The Preface Paradox

The Preface ParadoxAuthor(s): Sharon RyanSource: Philosophical Studies: An International Journal for Philosophy in the AnalyticTradition, Vol. 64, No. 3 (Dec., 1991), pp. 293-307Published by: SpringerStable URL: http://www.jstor.org/stable/4320263 .

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SHARON RYAN

THE PREFACE PARADOX

(Received 4 December, 1990)

It is often assumed that a person cannot be epistemically justified or rational in believing statements that she knows to be inconsistent.' The preface paradox, which was introduced by D. C. Makinson, can be told in a way that poses a serious threat to this assumption.2

I will present a version of Makinson's preface paradox that is about Mitzi, who has dilligently researched and written a fairly lengthy book. As she is proofreading her manuscript one last time before she sends it off to the publisher, she has a justified belief that 's, and s2 and . . . s" are all the sentences of my book.' Since she has worked very hard at researching her material, and has had many people whom she respects read drafts of her manuscript to catch any errors, it seems that Mitzi has good reason to believe of each sentence in her book, that it is true. Expressed formally, this is:

(1) JS(s1) & JS(s2) & .. *JS(Sn)

It seems reasonable to think Mitzi is justified in believing the conjunction of the sentences of her book is true when she is justified in believing each of the individual sentences of her book is true. Formally, this is:

(2) JS(s1 & s2 & .. *sn)

The epistemic conjunction principle at work behind this inference from

(1) to (2) is:

The Conjunction Principle:

(CP) If S is justified in believing p at t and S is justified in believing q at t, then S is justified in believing (p & q) at t.

Mitzi, our author, is a human being. Nobody's perfect. So, sometimes

Philosophical Studies 64: 293-307, 1991. C 1991 KluwerAcademic Publishers. Printed in the Netherlands.



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she makes mistakes. The fact that Mitzi, like the rest of us, is fallible and has written a fairly lengthy book, seems to make it epistemically rational for her to believe that she has made at least one mistake somewhere in her book. That we do think we would be epistemically justified in thinking she has made a mistake somewhere in her book is evidenced by the disclaimer found in the preface of nearly all academic books. Authors often write something to the effect that although they have been saved, to some extent, by their smart friends and enemies who read drafts of their manuscript, they no doubt made some mistakes and those mistakes are their own. Given Mitzi's justified belief about her own fallibility, it seems epistemically rational for Mitzi to believe that not all the sentences in her book are true. Given that she has a justified belief about the specific contents of her book, Mitzi's justified belief can be expressed formally as follows:

(3) JS - (S &S2 & .. * Sn)

Mitzi, let us suppose, desires to be epistemically rational and believe all and only what her evidence supports. So, since she is justified in believing all the sentences in her book are true and she is also justified in believing not all the sentences in her book are true, she is, as (CP) says, justified in believing the conjunction of these individual beliefs. She is, it seems, justified in believing all of the sentences of her book are true and not all the sentences of her book are true. Mitzi's epistemic situation can be formally expressed as follows:

(4) JS ((SI & S2 & .. Sn) & (SI & S2 & Sn))

Mitzi is as shocked as we are. She finds herself believing an explicit logical contradiction. She is a very smart scholar and she knows, among many other truths, that nothing of the form (p & - p) can be true. But believing this contradiction is what her evidence seems to support. (4) is in direct violation of a very reasonable assumption. If a person knows that what she is believing is of the form of a logical contradiction, she knows that what she is believing cannot be true. Believing under such circumstances is ordinarily thought of as a paradigm case of an epistemicaly irrational or unjustified belief. I will call the principle behind this assumption the "No Known Contradictions Principle." That principle can be stated as follows:



THE PREFACE PARADOX 295

The No Known Contradictions Principle:

(NKCP)No one is ever justified in believing anything she knows to be of the form (p & - p).

