impossible for him to believe [b] and not to believe that dogs have existed, and he would not believe that dogs had existed unless he was a posteriori justified in believing by empirical evidence that dogs had existed. For John has to believe [b] given his ability to recognize Paradox and the A Priori | 289 dog-propositions and his accptance of the philosophical theory that are dog-dependent. But in exactly the same way, he has to believe, at least on reflection, any conditional like [b] but with a different dogproposition as the antecedent. Thus, John has to believe that dogs have existed if (he believes that dogs have existed if he believes that if dogs bark, then dogs bark), and thus, by the closure of belief under known entailment, has to believe that dogs have existed. But no a posteriori justification for believing that dogs have existed need be part of John’s justification for believing [a]. He need not believe [a] even partly on the basis of believing that dog-propositions are dogdependent, and it is consistent with my description of John that his belief in [a] is much more secure than his belief in the philosophical theory that entails [b], so that he believes that should it transpire that there never were any dogs, then that would merely show that his philosophical view [b] was false. He may justifiably have such a conviction even if dog-propositions are dog-dependent. Here is an analogy. I believe that it is a necessary condition for experiencing pain that I be in a certain functional state, but should it transpire that I cannot be in that functional state, I would conclude that experiencing pain does not entail being in that functional state, not that I had never experienced pain. To be sure, John’s conviction that dog-propositions are dog-dependent may be so great that should he come to think that dogs have never existed, then he would also conclude that no proposition was ever referred to by his that-clause ‘that if dogs bark, then dogs bark’, and in that event his justification for believing [a], as well as his justification for believing [b], would contain his a posteriori justification for believing that dogs have existed. That is why my description of John leaves the truth-values of (1p) and (1i) open. Resolution A does not resolve the McKinsey paradox, but if what I have claimed in listing my agreements and disagreements with Resolution A is correct, then we will have a resolution when we see how one might be purely a priori justified in believing that dogs have existed, and, correlatively, why, as things are, John can have only an a posteriori justification for believing it. In the end, we shall see that the resolution of the McKinsey paradox turns essentially on a point that has nothing to do either with externalism or with a priori justification. 290 | Stephen Schiffer 3. resolving the mckinsey paradox Ceteris paribus, one is justified in believing q if one is justified in believing [p & (q if p)]. Suppose that one is justified in believing [p & (q if p)] and that cetera are paria. Then one is justified in believing q, and there are at least two possible scenarios as regards one’s being justified in believing q. Inherited Justification In this scenario,15 one has a justification for believing q that is inherited from a justification one has for believing [p & (q if p)], and therefore that justification for believing [p & (q if p)] does not include a justification one has for believing q which is independent of one’s being justified in believing [p & (q if p)]—that is, a justification one has for believing q which one would have even if one were not justified in believing [p & (q if p)]. If one’s being justified in believing q is not overdetermined, then one is justified in believing q wholly on the basis of being justified in believing [p & (q if p)]; one believes q on the basis of believing [p & (q if p)], and one’s justification for believing q just is (so to speak) one’s justification for believing [p & (q if p)]. Here is a mundane example of Inherited Justification. I believe that [(Smith’s child is ill) & (Smith will not attend today’s colloquium if his child is ill)], and my justification for believing that conjunction contains no independent justification that I have for believing that Smith will not attend today’s colloquium. Here I believe that Smith will not attend the colloquium on the basis of believing that [(Smith’s child is ill) & (Smith will not attend today’s colloquium if his child is ill)], and my justification for believing that Smith will not attend the colloquium derives entirely from my justification for believing that conjunction. In this example of Inherited Justification one comes to believe for the first time that Smith will not attend the colloquium on the basis of one’s coming to believe that [(Smith’s child is ill) & (Smith will not attend today’s colloquium if his child is ill)]. There are also examples of Inherited Justification in which one is already justified in believing q prior to 15 I trust it is clear that what follows is not a definition of some intuitive notion of inherited justification but is merely a label for the stipulated scenario. Likewise for the scenario labeled ‘Uninherited Justification’. Paradox and the A Priori | 291 becoming justified in believing [p & (q if p)]. This would be true of Lester in the following example. On Monday he cannot see how to prove a certain mathematical proposition q but is a posteriori justified in believing q on the basis of being told that it is true by a mathematician who would know. There is another mathematical proposition p such that on Tuesday Lester sees for the first time how to prove both p and (q if p), where neither proof relies on q, thus becoming purely a priori justified in believing [p & (q if p)], and thus via Inherited Justification also becoming purely a priori justified in believing q, in addition to his already being a posteriori justified in believing it. Uninherited Justification In this scenario, a justification one has for believing q is not inherited from a particular justification one has for believing [p & (q if p)]. Suppose that neither one’s being justified in believing [p & (q if p)] nor one’s being justified in believing q is overdetermined. Then one’s justification for believing q is one that one has independently of being justified in believing [p & (q if p)]. In this case, there is no sense in which one believes q on the basis of believing [p & (q if p)]; rather, one believes either p or (q if p)—and thus believes their conjunction—partly on the basis of believing q. To take a trivial example, since I am justified in believing that [(I am wearing a grey shirt) & (Jones was at the meeting if I am wearing a grey shirt)], I am