Non-Cognitivism and Inconsistency

zyxwv zyxw zyx zy The Southern Journal of Philosophy (1995) Vol. X X x I l l Non-Cognitivism and Inconsistency Folke Tersman Stockholm University There are many familiar ways in which moral discourse resembles factual discourse: moral opinions a r e expressed by sentences in the declarative mood; moral judgments occur i n propositional attitude contexts (“I believe that this is wrong,” etc.); we sometimes wonder if our moral opinions are incorrect; and so forth. This is acknowledged by moral realists and non-cognitivists alike, but, for obvious reasons, they relate differently to this resemblance. For realists, it provides arguments, and for noncognitivists, i t provides potential trouble. Realists claim that the various points of resemblance between moral and factual discourse indicate that moral discourse simply is a kind of factual discourse.’ However, in recent years a number of interesting attempts have been made in trying t o show that the realist appearance of moral discourse can after all be accommodated within a non-cognitivist view.2 Some points of resemblance between moral and factual discourse arise from the way we reason concerning moral issues. For instance, in moral reasoning, as in reasoning concerning matters of fact, we seek consistency. We tend to criticize a person whose moral opinions we find t o be inconsistent, and when inconsistency is exposed among our own moral views, we are inclined to revise them in such a way that the inconsistency is eliminated . A possible argument against non-cognitivism, along the line indicated above, is that it fails t o render this concern for consistency reasonable. If moral judgments essentially express statements capable of being true and false, there is a seemingly straightforward explanation of why we should seek con- zyx zyxwvu Folke Tersman is Assistant Professor of Philosophy at Stockholm University, Sweden. His doctoral dissertation examines the notion of reflective equilibrium, and his previous publications include “Utilitariani s m a n d the Idea of Reflective Equilibrium,” (Southern J o u r n a l of Philosophy 1991, vol. 29) and “Coherence and Disagreement,” (Philosophical Studies 1992, uol. 65). 361 zyxwv Folke Tersman sistency. At least one of the members of an inconsistent set of factual claims must be false. Thus, if we wish t o avoid accepting falsehoods, we should avoid inconsistencies. However, if moral judgments essentially express attitudes, this explanation will not do. Indeed, if we accept non-cognitivism, it might seem pointless to detect and eliminate inconsistencies among our moral views.4 The purpose of this paper is t o examine this argument. I will argue t h a t i t fails: non-cognitivism can adequately account for this particular piece of moral phenomenology. zyxw NON-COGNITMSM VERSUS MORAL REALISM I contrast non-cognitivism with moral realism. This might seem misleading in view of the fact that non-cognitivism is often conceived as a purely semantical thesis, while realism essentially involves ontological claims. However, I assume t h a t both positions involve semantical as well as ontological claims. What distinguishes these positions? Realists typically claim t h a t moral judgments a r e capable of being true.5 However, since the development of deflationary accounts of truth, this claim is accepted also by many non-cognitivists. Even the wellknown emotivist C. L. Stevenson insisted in his later writings that moral judgments may be true, since calling a moral judgment true is an appropriate way of expressing one’s agreement with it.6 Recent suggestions along t h i s line a r e made by, among others, Paul Horwich, who defends a “minimalist’?account of truth which he thinks lends support to the claim that normative judgments have truth value^.^ But non-cognitivists who hold that moral judgments are capable of being true may perhaps deny other views t o which rea l i s t s a r e committed, for instance t h e view t h a t moral judgments express beliefs a n d factual claims r a t h e r t h a n merely attitudes.8 To some extent, however, t h i s does also seem t o misrepresent the non-cognitivist position. Some noncognitivists, such as Stevenson and Allan Gibbard, admit that moral judgments do in certain cases express straightforward factual claims. According t o Gibbard, this holds for so-called thick judgments, such as “Jim is getting uppity,” which in a certain context (the old American south) expressed the claim that Jim is no longer abasing himself before white^.