With the exception of Graham Priest, nearly every philosopher is strongly committed to (NKCP).3 Thus, with the exception of Graham Priest, nearly every philosopher ought to be troubled by this version of the preface paradox.

Mitzi cannot be justified in believing the contradiction stated in (4). However, it seems that all the epistemic principles that led to (4) are true. Despite our strong reluctance to give up any of the epistemic principles that generate the paradox, that seems to be our only alterna- tive. The principle with the most intuitive plausibility is (NKCP). Thus, abandoning that principle will be the absolute, last resort.

Historically, it s the conjunction principle that winds up being rejected in discussions about versions of the preface paradox. Peter Klein,4 Henry Kyburg,s and D. C. Makinson6 for example, take this route out of versions of the preface paradox. Makinson's paradox is different from the one I have concocted. His version is best interpreted as a paradox about belief and not about epistemic justification. Kyburg has in mind a slightly different paradox as well. The version he discusses is one about probabilistic rules of rational acceptance. Rejecting the relevant conjunction principles in the versions of the paradox discussed by Makinson and Kyburg may very well be the best solution to their versions of the preface paradox. I am concerned about finding the best solution to the version of the paradox I gave about epistemic justification. Klein does have a paradox about epistemic justification in mind when he denies the conjunction principle.

With respect to the preface paradox about epistemic justification, one who believes the conjunction principle is false will deny that (2) is justified on the basis of (1). By denying (2), they avoid the contradiction stated in (4). Klein claims, "[s]imply put, there is nothing paradoxical about the situation envisioned in the Preface Paradox."7 He would argue that someone in Mitzi's situation is epistemically justified in believing, of each sentence of her book, that it is true. Klein would also hold that Mitzi is justified in believing not all of the sentences of her



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book are true. What Klein would deny, is that Mitzi is justified in believing all of the sentences of her book are true.

Mitzi's beliefs are not of the form (p & - p) if she does not believe (2). So, Klein's proposal saves Mitzi from violating the "No Known Contradictions Principle." That is a big point in favor of his proposal. However, Mitzi still has a set of beliefs that is known by her to be inconsistent. It is not possible that all of her beliefs are true. Klein's proposal flies in the face of the commonly held assumption that one is never epistemically justified in believing a set of statements that she knows to be inconsistent.

I find Klein's "solution" unsatisfying. Denying that Mitzi is justified in believing all the sentences of her book are true when she is justified in believing each individual sentence of her book is true, seems to be a desperate maneuver to avoid violating (NKCP). Granted, we need to figure out a way to avoid violating (NKCP). But, is Klein's attempt really very plausible?

Even if the conjunction principle is false, it still seems reasonable to think that Mitzi is epistemically justified in believing all of the sentences of her book are true if she is justified in believing each individual sentence of her book is true. Even if the conjunction principles does not make it so, Mitzi's evidence does. Even if it is not always true that one is justified in believing the conjunction of justified, individual beliefs, it is sometimes true that one is justified in believing the conjunction of justified, individual beliefs. In the words of Klein, "... it is nevertheless true that in some cases the very best warranting evidence available for a conjunction is the conjuncts."8

For example, if a newspaper reporter in Rochester, New York is justified in believing 'Michael Jordan can slam-dunk' and after watching an exciting University of Rochester philosophy department game of basketball, is also justified in believing 'Rich (a.k.a. 'Spud') Feldman can slam-dunk' she is justified in believing the conjunction that 'Michael Jordan can slam-dunk and Rich Feldman can slam-dunk.' Each of the conjuncts, with its justification, add up to justify the newspaper reporter's belief in the conjunction. This is true for some cases involving many conjuncts as well.

Consider a father with fifteen (or even more) children. It seems that if he manages to be justified in believing fifteen (or even more)




individual statements, each asserting the name of a different child, then he is justified in believing the conjunction of those statements. There are so many cases in which it is intuitively clear that a conjunction of beliefs is perfectly well justified on the basis of the individual conjuncts.