justified (ceteris paribus) in believing that Jones was at the meeting. But I believe that Jones was at the meeting because I saw her there, and that is also my justification for believing that Jones was at the meeting if I am wearing a grey shirt: since I know that Jones was at the meeting, I know that she was there whether or not I am wearing a grey shirt. There are interesting differences among cases of Uninherited Justification, and one kind of case is of special interest with respect to present concerns. In cases of this kind, one would not believe [p & (q if p)] on the basis of a justification that did not include an independent justification of a certain kind K for believing q—that is, a justification of kind K for believing q that was not itself a justification for believing [p & (q if p)]— because one knows that if q were true, one would have, and know that one has, an independent justification of kind K for believing q. For example, I know that if my pants were on fire, I would have, and know that I have, sensory evidence of an expected sort that that was 292 | Stephen Schiffer so. Consequently, for any proposition p, I would not believe [p & (my pants are on fire if p)] unless my justification for believing that conjunction included the expected sort of sensory justification for my believing that my pants are on fire. Thus, as things actually stand with me and my environment, I can have no Inherited Justification for believing that my pants are on fire. This is because there can be no proposition p such that I can believe [p & (my pants are on fire if p)] on the basis of a justification that does not include the obvious sort of sensory justification for believing that my pants are on fire: since I know that I would be justified in that way in believing that my pants were on fire if they were on fire, I would not believe anything that entailed that my pants were on fire unless I was already justified in the relevant way in believing that my pants were on fire. (It should be clear that the point of the pants example in no way depends on the fact that I do not now believe that my pants are on fire. For the same sort of reasons that are operative in that example, I cannot now have an Inherited Justification for believing that I am alive.) As opposed to examples of the preceding sort, nothing now prevents me from acquiring an Inherited Justification for believing that I have 15.6 GB of used space on my computer’s C drive. As it happens, I neither believe nor disbelieve that proposition, and I expect not to be justified in believing that I do, or do not, have 15.6 GB of used space on my computer’s C drive unless I do certain things to find out. So, when I click on the right place and read that I have 15.6 GB of used space on my computer’s C drive, nothing interferes with my believing that I have 15.6 GB of used space on my computer’s C drive. As things actually stand, I cannot have an Inherited Justification for believing that my pants are on fire or that I am alive, but I can easily have an Inherited Justification for believing that I have 15.6 GB of used space on my computer’s C drive. We are now in a position to see why John is in no position to become purely a priori justified in believing that dogs have existed.16 Even if he had never entertained the thought that dog-propositions are dog-dependent, John, a normal, well-educated New Yorker, would implicitly know that it would be extremely unlikely for dogs to have existed without his having 16 As already noted (p. 291 above), the fact that John is now a posteriori justified in believing that dogs have existed does not per se preclude him from also becoming purely a priori justified in believing that proposition. Paradox and the A Priori | 293 empirical evidence which justified him in believing that dogs had existed (that is to say—more or less—that John’s subjective conditional probability that he has good empirical evidence that dogs have existed, given that dogs have existed, is high). Consequently, given that cetera are paria, there can be no proposition p such that John would believe [p & (dogs have existed if p)] unless his justification for believing that conjunction included an empirical-evidence-based a posteriori justification for his believing that dogs had existed, and from this it follows that John cannot have a purely a priori inherited justification for believing that dogs have existed which derives from his believing both that he believes that if dogs bark, then dogs bark and that dogs have existed if he believes that if dogs bark, then dogs bark. Since it is pretty clear that no one can be in a position to have a purely a priori uninherited justification for believing that dogs have existed, we have explained why John is in no position to become purely a priori justified in believing that dogs have existed.17 Since we have seen that, and how, John might well be purely a priori justified in believing that he believes that if dogs bark, then dogs bark, the foregoing also explains why, as things actually are with John and the world, he can at best be impurely a priori justified in believing the philosophical theory that dog-propositions are dogdependent, and thus in believing that dogs have existed if he believes that if dogs bark, then dogs bark. We are also in a position to see how it is metaphysically possible for someone to be purely a priori justified in believing that dogs have existed. To see this, it will be helpful if we first switch to a different example, to a sketch of a near-fetched scenario in which a purely a priori justified belief in a contingent proposition combines with a purely a priori justified belief in a necessary proposition in a way that leads to one’s being purely a priori justified in believing a contingent proposition of a sort that one might not at first have supposed could be justifiably believed on a priori grounds. 17 If my claim about what John implicitly knows is correct, then he is also not in any position to have an impurely a priori justified belief that dogs have existed. But what if he merely implicitly believes that [it is fairly unlikely that dogs should have existed without his having some empirical evidence that that was so]? Might he then have an impurely a priori justified belief that dogs had existed? That question will implicitly get an affirmative answer when I show below how it is metaphysically possible for John to be purely a priori justified in believing that dogs have existed. 