^ However, Stevenson and Gibbard deny of course that moral judgments only express factual claims. They also hold t h a t moral judgments express attitudes, and that accepting a moral judgment essentially involves having a desire or tendency to act. To emphasize this, Gibbard suggests t h a t someone may accept the factual claims t h a t might be expressed by a moral judgment, and still, without confusion or inconsistency, reject the judgment.1° This is presumably denied by realists. zy 362 Non-Cognitivismand Inconsistency zyxw zyx But non-cognitivists can accommodate the claim that moral judgments express beliefs a n d factual claims in other and more general ways than to appeal to thick judgments. For instance, non-cognitivists could argue t h a t , although having a moral view is to have a desire, this state is also a belief, since i t is properly expressed by a sentence which is either true or false (given, for instance, a “minimalist” account of truth).” Realists may reply that this notion of belief conflicts with the Humean view which assigns distinctly different roles to beliefs and desires in the production of actions. But then again, some realists are not Humeans.12 Another claim typically made by moral realists is t h a t there a r e moral facts, and t h a t these exist independently of us.13 This claim is denied by some non-cogniti~ists.’~ However, if non-cognitivists can claim that i t is true that, say, an action is right, I see no reason why they must deny that this truth is a fact. Nor need they deny t h a t the wrongness of the action depends on, say, its consequences rather than their own feelings o r thinking^.'^ So, in claimingldenying t h a t t h e r e a r e moral facts, the participants of this debate have presumably a more robust notion of fact in mind, and this notion remains to be clarified. In any case, I will not explore these issues any further. In defending the claim that a non-cognitivist can account for our concern for moral consistency, I wish to employ premises which are as uncontroversial as possible. I will only make one crucial assumption about non-cognitivism: that it implies that having a moral view involves having a desire. In particular, I will not assume that non-cognitivists are entitled t o appeal t o moral facts, or to the aim of avoiding false beliefs, in trying t o account for our concern for moral consistency. INCONSISTENCY This leads t o another issue. In denying non-cognitivists the right to appeal t o moral truth and falsity, we also deny them a standard notion of inconsistency. According to this notion, a set of beliefs or statements is inconsistent if and only if i t is logically necessary t h a t a t least one of its members is false. How, then, should the notion of inconsistency be interpreted in this context? There have been many a t t e m p t s to construe a noncognitivist notion of moral inconsistency, and I will not try to adjudicate between these. My arguments for the claim t h a t non-cognitivism can account for our concern for moral consistency do, of course, rest upon assumptions about what, according t o non-cognitivism, moral inconsistency involves. For instance, I assume that a person has inconsistent moral views only if she has desires all of which cannot be satisfied.16 How- 363 zyxwv zyxw Folke Tersman ever, this and other assumptions presupposed by my arguments could be justified given many different non-cognitivist notions of moral consistency. Notice t h a t there is a limit t o how inconsistent a person can be, both with respect t o her beliefs and her desires (in the senses indicated above). The reason is that, unless we assume that a person is to a great extent consistent, we would not be able t o achieve knowledge of her beliefs and desires merely on the basis of her observable behavior. Since this is in principle possible, given the intrinsically social nature of language, we may conclude t h a t she is t o a large extent consistent. However, some inconsistency is surely possible, both among beliefs and desires. Thus, the question of why inconsistency should be avoided is still a live EXPLAINING AND JUSTIFYING We should distinguish between two ways for a noncognitivist t o account for our concern for moral consistency. One is t o explain why we have this concern. Another is t o show that it is justified or reasonable.18 A possible position for a non-cognitivist to take is to deny that our concern for moral consistency is rational, and t o argue t h a t i t is sufficient to account for i t i n the first way. On the other hand, assuming t h a t we generally do care about moral consistency, it might seem implausible t o attribute such an amount of irrationality. Therefore, if a non-cognitivist can rationalize our concern for consistency (and other features of moral discourse t h a t contribute to its realist appearance), a possible argument against non-cognitivism is blocked. According to Blackburn, this is indeed the most powerful argument available to a r e a 1 i ~ t .Anyway, l~ the aim of this paper is t o consider if a non-cognitivist can account for our concern for moral consistency in the second way. zy PRAGMATIC JUSTIFICATIONS OF MORAL CONSISTENCY Thus, the crucial question is: can a non-cognitivist justify our concern for moral consistency? This concern consists mainly in a disposition t o revise one’s moral views when these are shown to be inconsistent, and to make efforts in trying t o detect