WHY WE BELIEVE

MARIAM THALOS?

SUMMARY. The radical probabilist counsels the prudent never to put away uncertainty, and hence always to balance judgment with probabilities of various sizes. Against this counsel I shall advise in favor of the practice of full belief – at least for some occasions. This advice rests on the fact that it is sometimes in a person’s interests to accept certain propositions as a means of bringing it about that others recognize oneself as having accepted those propositions. With the pragmatists, therefore, I shall reject the view that belief formation must in every instance be a truth-directed affair. Unlike the pragmatists, however, I shall conclude that the enterprise of belief formation is not directed exclusively, or even primarily, at attaining knowledge. In other words, pursuit of that which it profits to believe, on the one hand, and pursuit of knowledge on the other, are distinct enterprises, which overlap (when they do) only accidentally. Key words: knowledge, full belief, epistemology, radical probabilism, instrumentalism, pragmatism, bayesianism

1. A PROBLEM OR TWO ABOUT FULL BELIEF

At the zenith of controversy over the legitimate form of inductive inference in science – an enterprise still held up for emulation to all who aspire to be rational, despite its fortunes post sociology of knowledge – a certain proposal was put forward which I will refer to here as the threshold proposal. According to this proposal, a contingent proposition gains entry into the body of belief, if and only if the probability conferred upon it, by the evidence at hand, meets or exceeds a threshold value. The threshold proposal is a normative one. It counsels two things: (1) categorial division of propositions into the accepted and the unaccepted, and (2) a single threshold principle, formulated in quantitative terms, whereby to divide the universe of contingent propositions. According to the threshold proposal, ? Thanks to Henry Kyburg, John Kearns and Barry Smith for very helpful comments

on earlier drafts, and to numerous anonymous referees. Journal for General Philosophy of Science 30: 317–339, 1999. © 1999 Kluwer Academic Publishers. Printed in the Netherlands.

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this procedure is what rationality – as a precondition for receptivity to epistemological directives – demands. In those days Henry Kyburg advanced considerations to the effect that, if we retain a two-category division of propositions as counseled in (1), the threshold principle (2) faces two grave difficulties that pull in opposing directions, so that both difficulties cannot be solved together. The first, and more celebrated difficulty, is that no threshold set below the level of absolute certainty can be set high enough to protect against inconsistency.1 For no matter how high the threshold level for acceptance is set, so long as it is set below absolute certainty, the body of accepted propositions can be anticipated to become inconsistent under ordinary circumstances. So suppose that a lottery is announced by an exceedingly reputable firm, and that potential ticketholders are solemnly assured that one ticket will be drawn from among one million. It is widely published that for any given ticket, its probability of being drawn is one in a million. So for any given ticket, its probability of not being drawn is one minus one in a million – very high. Let us assume this figure exceeds the threshold value. (Naturally, if it does not exceed the threshold value you favor, we simply sell more lottery tickets.) If you proceed on the advice of the threshold proposal, you will adopt each of one million propositions, each to the effect: Ticket #n will not be drawn. But of course these one million propositions, when conjoined, contradict the proposition that one ticket will be drawn, whose credentials (namely, the solemn assurances of eminently reputable parties) are precisely those by which you assign the probability of one in a million to each of the million propositions. And the problem is that you cannot repair this infirmity in your body of accepted propositions nonarbitrarily, without dispensing either of all one million propositions of the form ‘ticket #n will not be drawn’, or of the proposition that one ticket will be drawn, or both. But if you do not accept the propositions in questions under the conditions here announced, under what conditions can you accept them? The second grave difficulty for the threshold principle is precisely the opposite of the first. This difficulty is that the threshold will always be too high, never low enough to admit of deductive closure.2 For no matter where on the scale (0, 1) the threshold value is set, so long as it is set below the level of absolute certainty, it is always possible to find two propositions whose individual probabilities exceed the threshold level, but whose conjunction does not. This is true because the conjunction of two noncertain propositions is due a strictly smaller assignment of probability than each of the noncertain conjuncts. One eminent resolution of this dilemma is radical probabilism.3 Radical probabilism dispenses with division of propositions into those worthy