294 | Stephen Schiffer On Sunday, John, our neophyte philosopher from the previous example, is purely a priori justified in believing that he has certain beliefs. For example, he believes that he believes that there are prime numbers greater than 7, and that belief is not based on any sort of empirical evidence or made justified by any experience or sensation.18 We may even assume that his belief is empirically indefeasible: even if John were to learn that, like a chocolate Easter bunny, his head was hollow, that would just prove to him that you do not need a stuffed head to have beliefs. Since John is purely a priori justified in believing that he has a particular belief, there is no problem in allowing that on Sunday he is also purely a priori justified in believing that he has beliefs. Also on Sunday, John is aware of the philosophical issue of whether having beliefs necessitates having information-processing states with sentential structure, but he has read nothing about it and given it no thought.19 He has no opinion on that question one way or the other. He neither believes nor disbelieves that having beliefs necessitates having information-processing states with sentential structure, and this is not because he is acquainted with considerations both for and against that thesis which cancel each other out. It is because he is not aware of any relevant considerations. Now, it would be possible for John not to have an opinion one way or the other about the claim that having beliefs necessitates having information-processing states with sentential structure while also having some reason to think that people do in fact have some information-processing states with sentential structure. As it happens, however, John has no reason of any kind either to believe or to disbelieve that he or anyone else has information-processing states with sentential structure; he is not aware of any relevant considerations one way or the other; he has no opinion on the matter, and he can see no reason why the fact of the matter, whatever it is, would manifest itself in empirical evidence to which he would have access. On Monday things begin to change when John delves into the literature on cognitive architecture and is impressed with various a priori 18 A person will believe that she believes that such-and-such only if she believes that she exists, but I take it that one is purely a priori justified in believing that one exists by virtue of one’s being purely a priori justified in believing that one believes that such-andsuch. This is the moral of Descartes’s Cogito. 19 This example was suggested to me by Martin Davies’s discussion of cognitive architecture (Davies 1998, 2003). As will soon be apparent to those familiar with Davies’s papers, Davies and I disagree about what the example is an example of. Paradox and the A Priori | 295 arguments by, among others, Brian Loar (1981), Martin Davies (1992), and myself (Schiffer 1993)20 —arguments whose conclusions entail that having beliefs necessitates having information-processing states with sentential structure. John spends the rest of that day and all day Tuesday and Wednesday rereading these works and thinking hard about their arguments, which he finds more and more persuasive. By Thursday, John has reconstructed an a priori argument he believes is sound and whose conclusion is that having beliefs necessitates having information-processing states with sentential structure. It is doubtful that John can be said to know that his argument is sound, even if it is, but our issue is about justified belief, and it does seem to me plausible that John’s philosophizing should have been well enough conducted so that he is purely a priori justified in believing that his argument is sound and, therefore, that having beliefs necessitates having informationprocessing states with sentential structure (the idea is that belief states are either identical to such states or else realized by them). John is also, of course, purely a priori justified in believing that if (he has beliefs and having beliefs necessitates having information-processing states with sentential structure), then he has information-processing states with sentential structure. In this way, John comes to believe that he has information-processing states with sentential structure, even though he has no empirical evidence or other a posteriori justification for this belief. But John’s newly acquired belief was derived from two purely a priori justified beliefs, and so is itself purely a priori justified. To be sure, John is well aware that future scientific research might prove him wrong, might discover that our internal information-processing states do not have sentential structure, and if that should transpire, then, while he would not stop believing that he has beliefs, he would cease to believe the philosophical theory he is currently purely a priori justified in believing. Nevertheless, John’s justification for believing that he has information-processing states with sentential structure is an instance of Inherited Justification. Moreover, since his justification is inherited from pure a priori justifications, it is itself a pure a priori justification. Let me briefly recap John’s progress, and register a slight qualification. John began in an initial state in which he was purely a priori justified in believing that he had beliefs and in which he had no reason to believe or to disbelieve that he or anyone else had 20 These three works are cited in Davies (2003). 296 | Stephen Schiffer information-processing states with sentential structure. Thus, when John encountered the philosophical argument and was persuaded by it on wholly a priori grounds, nothing interfered with his being purely a priori justified in believing both that he has beliefs and that he has information-processing states with sentential structure if he has beliefs. And since pure a priori closure (suitably understood) is correct, it follows that John was then also purely a priori justified in believing that he had information-processing states with sentential structure. The slight qualification to which I just alluded is that a pure a priori justification was stipulated to be a justification with no a posteriori component, but all that really matters for the issues at hand is that John’s justification for accepting the philosophical argument about cognitive architecture does not in any way rely on his being a posteriori justified in believing that anyone actually has information-processing states with sentential structure. It is irrelevant for present purposes if, for example, John’s justification, like the philosopher’s justification for believing that a proposition is knowable only if it is determinately true, includes the fact that he has not been able to think of any counter-examples to a certain claim. But rather than complicate the discussion with such qualifications, it is harmless and expositionally convenient to suppose that John’s justification for accepting the