Think carefully about Mitzi's situation. Mitzi's book made it past the scrutiny of a lot of smart people. It is reasonable to assume that books get positively reviewed by one's colleagues because the individual sentences are well supported. But, there seems to be more to it than that. It seems very reasonable to think that part of her justification and her colleague's justification for believing the individual sentences is that they fit together and form a coherent story. Thus, even if (2) is not forced by (1) via (CP), it seems perfectly reasonable to think that (2) is true if (1) is true. If Mitzi is really justified in believing each individual sentence, it seems most reasonable to think she is also justified in believing all of the sentences of her book are true. Thus, I think Klein's alleged solution is unconvincing.

However, if this "solution" is the only option other than denying the "No Known Contradictions Principle", then I'm with Klein. Fortunately, things are far less grim than they seem. In order to solve the preface paradox, one need not deny (NKCP) or (CP). By more carefully thinking about our fallibility and the stipulated facts about this case, I think we can find a modest solution that allows us to avoid abandoning either of these principles and preserves the assumption that one cannot be epistemically justified in believing a set of statements that she knows is inconsistent.

Think more carefully about what it means to be fallible. It was the fact that Mitzi, along with the rest of us, is fallible that led us to accept that she should deny the conjunction of the individual sentences of her book. When we say that a person is fallible we mean roughly the following:

(FP) A person, S, is fallible if even when S tries very hard to believe what fits her evidence, she nevertheless sometimes makes mistakes.9

As Klein asserts, one would be guilty of epistemic hubris if one denied that all human beings are fallible.'0 Charges of guilt aside, I think it is clear that (FP) is not very clear. The word 'mistake' is



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ambiguous. (FP) can be read in at least two importantly different ways. On one reading, 'mistake' could be taken to be a failure to believe what one's evidence supports. On another reading of (FP), a mistake could be a belief which is justified but false. These two interpretations of (FP) can be stated as follows:

(FP1) A person, S, is fallible if S fails to believe all and only the statements that fit her evidence.

(FP2) A person, S, is fallible if there is some p such that S is justified in believing p, but p is false.

Each interpretation of 'mistake' does express a kind of fallibility we are all subject to, but neither interpretation of 'mistake' leads us to a paradox. Let us interpret the fallibility principle in the way suggested in (FP1) and see where that leads us. That sort of mistake is one we are all familiar with. That is the sort of mistake that I think it seems reasonable to think most of us make quite often. Typically, our intellectual rivals show us that our arguments are invalid or that premises in our arguments lack support. We rarely have justified, false beliefs pointed out to us. Usually we find out that we believed irrationally rather than rationally but falsely. Recognition of this sort of fallibility certainly does seem to give us the sort of evidence that justifies most of us in failing to believe that all of our beliefs are true. Most of us lack the evidence necessary for thinking that all of the statements we believe to be true are really true.

If the author in this example has, as Klein puts it, "what seems to be an epistemic characteristic of our nature" then it seems clear that she is not justified in believing the conjunction of all the sentences of her book."1 If she lacks sufficient evidence for thinking that the conjunction is true, she is not justified in believing the conjunction. Thus, it seems that (3) is true. It seems that the author, after recognizing her fallibility ought to believe that not all of the sentences of her book are true.

Though it seems epistemically rational for Mitzi to deny the conjunction of the individual sentences of her book, recognition of her justificatory fallibility does not constitute good enough evidence for believing that not all of the sentences in her book are true. While she lacks sufficient evidence for believing the conjunction of sentence is true, she




does not have enough evidence to think the conjunction is false. All she can justifiably believe is that she probably has one unjustified belief. Some unjustified beliefs are false and some are true. She has no good reason to make the assumption that she has at least one false, unjustified belief. If her book made sense, there is at least as much reason to think her unjustified belief is true as there is to believe it is false. The mere absence of evidence about the truth justifies a different attitude. Absence of evidence supports her suspension of judgment about the conjunction and not disbelief in the conjunction. So, we are not in a position to reasonably think that (3) is true. In order for (3) to be true, we need an example where the person is justified in denying the conjunction; not a case in which she is justified in suspending judgment about the conjunction.