such inconsistencies. One obvious way of justifying this disposition is t o show that it is bad or undesirable for a person to have inconsistent moral views. A person whose moral views a r e inconsistent has desires all of which cannot be satisfied. One suggestion to the effect that it is bad or undesirable to have inconsistent moral views is t h a t a t least one of the desires of a person in such a state 364 z Non-Cognitivism and Inconsistency zyx must be frustrated. Lars Bergstrom objects t o this suggestion on the ground t h a t there need not be anything irrational in having a desire which will inevitably be frustrated. However, it may still be undesirable t o be in such a state.20 Another suggestion t o the effect t h a t i t is bad t o have inconsistent moral views is that inconsistent moral views would fail to provide practical guidance in certain situations, and thus perhaps lead to paralysis or inefficient behavior.21Indeed, Blackburn thinks that this reasoning shows why inconsistent desires in general are bad in a way quite analogous to the way in which inconsistent beliefs are bad. The latter cannot represent the world properly; but the former cannot represent how to behave in the world properly: they cannot mate together with beliefs, in the usual belief-desire psychological framework to direct effective action.22 This suggestion is also rejected by Bergstrom, partly on the ground that paralysis “may be a quite appropriate response in some situation^."^^ However, a non-cognitivist could reply that, although having inconsistent desires may not be irrational in general, the aim of engaging in moral thinking is t o formulate views which helps one t o avoid paralysis and to obtain practical guidance in situations t o which moral considerations apply, and a person whose moral views are inconsistent has failed t o achieve this aim.24Bergstrom might object that some people do not have this aim, but the realist faces the same kind of objection: some people may not want to avoid false beliefs. Moreover, Bergstrom’s claims show a t most t h a t a noncognitivist view cannot explain why it is always bad or irrational to have inconsistent moral views. It might still be bad in m a n y situations-e.g., in situations where paralysis is undesirable. This is important since the crucial question here is whether a certain disposition is rational-to seek consistency among one’s moral views-and the fact, if i t is one, t h a t i t is bad in many cases to have inconsistent moral views may suffice to justify our having this disposition. Anyway, a non-cognitivist can appeal to other considerations. She may claim that if a person has inconsistent moral views, this may negatively affect the ways in which others are likely to treat her. For instance, a person whose moral views are inconsistent may be disposed to utter contradictory recommendations, and this may lead others to regard her as “an unreliable source of practical advice.”25Moreover, a person whose moral views are inconsistent may be unpredictable in certain situations, and this may negatively affect the willingness of others t o cooperate with her.26 A suggestion along this line is made by Allan Gibbard. According to Gibbard, normative discussion plays a crucial role zyxw 365 zyxwv Folke Tersman in the coordination of actions, feelings, and expectations. This is partly because normative discussion tends towards consensus, which in turn is due t o the fact that the participants are responsive to demands for consistency-that is, disposed to revise t h e i r views when these a r e shown t o be inconsistent. Someone who does not have this disposition will usually fail to engage others in normative discussion. This is a serious loss, since the benefits of being able to do so are extremely important.27 Gibbard thinks t h a t these considerations directly justify only a limited concern for consistency-a responsiveness t o demands for “local” consistency. This kind of consistency falls short from t h e “global” kind t h a t philosophers seek, a n d amounts roughly to a willingness t o accept judgments “all see a s following” from what one claims in normative discussion. However, Gibbard holds that things may be said also in favor of seeking global consistency. Being responsive to demands for local consistency involves the risk of finding oneself committed t o accept normative conclusions that follow from what one has claimed in normative discussion, but that one finds unacceptable. A person who h a s achieved global consistency h a s already confronted and considered these possibilities, and has been able to revise her views so as to avoid such unacceptable conclusions. According to Gibbard, she has made herself “proof against sophistry andproof against the push of logic t o faiaticism.”28 But Gibbard admits that there are cases where it would be unreasonable t o seek consistency. The search for consistency has costs-it takes effort and time-and these may sometimes outweigh its