philosophical argument about cognitive architecture is purely a priori, as well it might be, so long as that justification does not include an a posteriori justification for believing that he, or anyone else, has information-processing states with sentential structure. That completes my characterization of John as regards his views about cognitive architecture and my case for concluding that on Thursday he is purely a priori justified in believing that he has information-processing states with sentential structure. In view of this, it is clear what we should say about the mutually incompatible propositions (1*)–(4*): (1*) (2*) (3*) John is purely a priori justified in believing that he has beliefs. John is purely a priori justified in believing that he has information-processing states with sentential structure if he has beliefs. For any propositions p, q, if one is purely a priori justified in believing both p and (q if p), then, ceteris paribus, one is purely a priori justified in believing q. Paradox and the A Priori | 297 (4*) Even when cetera are paria, one cannot be purely a priori justified in believing that anyone has information-processing states with sentential structure. What we should say about (1*)–(4*) is that (1*)–(3*) are true, but that (4*) is false, since cetera are paria and John is purely a priori justified in believing that he has information-processing states with sentential structure. What I propose we should say about (1*)–(4*) stands in marked contrast with what I proposed we should say about the mirroring set of propositions (1p)–(4p): (1p) John is purely a priori justified in believing that he believes that if dogs bark, then dogs bark. (2p) John is purely a priori justified in believing that dogs have existed if he believes that if dogs bark, then dogs bark. (3p) For any propositions p, q, if one is purely a priori justified in believing both p and (q if p), then, ceteris paribus, one is purely a priori justified in believing q. (4p) Even when cetera are paria, one cannot be purely a priori justified in believing that dogs have existed. Now (3p) ¼ (3*), and we may deem John to be such that (1p) is true. But (2p) is false: given that John is a normal New Yorker, he will be justified in believing that dogs have existed if he believes that if dogs bark, then dogs bark only if he has empirical evidence which a posteriori justifies his believing that dogs have existed. And while I suggested—a suggestion I have yet to explain or justify—that (4p) is false owing to its being metaphysically possible for a person to be purely a priori justified in believing that dogs have existed, I also implied that if we replace (4p) with (40 p) Even though cetera are paria, John is not purely a priori justified in believing that dogs have existed we shall have replaced it with a true proposition, while maintaining a set of mutually incompatible propositions. At the same time, it follows from what I said that its counterpart, (4**) Even though cetera are paria, John is not purely a priori justified in believing that he has information-processing states with sentential structure 298 | Stephen Schiffer is false, since cetera are paria and John actually is purely a priori justified in believing that he has information-processing states with sentential structure. What explains these differences between Structure and Dog (as I shall call these two scenarios)? We know the answer. John is in a position to have a justification for believing that he has information-processing states with sentential structure which is inherited from a justification— even a pure a priori justification—he has for believing that [(he has beliefs) & (he has information-processing states with sentential structure if he has beliefs)], but he is not in a position to have any justification for believing that dogs have existed which is inherited from a justification he has for believing that [(he believes that if dogs bark, then dogs bark) & (dogs have existed if he believes that if dogs bark, then dogs bark)]. And the reason this is so turns much less on the a priori/a posteriori distinction than it does on the distinction between Inherited and Uninherited Justification. More exactly, what it crucially turns on is the fact that, prior to coming to believe the philosophical theory that having beliefs necessitates having information-processing states with sentential structure, John did not believe, implicitly or otherwise, that he would have any kind of reason, let alone one based on empirical evidence, to believe that he had information-processing states with sentential structure, if that were so, whereas prior to coming to believe the philosophical theory that dog-propositions are dog-dependent, John did implicitly believe that he would have good empirical reasons to believe that dogs had existed, if that were so. The Dog side of that difference puts severe constraints on what inherited justifications John can have for believing that dogs have existed in a way that explains why he is precluded not only from being purely a priori justified in believing the philosophical theory that dog-propositions are dog-dependent, a theory that if true is necessarily true, but from having any justification for believing that dogs have existed which is inherited from any justification he has for believing the conjunction. But the Structure side of that difference itself leaves entirely unconstrained what kinds of inherited justifications John can have for believing that he has informationprocessing states with sentential structure in a way that explains why he is not precluded from being purely a priori justified in believing the philosophical theory that having beliefs entails having informationprocessing states with sentential structure, also a theory that if true is Paradox and the A Priori | 299 necessarily true. As I said, the difference between Dog and Structure turns for the most part on the distinction between Inherited and Uninherited Justification. It remains to explain why (4p) is false, why, that is, it is metaphysically possible for someone to be purely a priori justified in believing that dogs have existed. The reason it is metaphysically possible is simply that it is metaphysically possible for someone to be in the same position vis-à-vis the proposition that dogs have existed that John was in vis-à-vis the proposition that he has states with sentential structure prior to his accepting the philosophical argument about cognitive architecture. That is to say, it is possible for someone to have the concept dog but have no reason either to believe or to disbelieve that dogs had ever existed. A possible world in which a normally situated normal person who had the concept dog but had no reason to