The sense of fallibility captured in (FP2) seems to lend more plausibility to thinking that we have an example where an author ought to deny that all of the sentences of her book are true. If we add the reasonable assumption that she sometimes has justified, false beliefs (i.e. (FP2)) and that she knows this fact about herself, it seems correct to think she ought to believe at least one sentence in her book is false. In order to make this sort of situation plausible, imagine that this author has written several other books. As is true of her current book, suppose that she has worked exceptionally hard and has put all of her books through the scrutiny of the very best thinkers on the subject. Neverthe- less, let us assume she has always wound up believing at least one false statement and she is aware of this fact. It seems that she has a good inductive argument to support believing the denial of the conjunction of the sentences in her current book.

Typically, even authors who work as hard as they can, wind up with at least one false sentence. The length of her manuscript and recognition of (FP2) provide the author with evidence for thinking there is at least one falsehood among the many sentences of her book. So, although (FP1) merely provided evidence for the suspension of judgment about the conjunction of sentences in her book, and did not constitute sufficient evidence for the denial of the conjunction of sentences in her book, it seems as though (FP2) does the trick. Under these circumstances, I think she ought to deny the conjunction of sentences in her book. Thus, let us grant (3).



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Although (FP2) serves as adequate justification for (3), I think the facts about the case, (FP1), and (FP2) provide no good reason to think (1) is true. In fact, I think (FP1) provides reason for doubting (1) is true of any authors of fairly lengthy books. The fact that she worked very hard and has had several great thinkers read through drafts of her manuscript give her reason to think that the book is fairly good. She has reason to believe this book is, on the whole, well justified and mostly correct about the facts. However, putting one's book through hard work and tough criticisms does not give one sufficiently good reason to believe every single sentence is true.

If Mitzi is like the rest of us, she is motivated not only by a healthy quest for the truth, but by deadlines, wishful thinking, and a desire to live a happy life. So too are the most loyal, intellectually curious, brilliant colleagues. Those motivations often conflict and lead us either to believe things we are not epistemically justified in believing or to doubting or denying things that we are epistemically justified in believing. It seems extremely reasonable to assume that none of us who write books are ever actually justified in believing each sentence in our books. Perhaps we have worked hard at researching, but we fail to state all and only justified sentences. We may succeed for the most part, but we no doubt always fail on a few sentences. It seems that thinking that this author's book contains all and only justified individual sentences is very unreasonable if the evidence for that claim is merely that she worked as hard as she could and her ideas survived the careful exami- nation of even the very best critics. If our author and her critics are like the rest of us in this respect, this example poses no paradox because there is no good reason to think (1) is true. Just like all of us, she will not be justified in believing each sentence of her book. Without (1), there is nothing on which to use (CP) to derive (2). So, the paradox is solved before the conjunction principle makes its entry on the scene. Most of us justifiably, and with perfect consistency, believe that not all of a set of our beliefs are true but do not justifiably believe each individual member of the set is true.

What I have shown thus far is that the epistemic version of the example introduced by Makinson is not paradoxical. While (3) is true on a reasonable filling out of the example, we have no reason to think (1) is true.




Unfortunately, things are not that easy. It looks like we can get a paradox back if we change the example and make it more reasonable to think (1) is true. However, I think the circumstances under which (1) is true are very odd and our intuitions about what to think about (3) under such circumstances ought to respect the odd circumstances of the case. It is important to be clear about the sorts of assumptions we are committed to in the preface paradox if (1) is to turn out true. If (1) is true, the example is about a person who, unlike most real authors, is justified in believing each sentence of her book. This is not merely a case in which the author believes or asserts each of the sentences of her book, but it is a case in which she is actually justified in believing each of the sentences of her book. This is not merely a case in which the author believes she is justified in believing each of the sentences of her book, it is a case in which she actually is justified in believing each sentence of her book. In addition, it must be true that she is now, months or perhaps years after researching some of the material, still justified in believing each and every sentence in her book. That is, in some sense or other she must still "have evidence" for each sentence of her book.