gains. Moreover, normative discussion might in certain cases yield a consensus which i t would be better for some of the participants t o avoid, and the benefits of normative discussion may be achieved also by someone who is not responsive to demands for consistency, since it suffices that one a p p e a r s to be s o disposed, and this appearance may be produced through hypocrisy and skilled fudging.29 Similar things may be said about other suggestions taking a s their point of departure the importance of appearing as if one cares about consistency-one can appear this way and be in another. On the other hand, trying t o appear to be what one is not has costs of its own, and may require more skill and effort than one can muster. A non-cognitivist can appeal to yet other considerations. In the spirit of Gibbard‘s suggestions, she may focus less on what is bad i n the s t a t e of having inconsistent moral views, and more on what is good in the activity of seeking consistency. For instance, engaging in this activity requires working out the implications of one’s moral views, and this might help one in applying them. zyxwv zy 366 Non-Cognitivism and Inconsistency I could mention f u r t h e r considerations t o which a noncognitivist can appeal, but I will spare the reader. I think t h a t those already mentioned a r e enough to indicate why at least some concern for moral consistency m a k e s sense. However, they do not show t h a t it is always bad or irrational to have inconsistent moral views, nor t h a t it is always rational to seek consistency. Sometimes paralysis may be appropriate. Sometimes it is good to be unpredictable. Sometimes hypocrisy and fudging might be better t h a n actually being concerned about consistency. zyxw zyxwvu REALISM AND INCONSISTENCY Before assessing t h i s conclusion, I will t u r n t o a n o t h e r question: why a r e realists supposed to be in a better position to justify our concern for consistency? I have assumed t h a t realists, unlike non-cognitivists, can appeal to t h e aim of avoiding false beliefs in trying to justify our concern for consistency, but why is this supposed to make all the difference? Bernard Williams suggests t h a t t h e crucial difference between this justification a n d the various pragmatic justifications mentioned i n t h e previous section is t h a t t h e former is “ e x c e p t i o n l e ~ s .This ” ~ ~ could mean t h a t a realist can explain why it is always bad or irrational to have inconsistent beliefs. Lars Bergstrom illustrates how: zyxwvu What is wrong with having inconsistent beliefs? The general answer to this question is, I think, that inconsistent beliefs are necessarily mistaken and that we do not want our beliefs to be mistaken. In so far as our beliefs are factual, the whole point of having them is that they should correspond to the facts, and inconsistent beliefs cannot correspond to the facts (whatever the facts are).31 I n other words, since we wish to avoid false beliefs, a n d since the fact t h a t one’s beliefs are inconsistent implies t h a t at least one of t h e m is false, it is irrational to have inconsistent beliefs. The problem with t h i s argument is t h a t we do not merely w a n t t o avoid false beliefs. We also want to believe truthsotherwise we should simply avoid belief altogether. I n other words, i n epistemic m a t t e r s , we have (at least) two aims: to believe t r u t h s a n d not to believe falsehoods. Does this double aim explain why it is always irrational to have inconsistent beliefs? It seems not. I believe t h a t a t l e a s t one of my beliefs is false, b u t I do not know which. This makes my system incon. ~ ~insistent, but it is not clear t h a t it makes me i r r a t i ~ n a lFor s t a n c e , I could s t i l l , surely, h a v e r e a s o n s for e a c h of my 367 zyxwv Folke Tersman beliefs, s o t h a t each of them is justified, a t least to some extent. Moreover, eliminating this inconsistency would require either rejecting many beliefs in which I am not completely certain, or the belief that a t least one of my beliefs is false (to which I am actually quite strongly attached). When each of these beliefs stands a good chance of being true, neither of these options seems a t t r a ~ t i v e . ~ ~ A fall, t e r my aim is not merely t o avoid falsehoods, but also t o believe But perhaps there are other ways for a realist to argue t h a t i t is always irrational t o have inconsistent beliefs. For instance, as Karl Popper has reminded us, any claim, including contradictory claims, follows logically from a n inconsistent set of Thus, i t might be argued, if it would be rational for a person t o have inconsistent beliefs, i t would also be rational for her to accept contradictions. Since this is clearly irrational, it is irrational t o have inconsistent beliefs. An essential premise of this argument seems t o be that i t is rational t o accept what follows from one’s beliefs, a t least t o the extent t h a t one’s