believe or to disbelieve that dogs had existed is probably very distant indeed from the actual world, but it need not be. Suppose that in the near future there is a nuclear holocaust in which only a very few people and other mammals survive, none of which are dogs, and all physical evidence of dogs which could be recognized as such is destroyed. The world that remains is in a virtual state of nature. A version of English survives, however, and one of the surviving adults speaks on occasion to his surviving daughter about dogs, describing them and drawing pictures of them (he is a good artist) in considerable detail. Unfortunately, the adult’s mind was disturbed by the holocaust, and as his daughter matures, it becomes clear to her that her father’s renderings of what the world was like before the holocaust are not to be trusted. At a certain point in her development, she has the concept dog but neither believes nor disbelieves that there ever were any dogs, and she can see no reason why the fact of the matter, whatever it is, should reveal itself to her in empirical evidence to which she has access. Now her father was a philosophy professor in a major New Jersey department, and he is never more lucid as when he is explaining to his daughter that theory of natural kind concepts according to which (a) dog is a natural kind concept if it is metaphysically possible that there were dogs and (b) dog-propositions are dog-dependent if dog is a natural kind concept. At the same time, the daughter has become convinced on the basis of a priori conceivability considerations that the existence of dogs is metaphysically possible, and we may suppose that her belief in that proposition is purely a priori justified, even if the 300 | Stephen Schiffer argument sustaining it is not altogether sound.21 In this way, the daughter acquires via Inherited Justification the defeasible but purely a priori justified belief that dogs have existed, and we see that it is metaphysically possible for someone to be purely a priori justified in believing that dogs have existed. That concludes my resolution of the McKinsey paradox with which I began this paper, but it will be instructive to look at the problem again from a slightly different angle, one that relates the results reached about Structure and Dog to what Crispin Wright (1985) has called ‘‘transmission of warrant’’, and to the classical Cartesian argument for skepticism about perceptual knowledge. 4. mckinsey paradox, skepticism, inherited justification, and transmission of warrant Consider the following version of the classical Cartesian skeptical argument, where it is understood that I know that if there is a blue cube before me, then I am not a BIV (a bodiless brain in a cubeless vat whose every sensory experience is caused by electrochemical stimulations administered by a computer): (1) I am not justified in believing that there is a blue cube before me unless I have a justification for believing that I am not a BIV which is independent of my current sensory experience. (2) I have no such justification. (3) ; I am not justified in believing that there is a blue cube before me. Philosophers are divided in their response to this sort of argument. One big division would occur over premise (1). Some philosophers, such as James Pryor (2000) and Christopher Peacocke (2003), would reject this 21 Is there a sound purely a priori argument whose conclusion is that dog-propositions are dog-dependent? I doubt it, and this may be a further difference between Dog and Structure, since it does seem to me more plausible that there is a sound purely a priori argument to show that having beliefs necessitates having information-processing states with sentential structure. But this paper is about the McKinsey paradox when stated in terms of belief justification, not in terms of knowledge (the terms in which that paradox is usually stated), and it is of course possible for someone to become purely a priori justified in believing a proposition, even though the a priori argument that sustains her belief has a false premise. Paradox and the A Priori | 301 premise. These philosophers would hold that one needs an independent justification for disbelieving that one is a BIV only if one has reason to suspect that one might be a BIV; in ordinary circumstances, wherein one has no such reason, one’s experience as of a blue cube’s being before one directly justifies one in believing that there is a blue cube before one, and thereby also justifies one in disbelieving that one is a BIV, provided one is also justified in believing that one is not a BIV if there is a blue cube before one. Other philosophers, such as Crispin Wright (2003) and Martin Davies (2003),22 would accept (1). Their view, roughly speaking, is that in order for one’s experience as of p’s being the case to justify one in believing p one must be entitled independently of that experience to disbelieve any hypothesis which one knows to be both incompatible with p and such that one would have precisely the same sort of experience if that hypothesis were true. (Disagreement about premise (1) goes along with disagreement about premise (2), and here things can get sticky.23 My focus now is just on premise (1).) The dividing issue just rehearsed may be rejoined as an issue about Inherited Justification. Can one have a justification for believing that one is not a BIV that is inherited from one’s justification for believing both that there is a blue cube before one and that one is not a BIV if there is a blue cube before one, or is it that such justification cannot be inherited, because, given one’s awareness of the entailment, in order to be justified in believing that there is a blue cube before one, one must be independently justified in believing that one is not a BIV? Both sides of the dispute should accept the (appropriately qualified) closure principle that, ceteris paribus (and we may assume throughout that cetera are paria), one is justified in believing q if one is justified in believing both p and (q if p). The issue is about whether one can justifiably believe both that there is a blue cube before one and that one is not a BIV if there is a blue cube before one without being independently justified in believing that one is not a BIV. Those in the Peacocke–Pryor camp say that is not required, that one can inherit one’s justification for believing that one is not a BIV from one’s justification for believing the two other propositions. Those in the Davies–Wright camp deny this; they hold that a justification for believing that one is not a BIV cannot be inherited from a justification one has for believing the other two propositions, and 22 23 Davies (forthcoming), however, indicates a change of mind. See Schiffer (2004). 