Although it is rare, to say the least, that any human being actually is in such remarkable circumstances, it is possible. When we consult our intuitions about what a person is justified in believing under these conditions, let us not forget the unrealistic conditions that we set.

Try to imagine conditions under which an author has sufficient evidence to justify each sentence of her book. One rather convincing case is if Mitzi writes a fairly short and simple book on, say, addition for first graders. It is fairly reasonable to think she will succeed at writing only sentences which are such that each one is justified for her. After all, the subject matter is fairly easy and she is not particularly vulnerable to justificatory errors. If she has several experts on elemen- tary arithmetic mull over drafts of her book, it is very likely that they will catch any unjustified claims she might have made. However, under these conditions, I see no reason for Mitzi to think she has written any false sentences. It seems more than reasonable to think that her colleagues reading the manuscript would rather easily find both sorts of mistakes. Furthermore, it seems that the evidence gained by having all justified individual sentences in a short and simple manuscript should



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add up to justify her belief in the conjunction. Since the individual beliefs in such a case are so securely justified, it seems that the conjunction is secure as well. The conjunction is not as vulnerable to error as it would be under more ordinary circumstances. In the conditions of this example, failing to believe the conjunction of all the sentences would be overly modest and epistemically unjustified. So, this example seems to be one where Mitzi ought to believe each of the sentences of her book is true but she should also believe that all of the sentences of her book are true. Hence, if (1) is true, (3) is false.

A defender of the paradox might bring the inductive argument stated earlier, to bear on this example. Although that argument seemed reasonable in the original case, I think it fails under the conditions of this example. To begin, if one is to use induction from past cases, the past cases must be similar in all relevant respects. It is difficult to believe that she has written several other books on addition for first graders, has had all justified sentences, but always manages to believe and write at least one false sentence. However, suppose that contrary to what seems likely, that this has happened several times before. If so, she does have some inductive evidence to justify her belief that probably not all of the sentences in this most recent book are true. She ought to consider that evidence when she decides whether or not to believe that she has all true sentences in this book. She does, we should not forget, have a lot of other evidence to use in making a judgment about the conjunction of sentences. In addition to the inductive argument, she has, we have supposed, good evidence for each sentence in her book. Again, this is not true for most of us when we make judgments about the truth value of a set of beliefs. Most of us are confident that we lack this evidence when we ask ourselves if we believe that all of some set of our beliefs are true. Our author is in an exceptionally epistemically privileged position. She actually has evidence that supports each sentence of her book. That is a whole lot of evidence. I think the evidence supporting each of the individual conjuncts adds up and outweighs the inductive evidence this author has about believing a falsehood. No matter how many books she writes and winds up with a false sentence, if the books are short and on such simple topics, and each of the sentences is actually justified for her, she should always think that all of the sentences are true.




My position may seem to go against common sense. After all, if she has always and not merely sometimes made a mistake when reasoning under these conditions, it seems that she should think she made one now, in this book. Perhaps it is true that my position goes against general common sense. However, so do the conditions of this example. What matters when we consult our intuitions about this case is not general common sense, but as much common sense as we can muster under these circumstances. These circumstances are of an author who has written several short and simple books about addition for first graders. In each book she is justified in believing each individual sentence. That is not an ordinary situation. She becomes justified partly on the basis of the testimony of the approval of her proof readers on this short and simple book. Nevertheless, she amazingly states a false claim every time. Common sense under these weird conditions tells me that she ought to believe that this odd situation of getting false beliefs will not happen again, no matter how many times it did happen. She should not have expected it to happen in the past for such simple and well researched material, and she should not expect it to happen in the future. If she was diligent enough to believe all and only those statements she was justified in believing in those other books, she was not justified in thinking she would make a mistake in any of her past books. She did have justified, false sentences in those other books and perhaps she will have one or more false sentences in the book for which she is writing the preface. She is justified in thinking she might, despite her best efforts, have believed a justified false sentence this time. But she is not justified in thinking she actually has believed at least one false sentence this time. Thus, I think the author in these circumstances ought to believe all the sentences of her book are true and she should not believe she made a mistake.