beliefs a r e rational. This premise seems dubious. Whatever my beliefs are, they imply any necessarily true claim, including complicated logical theorems. However, the mere fact t h a t these theorems follow from my beliefs does not make i t rational for me to accept them, regardless of whether my beliefs a r e rational. For instance, I could have been told by a n otherwise reliable logician t h a t some of these claims are proven false. However, a realist can respond t o the claim t h a t i t need not be irrational to have inconsistent beliefs in other ways. For instance, she may point out that this only shows that the “badness” of having inconsistent beliefs may be outweighed by other considerations, and that a crucial difference between a realist and a non-cognitivist is t h a t a realist can explain why there is always something bad in having inconsistent moral views, namely that at least one of the beliefs of a person in such a state must be false. On the other hand, something very similar may be said by a non-cognitivist: there is always something bad in having inconsistent moral views, since a t least one of the desires of a person in such a state must be frustrated. Notice t h a t , by claiming t h a t i t need not be irrational to have inconsistent beliefs, I do not wish to deny that a realist can explain why detecting and eliminating inconsistencies among one’s views is reasonable as a general strategy. For instance, she might argue that inconsistent beliefs would fail to provide practical guidance in certain situations, and thus perhaps lead t o paralysis. Or she might claim that being engaged in a certain “scientific” practice, where eliminating inconsistencies is an essential part, helps t o obtain interesting true beliefs in the long run. zyxwv 368 Non-Cognitivism and Inconsistency However, as we saw, a non-cognitivist can also justify seeking consistency. Of course, a non-cognitivist cannot justify seeking consistency at all costs, but nor can the realist. Time shortage, limited recourses of brain circuitry, and so forth, may make it unreasonable for a person t o try to eliminate all inconsistencies in her system, especially if she has reason to believe t h a t these inconsistencies will not in any serious way prevent her from achieving other aims (i,e., other t h a n the double aim of believing truths and not believing falsehoods). CONCLUSION zy There may still be a difference in degree. Unlike a noncognitivist, a realist can appeal to the aim of avoiding false beliefs. She can therefore, perhaps, justify a more strict concern for consistency. On the other hand, our concern for moral consistency may not be that strict. Maybe we care less about consistency among our moral views t h a n among beliefs in other areas. This might even suggest that realists in a sense misrepresent our concern for moral consistency by rationalizing i t in the same way as our concern for consistency in other areas. In any case, I conclude t h a t this particular piece of moral phenomenology does not provide a reason to prefer moral realism to non-cogniti~ism.~~ zyxwvu zyxwvu zy zyx NOTES See, e.g., Brink, D., Moral Realism and the Foundation of Ethics (Cambridge: Cambridge University Press, 1989), esp. chapter 2. Simon Blackburn and his “quasi-realism” provides a prominent example, although he prefers the term “projectivism”to “non-cognitivism.” See, e.g., Spreading the Word (Oxford: Oxford University Press, 1984), esp. chapter 6.See also Gibbard, A., Wise Choices, Apt Feelings (Oxford: Facts and Clarendon, 1990), esp. chapters 8 through 13, and Price, H., the Function of lkuth (Oxford: Blackwell, 1989). In what follows, I simply take it for granted that we have this concern for consistency, although different persons may have it to different extents. According to Lars Bergstrom, this is a reason for accepting moral realism. See his “Outline of a n Argument for Moral Realism,” Grazer Philosophische Studien 12/13 (1981), 215-225. See also Schueler, G. F., “Modus Ponens and Moral Realism,” Ethics (1988), 501-517, and TBnnsjo, T.,Moral Realism (Savage, Maryland: Rowman & Littlefield, 19901, 119-121. See, e.g., Brink, Moral Realism, 7, and Boyd, R., U H ~ to w Be a Moral Realist” in Sayre-McCord (ed.), Essays on Moral Realism (Ithaca: Cornell University Press, 1988), 182. By “moral judgments” I refer to the sentences we use when expressing moral opinions: i.e., sentences typically containing words such as “good,””right,” and so on. See, e.g., Facts and Values (New Haven: Yale University Press), 216. 