302 | Stephen Schiffer this because, given awareness of the entailment, one cannot be justified in believing that there is a blue cube before one unless one is independently justified in believing that one is not a BIV. The dividing issue may also be rejoined as an issue about transmission of warrant. John, the subject of our previous examples, was stipulated to be a normal, rational, intellectually mature member of our society, and we may ask about his epistemic position with respect to this Moorean inference: Cube There is a blue cube before me. If there is a blue cube before me, then I am not a BIV. ; I am not a BIV. It seems to me that both those who accept premise (1) of the Cartesian skeptical argument and those who reject it ought to agree that two things are true of John vis-à-vis Cube. First, John cannot actively believe Cube’s premises without at the same time actively believing its conclusion, and second, John is justified in believing Cube’s conclusion if he is justified in believing its premises. Given this, the dividing issue re-emerges in the following way. Recall that on my stipulated use of ‘warrant’ and ‘justification’, those two terms are used interchangeably, and one’s justification for believing a proposition, when one is justified in believing it, is whatever makes one justified in believing it. Further, in order to avoid other presently irrelevant complexities, I shall assume that if John is justified in believing that he is not a BIV, then his being so justified is not overdetermined, that is, that he has just one justification for that belief; and I shall also assume that John has no reason to suspect that he may be a BIV. Relative to these stipulations, the division between those who reject premise (1) of the Cartesian argument and those who accept it comes to this. Those who reject premise (1), such as Peacocke and Pryor, will claim that John is justified in believing Cube’s premises, and thus in believing its conclusion; that his justification for believing its conclusion just is his justification for believing the conjunction of Cube’s two premises, and therefore his justification for believing the first premise does not include a justification for believing the conclusion. For these theorists, John’s justification for believing the first premise is, roughly, the fact that he seems to see a blue cube before him while having no reason to Paradox and the A Priori | 303 suspect that any defeating hypothesis may be true, and his justification for believing the second premise is the obvious a priori justification, which neither side of the dividing issue challenges. As I understand talk of ‘‘warrant transmission’’,24 these theorists would hold that in this case John’s warrant, or justification, for the premises of Cube transmits to its conclusion. Those who accept premise (1) of the Cartesian argument, such as Davies and Wright, will claim that John, who has the whole inference in mind, is not justified in believing Cube’s first premise unless he has an independent justification for believing its conclusion. Consequently, if he is justified in believing the conjunction of its premises, then his justification for believing that conjunction cannot be his justification for believing Cube’s conclusion. His justification for believing the conjunction of the two premises will include his justification for believing the conclusion, assuming he has such a justification, but it will include other things, such as his seeming to see a blue cube, which are extraneous to his justification for believing that he is not a BIV. If he is justified in believing that he is not a BIV, that justification is one that he would have even if he was not justified in believing either of Cube’s premises. As I understand talk of ‘‘transmission of warrant’’, these theorists would hold that, if John has a warrant for Cube’s premises, it does not transmit to its conclusion. It should be clear that, at least for the cases at hand, the issue about transmission of warrant is identical to the issue about Inherited Justification: in these cases, warrant is transmitted just in case justification is inherited. In fact, I find talk of warrant transmission to be at best misleading in a couple of ways, and I can make no good sense of the notion other than in terms of the distinction between Inherited and Uninherited Justification. Putting that point aside, however, I shall now continue the discussion mostly in terms of transmission of warrant, since I want presently to connect my views on these matters with those of Crispin Wright. My own position (Schiffer 2004) on the Cartesian argument, and thus on Cube, differs from that of both camps but is much closer in spirit to 24 There is reason to doubt whether the conditions for transmission of warrant proposed by theorists such as Wright and Davies actually capture the phenomenon they meant to capture; see Silins (forthcoming). I intend my claims about warrant transmission (relative to my stipulations about ‘warrant’) to cohere with the intended application of that expression of art. 304 | Stephen Schiffer the Wright–Davies camp, which holds that premise (1) of the Cartesian argument is true, and that therefore warrant fails to be transmitted in Cube, since one’s sense experience as of a blue cube’s being before one will not justify one in believing that there is a blue cube before one unless one is justified in disbelieving that one is a BIV in a way that is independent of that experience (and, of course, all other similar sensory experience). But my purpose now is not to address that debate. Rather, let us assume that the correct response to Cartesian skepticism entails that, for the reasons I gave, warrant fails to be transmitted in Moorean inferences such as Cube and ask how this might bear on the McKinsey paradox which is this paper’s primary concern. So let us return to the Dog setup and imagine John contemplating this inference: Dog* I believe that if dogs bark, then dogs bark. Dogs have existed if I believe that if dogs bark, then dogs bark. ; Dogs have existed. It follows from my proposed resolution of the McKinsey paradox, relative to my stipulations about John, that Dog*, like Cube, suffers from transmission failure, since, as I argued, John’s justification for believing the conclusion of Dog* is not inherited from his justification for believing its premises. John’s mixed warrant for the second premise —that is, his justification for believing the premise—will not transmit to the conclusion, because it itself includes John’s independent a posteriori warrant for the conclusion. The question I want to consider now is an instance of one raised by Crispin Wright in a couple of recent articles: does