If she ought to admit that she made a mistake somewhere or other in her book, it is a moral, or practical, or socially constructed, obligation. To do so would show a kind of modesty that is sometimes valued as a character trait. However, if she continues to be rational, she will not believe that she really has made a mistake. Since (3) is not true in this case, it is not available to be conjoined with (2) to justify (4). Hence, there is no paradox found in this second, preface paradox example either. I think this will be true in all plausible versions of a preface



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paradox example. Whenever the conditions are odd enough for it to seem reasonable to hold that each of a set of individual beliefs is justified for a person, it seems most reasonable to think the conjunction is justified on the basis of the justified, individual statements.

Consider a third version of the preface paradox example. Suppose our author of the book on addition has a new group of experts show up on the scene and they tell her that she asserted a falsehood somewhere in her book but they do not say which assertion is false. This version seems to bear a resemblance to the lottery paradox.12 However, there is an important difference. In this case, I think the person does not know, or have a justified belief, that one sentence is false. I think she ought to think these experts are wrong. As the story goes, she has gathered evidence for each sentence of her book and she and a bunch of other experts have already rationally approved of each sentence of her book. Remember, she is not merely justified in believing she is justified in believing each sentence. She is really justified in believing each sentence. I do not think this new evidence offered by the new experts is worthless, but until she is shown the errors of her ways, she ought to hang on to her beliefs. If we add to the example that the experts show her which belief is false and they explain why, then Mitzi ought to revise her beliefs. Once she is given specific evidence to the contrary, by being shown which belief is false and why, she ought to deny the conjunction. But then, her evidence no longer justifies her in believing each of the individual sentences. So, on close inspection, this third version of the example also fails to pose a paradox.

Consider a fourth version. This time, imagine an author who is exactly like all the best scholars. She works hard and is smart and modest enough to think that she is subject to both types of fallibility. Imagine that she writes a long, rather complicated book and has several people whom she knows and respects read drafts of her manuscript to catch any errors. Imagine also, that by a stroke of good luck and hard work, she happens to have actually stated all and only justified sentences in her most recent book. In addition, suppose that in the past she has had errors pointed out to her of both sorts after the publication of her book. That is, she has stated unjustified claims and false claims in other books and she knows it. So, in this case, the only unusual feature is that she is in fact justified in each sentence. Now, the facts of the case definitely support (1).




In this case, the length of her manuscript and her past failures constitute good reason for her to believe that she is not justified in believing all of the sentences are true. In this story, the author is not justified in thinking that she is actually justified in believing each individual sentence of her book either. Remember, unbeknownst to her she happens to be lucky. Thus, the following is true in this fourth version of the preface paradox example:

(1*) - JS (JS(s1) & JS(s2) & . JS(sn)

(2*) - JS ((s1 & s2 & .S)

It might be argued that the evidence of past failures, and the fact that the book is so long and complicated, justifies Mitzi in believing that at least one sentence in this book is false. Thus, one might argue that (3) is true.

While I think Mitzi is not justified in thinking so, (3) is actually false in these circumstances. Mitzi has a lot of strong evidence for believing the conjunction of her individual sentences. As luck has it in this story, Mitzi actually is justified in believing each of the individual conjuncts. This evidence adds up to justify the conjunction. The denial of the conjunction is not what Mitzi's evidence actually supports.