369 zyxw zyxw zyxwvu zyxwvu zyx Folke Tersman ’ See Horwich, P., “Gibbard’s Theory of Norms,“ Philosophy and Public Affairs 22 (19931, 67-78. I n fact, t h e literature is full of noncognitivists who are willing to claim that moral judgments may be true. See, e.g., Blackburn, Spreading the Word, p. 196, and Smart, J. J. C., Ethics, Persuasion and Truth (London: Routledge a n d Kegan Paul, 19841, 97. Stevenson insisted t h a t t h e fact t h a t a moral judgment is either true or false shows “nothing whatsoever about whether it expresses a belief or a n attitude” (Facts and Values, 216). Gibbard, Wise Choices, 113. See also Stevenson, Facts and Values, 9, 16, 169, 206, and 221. lo Gibbard, Wise Choices, 119. See also Stevenson, Facts and Values, 15, 30. l1 For suggestions along this line, see Horwich, “Gibbard’s Theory of Norms,” Divers, J., a n d Miller, A,, “Why Expressivists about Value Should Not Love Minimalism about Truth,” Analysis 54 (1994), 12-19, and Blackburn, S., “Attitudes and Contents” in Essays in Quasi-Realism (New York: Oxford University Press, 19931, 185. l2 See, e.g., Dancy, J., Moral Reasons (Oxford: Blackwell, 1993), esp. chapter 1, and McDowell, J., “Are Moral Requirements Hypothetical Imperatives?” Proceedings of the Aristotelian Society 52, suppl. (19781, 1329. See, e.g., Bergstrom, “Outline of a n Argument for Moral Realism,” 216-217, and Brink, Moral Realism and the Foundation of Ethics, 7. l4 See, e.g., Gibbard, Wise Choices, 23. See Blackburn, Spreading the Word, 217-220, and Gibbard, Wise Choices, 164-166, about this. See, e.g., Blackburn, “Attitudes and Contents,” 188-197, for a suggestion along this line. l7 For one of many defenses of the reasoning i n this paragraph, see Donald Davidson’s “Belief and the Basis of Meaning,” reprinted in Inquiries into Truth and Interpretation (Oxford: Clarendon Press, 19841, 141-154. See also my “Coherence and Disagreement,” Philosophical Studies 65 (1992), esp. 308-311. Since I assume t h a t inconsistency is possible, I need not elaborate this point. l8 It might be discussed to what extent these ways are distinct, given that explaining intentional behavior necessarily involves some element of rationalization. However, as long as we accept t h a t irrational behavior is possible, we can coherently hold that they are distinct. l9 “Errors and the Phenomenology of Value,” in Honderich, T. (ed.), Morality and Objectiuity (London: Routledge and Kegan Paul, 19851, 1112. 2o In fact, Bergstrom seems to agree with this. See “Outline of a n Argument for Moral Realism,” 221. 21 See, e.g., Blackburn, Spreading the Word, 195, and “Attitudes and Contents,” 190-191. See also Williams, B., “Consistency and Realism” in Problems of the Self (Cambridge: Cambridge University Press, 1973), 205. 22 Blackburn, “Attitudes and Contents,” 190. 23 Bergstrom, “Outline of a n Argument for Moral Realism,” 221. 24 Blackburn argues that inconsistent moral views “cannot fulfil the practical purposes for which we evaluate things.” (Spreading the Word, 195.) 25 J. J. C. Smart made this point i n Ethics, Persuasion and Truth, zyxw zyxwvu 370 zyx zyxwvu zyxwvut zy zyxw zyx Non-Cognitivism and Inconsistency 18-19. 26 The advantages of being predictable a r e explored by Robert Axelrod in The Evolution of Cooperation (New York: Basic Books, 1984). 27 Gibbard, Wise Choices, 73-75 and 287-291. Notice t h a t Gibbard thinks t h a t these considerations not only explain why we should care about normative consistency, but also why we do care, since they indicate that being responsive to demands for consistency in normative discussion is fitness-enhancing. 28 Gibbard, Wise Choices, 290. Gibbard’s reasoning a t this point is not transparent, nor is my account of it. However, since it h a s little bearing on the argument in this paper, I disregard this shortcoming. 29 Gibbard, Wise Choices, 288, 291. 30 Williams, “Consistency and Realism,” 201. 31 Bergstrom, “Outline of a n Argument for Moral Realism,” 219. Notice that there is a n ambiguity here. The fact that a set of beliefs is inconsistent implies t h a t it is necessary t h a t at least one of them is mistaken, not t h a t any of them is necessarily mistaken. Of course, the conjunction of these beliefs is necessarily mistaken, but a person need not accept this conjunction just because she accepts its conjuncts. I will return to this point. 32 For a discussion about this, see Foley, R., The Theory of Epistemic Rationality (Cambridge: Harvard University Press, 1987), esp. 241-260. 33 To see how each of a n inconsistent set of claims can stand a good chance of being true, consider this lottery case: the lottery contains one billion tickets and only one winner. For each of the tickets, the probability of the claim that it will not win is extremely high. However, the conjunction of these claims (that ticket number one will not win, that ticket number two will not win, and so on) and the claim that one of the tickets is the winner is inconsistent. 34 There are other obvious ways of arguing that it need not be irrational to have inconsistent beliefs. For instance, someone may have inconsistent beliefs and still, for good reason, believe t h a t her beliefs are consistent. 36 Conjectures and Refutations (London: Basic Books, 1962), 317, 319. 36 I wish to t h a n k L a r s Bergstrom, H a n s Mathlein, Christian Munthe, and Torbjorn Tannsjo for valuable comments on a n earlier version of this paper. 371