transmission of warrant fail in Dog* for the same sort of reason it fails in Cube (assuming it does fail in Cube)? Wright (2000) defends a view which suggests that he would answer yes (although, as I shall presently note, he qualifies that view in an even more recent paper). Reconstructed in terms best suited both to my formulations of Cube and Dog* and to my own construal of transmission failure, his proposal suggests the following unitary account of transmission failure in those two inferences. (a) Assume that John is justified in believing the premises of both Cube and Dog*. Then what suffices for, and explains, the transmission failure in both Cube and Dog* is that in both cases there is a proposition C such that (i) part of John’s warrant for the first premise consists in Paradox and the A Priori | 305 his being in a state that is subjectively indistinguishable from the state he would be in if C were true and (ii) C would be true if the conclusion were false. (b) In Cube, C ¼ the proposition that the thinker is a BIV who is now having a visual experience as of a blue cube’s being directly in front of him, and it is clear how the explanation goes. (c) In Dog*, we have the following. (i) The first premise—the proposition that John believes that if dogs bark, then dogs bark—entails (on the assumption that the second premise is a necessary truth) the conclusion, the proposition that dogs have existed. (ii) C ¼ the proposition ‘‘that the seeming-thought which [John] attempt[s] to express by [‘I believe that if dogs bark, then dogs bark’] is content-defective owing to the reference failure of the purported natural kind term’’25 ‘dog’ in John’s language, and thus (iii) part of John’s warrant for the first premise consists in his being in a state which is subjectively indistinguishable from the state he would be in if C were true. I do not think this attempt to give a unitary explanation of the two kinds of transmission failure succeeds. I have some reservations about whether Wright’s proposal adequately explains the transmission failure in Cube, but I grant that it offers a reasonable first shot.26 Roughly speaking, it tells us that the warrant provided by my visual experience as of seeing a blue cube cannot transmit to a warrant for believing that I am not a BIV because I would have just the same visual experience if I were a BIV. There are several reasons why this account doesn’t seem to explain the transmission failure in Dog*. First, and most important, while John’s state of believing Dog*’s first premise is subjectively indistinguishable from the state he would be in if C were true, it is not the case that John’s warrant for that premise consists even in part in his being in a state that is subjectively indistinguishable from the state he would be in if C were true. That is not an unreasonable thing to say about John’s warrant for the first premise in 25 Wright (2000: 156). Let C* be the proposition that I seem to see a blue cube before me but there is not one there. It seems to me false that I am not justified in believing that there is a blue cube before me unless I have an independent justification for disbelieving C*: that would introduce a circularity from which it would be impossible to escape. Hypotheses suitable for making a Cartesian skeptical argument must be hypotheses whose truth would explain one’s relevant sense experience. Yet it follows from Wright’s proposal that C* is an acceptable value of his ‘C’ and that, consequently, it should be suitable for incorporation into a Cartesian argument. 26 306 | Stephen Schiffer Cube, because part of his warrant for believing that there is a blue cube before him is that he is having a visual experience of a certain sort. But there is no sensation or experience of any kind that is part of John’s warrant for believing that he believes that if dogs bark, then dogs bark. There is no Nagelian ‘‘what it is like’’ to be in that belief state; in the sense of ‘‘subjective indistinguishability’’ in play, John’s state of believing that he believes that if dogs bark, then dogs bark is just as subjectively indistinguishable from his state of believing that there are prime numbers greater than 7 as it is from the state he would be in if C were true. The account of what justifies John in believing that he believes that if dogs bark, then dogs bark makes no reference to anything that would make ‘‘subjective indistinguishability’’ relevant. (It might be protested that Wright’s point is merely that for all John noninferentially knows for certain, he is suffering from an ‘‘illusion of content’’: he thinks there is a proposition to which ‘the proposition that he believes that if dogs bark, then dogs bark’ refers and which he believes, but if there never were any dogs or dog-like creatures, there would be no proposition to which the singular term refers, and thus he would be mistaken about what he believes. This response, however, is implicitly addressed in the next objection.) Second, if the Wright-suggested account of transmission failure in Cube and Dog* were correct, we should have transmission failure when John reasons Structure* I have beliefs. If I have beliefs, then I have information-processing states with sentential structure. ; I have information-processing states with sentential structure. For here C might be the proposition that none of John’s informationprocessing states have sentential structure, which would induce a kind of illusion of content, given the truth of the second premise: in uttering the first premise John would not be expressing the belief he in fact is and takes himself to be expressing, since John would have no beliefs to express. But if what I said before about (1*)–(4*) is correct, there is not transmission failure in this case, for in this case John’s purely a priori justification for believing the conclusion is inherited from his purely a priori justification for believing both premises. As a result of being purely a priori justified in believing the premises of Structure*, John Paradox and the A Priori | 307 becomes purely a priori justified (albeit defeasibly) in believing its conclusion. John remains purely a priori justified in believing that he has beliefs without an independent warrant for believing that he has information-processing states with sentential structure, notwithstanding that John would be suffering a kind of illusion of content in producing the first premise should his second premise be true and he lacks states with sentential structure. Third, as Wright makes clear in his most recent publication on this subject (2003), he would concede that it cannot be supposed that ‘dog’ in John’s idiolect would fail to refer if dogs had never existed. Perhaps in the relevant subjectively