However, I will grant that Mitzi is not justified in believing that she is justified in believing the conjunction of individual sentences in her book. However, this is a meta-belief, and is captured by (2*), not (3). Even though (3) is false, Mitzi is not justified in believing (3) is false. This is because Mitzi is not justified in believing she got lucky. In order to justifiably believe (3) is false she would need a good reason for thinking she made no mistakes. So although Mitzi actually is justified in believing each sentence, and the conjunction of those individual sentences, she is not justified in believing she is justified in believing each sentence of her book and the conjunction of those individual sentences. Thus, with regard to her meta-beliefs, Mitzi is not justified in believing (1) is true, she is not justified in believing (2) is true, and she is not justified in believing (3) is false. Nevertheless, with regard to her first-order beliefs, (1) and (2) are true, but (3) is false. So, once again, the story fails to provide a convincing case in which (1) and (3) are both true.

Thinking about this example in the way I have argued that we



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should, has a slightly odd and interesting result, but not a paradoxical result. The result of my solution is that one is not always justified in believing that one is justified in believing a statement p when one is justified in believing p. That does not seem like such a bad view.

I have shown that the examples I have considered as potential examples of a preface paradox about epistemic justification, are not paradoxical after all. I think most hard working, intellectually respon- sible authors are actually in a situation in which they should believe, 'Most of the sentences in my book true' and 'Not all of the sentences of my book are true.' Those beliefs are both consistent and rational. Convincing cases in which a person is actually justified in believing each sentence in one's book are cases in which it is most reasonable to think that the person is also justified in believing the conjunction of those sentences are true. In such cases, tradition about what to write in a preface is a declaration of modesty and not rational belief. On the other hand, cases in which it seems reasonable for a person to deny the conjunction of sentences in her book seem to be cases in which the person is not justified in believing the individual conjuncts either. A convincing example in which (1) and (3) are both true has not been given. Perhaps such a case is possible. I have certainly not established that such a case is not possible. I invite someone to construct such a case.

Without denying the Conjunction Principle or the No Known Contradictions principle, the preface paradox has been solved. The preface paradox does not force us to abandon the intuitively plausible assumption that believing a set of statements that one knows to be inconsistent is never epistemically justified or rational. Other paradoxes may threaten that assumption.13 The preface paradox, however, has proved to be a false alarm.14

NOTES

1 For interesting discussions of this assumption, see Richard Foley "Justified Incon- sistent Beliefs," American Philosophical Quarterly 16 (October 1979): 247-257; Peter Klein "The Virtues of Inconsistency," The Monist (January 1985): 105-135; Keith Lehrer "Reason and Consistency," Analysis and Metaphysics (ed.) Keith Lehrer (Dordrecht: D. Reidel Publishing Company, 1975), 57-74. 2 D.C. Makinson, "The Paradox of the Preface," Analysis, 25 (1965): 205-207.




I Graham Priest "Contradiction, Belief, and Rationality," Proceedings of the Aristo- telian Society 86: 99-116. 4 Klein, "The Virtues of Inconsistency". 5 Henry Kyburg, "Conjunctivitis" in Marshall Swain, ed., Induction, Acceptance, and Rational Belief (Dordrecht: D. Reidel Publishing Company, 1970), 55-82. 6 D. C. Makinson, "The Paradox of the Preface". 7 Klein, 132. 8 Klein, 123. 9 Klein, 131.

0 Klein, 131. l Klein, 131. 12 See Kyburg's "Conjuctivitis" for the original statement of the lottery paradox. 13 See chapter five of my doctoral dissertation, Rational Belief in the Impossible (University of Rochester: 1991), to see that the lottery paradox also fails to refute this assumption. 14 I am grateful to Earl Conee, Randall Dipert, Thomas Donahue, Richard Feldman, Marvin Kohl, Kenneth Lucey, David Palmer, Morton Schagrin, Raymond Wong, and an anonymous referee from Philosophical Studies for helpful comments on previous drafts of this paper.

Department of Philosophy West Virginia University Morgantown, WV26506 USA



The Preface Paradox

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