indistinguishable state of affairs John’s ‘dog’ refers to things that look and behave exactly like dogs but belong to a species other than Canis familiaris.27 Fourth, implicit in Wright’s account of transmission failure in Dog* is the claim that the assumption that dog-propositions are dog-dependent is needed to explain why warrant fails to be transmitted in that inference. But even if dog-propositions are not dog-dependent, John would still have his warrant for believing the premises of Dog*, and, as that warrant necessitates John’s being a posteriori justified in believing that dogs have existed, it would still fail to transmit to the proposition that dogs have existed. Fifth, since John might cease to believe only his second premise if he should come to doubt the conclusion of Dog*, it cannot be that the failure of John’s warrant for the premises of Dog* to transmit to its conclusion is to be explained in terms of the failure of his warrant for the first premise to transmit to the conclusion. If what I said in the preceding section is correct, transmission failure in this case is explained by John’s having a mixed justification for believing that dogs have existed if he believes that if dogs bark, then dogs bark by virtue of the dependence of that justification on his having an independent a posteriori justification for believing that dogs have existed. I do not think a unitary account can be given of the transmission failures in Cube and Dog*. In Cube, transmission of warrant fails because if one were a BIV, one would have just the same experiential warrant one actually has for believing that there is a blue cube before one—namely, one’s seeming to see a blue cube before one—and that is 27 Wright’s revised view, I believe, does not escape the other objections I am raising to the view it revises. 308 | Stephen Schiffer why one will not be justified in believing that there is a blue cube before one unless one is independently warranted in disbelieving that one is a BIV. In Dog*, however, when transmission fails, as it does in John’s case (I argued that in certain possible worlds it does not fail), it is because of the connection John takes to obtain between dogs having existed and his having empirical evidence of a certain kind that dogs have existed. Owing to what John takes that connection to be, he will not, as explained in the preceding section, believe any proposition that entails that dogs have existed unless his having empirical evidence of a certain kind renders him a posteriori justified in believing that dogs have existed. I said John might be such that only his justification for his philosophical theory of the dog-dependence of the concept dog was empirically defeasible by evidence that dogs never existed, but, as already indicated, nothing much changes if we suppose he would conclude that there never were any dog-propositions if he came to believe there never were any dogs. That would just show that he had mixed justifications for both premises, each justification dependent on his having an a posteriori justification for the proposition that dogs have existed. Besides, if John were to be suffering an illusion of content, he would not have the justification he has for believing that he believes that if dogs bark, then dogs bark. For that justification, I should think, essentially includes the fact that he does believe that if dogs bark, then dogs bark.28 references Boghossian, Paul (1998) ‘What the Externalist can Know a Priori’, in C. Wright, B. C. Smith, and C. Macdonald (eds.), Knowing our own Minds (Oxford), 271–84. —— (2003) ‘Blind Reasoning’, Proceedings of the Aristotelian Society, supplementary volume, 77: 225–48. Davies, Martin (1992) ‘Aunty’s own Argument for the Language of Thought’, in J. Ezquerro and J. M. Larrazabal (eds.), Cognition Semantics and Philosophy: Proceedings of the First International Colloquium on Cognitive Science (Dordrecht), 235–71. 28 Thanks to Yuval Avnur, Paul Boghossian, Emma Borg, Jonathan Dancy, Alice Drewery, Tamar Szabó Gendler, Allan Gibbard, Hanjo Glock, John Hawthorne, Paul Horwich, Nikola Kompa, Anna-Sara Malmgren, Susana Nuccetelli, Christopher Peacocke, Jim Pryor, Sven Rosenkranz, Josh Schechter, Celia Teixeira, and Crispin Wright. Paradox and the A Priori | 309 —— (1998) ‘Externalism, Architecturalism, and Epistemic Warrant’, in Crispin Wright, Barry C. Smith, and Cynthia Macdonald (eds.), Knowing our own Minds (Oxford), 321–61. —— (2003) ‘The Problem of Armchair Knowledge’, in S. Nuccetelli (ed.), New Essays on Semantic Externalism and Self-Knowledge (Cambridge), 23–57. —— (forthcoming) ‘Epistemic Entitlement, Warrant Transmission, and Easy Knowledge’, Proceedings of the Aristotelian Society, supplementary volume, 78. Ezquerro, Jesús, and Jesús M. Larrazabal (eds.) (1992) Cognition, Semantics, and Philosophy: Proceedings of the First International Colloquium on Cognitive Science (Dordrecht). Harman, Gilbert (1986) Change in View: Principles of Reasoning (Cambridge). Jackson, Frank, and Michael Smith (eds.) (2004) Oxford Handbook to Contemporary Philosophy (Oxford). Lewis, David (1983a) Philosophical Papers, i (Oxford). —— (1983b) ‘Radical Interpretation’, Philosophical Papers, i (Oxford), 108–32. Loar, Brian (1981) Mind and Meaning (Cambridge). McKinsey, Michael (1991) ‘Anti-Individualism and Privileged Access’, Analysis, 51: 9–16. Nuccetelli, Susanna (ed.) (2003) New Essays on Semantic Externalism and Self-Knowledge (Cambridge). Peacocke, Christopher (1992) A Study of Concepts (Cambridge). —— (2003) The Realm of Reason (Oxford). —— (2004) ‘The A Priori’, in F. Jackson and M. Smith (eds.), Oxford Handbook to Contemporary Philosophy (Oxford). Pryor, James (2000) ‘The Skeptic and the Dogmatist’, Noûs, 34: 517–49. Sawyer, Sarah (1998) ‘Privileged Access to the World’, Australasian Journal of Philosophy, 76: 523–33. Schiffer, Stephen (1993) ‘Actual-Language Relations’, Philosophical Perspectives, 7: 231–58. —— (2003) The Things we Mean (Oxford). —— (2004) ‘Skepticism and the Vagaries of Justified Belief’, Philosophical Studies, 119: 161–84. Silins, Nicholas (forthcoming) ‘Transmission Failure Failure’, Philosophical Studies. Williamson, Timothy (2000) Knowledge and its Limits (Oxford). Wright, Crispin (1985) ‘Facts and Certainty’, Proceedings of the British Academy, 71: 429–72. 310 | Stephen Schiffer Wright, Crispin (2000) ‘Cogency and Question-Begging: Some Reflections on McKinsey’s Paradox and Putnam’s Proof’, Philosophical Issues, 10: 140–63. —— (2003) ‘Some Reflections on the Acquisition of Warrant by Inference’, in Susanna Nuccetelli (ed.), New Essays on Semantic Externalism and Self-Knowledge (Cambridge), 57–79. —— Barry C. Smith, and Cynthia Macdonald (eds.) (1998) Knowing our own Minds (Oxford).