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of adoption, on the one hand, and those unworthy on the other, so has no need of thresholds. Radical probabilism bids us confer upon propositions degrees of belief, or partial belief, in place of the full-blown affair, never permitting a contingent proposition to be drawn close in any form of embrace, whilst other contingent propositions are unembraced, for this would lead once more to creation of a two-caste system, and thereby a revival of thresholds. The radical probabilist argues that a proper normative theory of rationality does not in reality demand categorial division of contingent propositions. For every piece of behavior that reason calls an individual to perform – in particular: perception, deliberation, carriage of decision – can be performed perfectly well, if not even better, under processes utilizing noncategorial assessment. And every piece of behavior that can be explained (in a particular social scientific theory, for instance) by positing that subjects utilize a categorial division of propositions, can be explained equally well, if not better, by positing that subjects confer degrees of esteem on the relevant propositions.4 In fact, the Bayesian probabilists say that the inference engines of science itself, which pass standards of good reason in the preponderance, are better explicated in terms of comparative-merit appraisals of propositions, rather than in terms of acceptance criteria.5 What can be done with acceptance criteria can be done equally well or better with rules for continuous modification of relative-merit assessments. These radical probabilist arguments notwithstanding, we mortals nevertheless report investing some of those contingent propositions we entertain, not with degrees of esteem of one sort or another, but with full belief. We report making discriminations by category among the contingent propositions on offer, not just discriminations by degree. Do these reports convict us of irrationality? (Or, if the suggestion of irrationality is unnecessarily categorial: are we less than fully rational in our dealings with propositions?) Perhaps we are instead simply mistaken, that we do not in reality discriminate by category, and that talk of acceptance, when it erupts, should be interpreted as reflecting high, rather than low, regard for the propositions referred to. If this is true, then ‘degree-of-belief’ may be treated as the theoretician’s term of art for what in fact we do.6 Or, finally, does division of propositions into categories, as such, serve a function that quantitative, noncategorial, relative-merit assessment of propositions cannot serve after all? I favor the last proposal.

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2. T WO CHEERS FOR CATEGORIAL ASSESSMENT

For the most part, philosophers writing nowadays decline to choose decisively between categorial and noncategorial evaluations of propositions, on the assumption that the choice matters but little since, as the radical probabilist maintains, anything that can be done or explained with full belief can be done or explained just as well or better with degrees of belief. And the noncategorial scheme of evaluation is sometimes considered a sort of friendly improvement on a more outmoded categorial idea. For example, Bas van Fraassen writes that “Pascal and the Port-Royal Logic taught us that the opinions which enter our practical deliberations, just like the evaluations of good and evil, are not simple. . . .We must think in terms of probability.”7 And Richard Foley writes: “An account of rational degrees of belief simply adopts a more fine-grained approach to doxastic attitudes than does an account of rational beliefs.”8 However a small but distinguished company of philosophers stands out as having taken a strong stand on the preferability of categorial evaluation over radical probabilism, as against those who take a strong stand on the other side. C. I. Lewis, who understood probability as a logical relation holding between a proposition and a ground, is perhaps the first person to worry whether it can make sense to assign a contingent proposition a probability less than one, if no other contingent proposition is taken as certain.9 Gilbert Harman makes the point that the radical probabilist faces enormous practical complexities, since the task of assigning probabilities to each and every proposition – not just those compatible with one’s certainties – is truly formidable.10 Isaac Levi, longtime critic of probabilism, has maintained that division of propositions into the categories of accepted and unaccepted serves certain functions that cannot be served by a noncategorial scheme of appraisal.11 He claims that beliefs function as a standard of serious possibility. It is only relative to certain fixed belief that any sort of quantitative, noncategorial assessment can be made of others. Once a proposition is accepted, all possibilities incompatible with it are ignored, and the rest invested with some measure of likelihood. Robert Nozick, while more sympathetic to radical probabilism than the others, also expresses a Lewis-like concern whether radical probabilism can be formulated coherently.12 He worries that it cannot make sense for an individual to assign degrees of uncertainty to some propositions when none are believed outright, since to assign degrees of uncertainty to something presupposes a decision situation which is believed to be a decision situation. What function would assignments of probability otherwise serve?

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Henry Kyburg, also a longtime critic of radical probabilism, makes the point that categorial assessment has features or manifestations which do not also belong to partial belief. Science with a rule of acceptance is a very different beast from science without such a rule. For science sans rules of acceptance (which, according to Kyburg, is not the science actually conducted in universities) would have no place in it for deductions from high-level theories (like for example quantum theory). For it does not even contain these high-level theories. Science without rules of acceptance consists merely of a set of observation statements taken together with analytic probability statements.13 3. T HE ASSUMPTION

While directing attention to certain unsatisfactory aspects of radical probabilism, the opponents named above still share an assumption with the radical probabilist, one that concerns the function of propositional attitudes in the economy of prudent belief. This assumption, as I shall now argue, prevents us noticing a function of dividing propositions into accepted and unaccepted, that cannot be served, at least nowhere near as effectively, by a noncategorial scheme of appraisal. Whatever else might be true of the prudent individual, she must be in possession of a capability for putting means to use for achieving her ends. An important question is: are the ends of a prudent individual prescribed by prudence itself, or are they self-given? This is an important question, because we wish to know what kind of aims should be had by a prudent individual vis-à-vis belief. Is knowledge (or even true opinion) an aim prescribed by prudence, or is it self-given? Could a prudent individual refuse to aim at knowledge or true opinion? In other words, if prudence is the sole concern, does it direct an individual to pursue truth for the truth’s own sake, or does it rather direct an individual to pursue truth merely for the sake of whatever else the individual happens independently to desire, to the extent that pursuit of truth would help achieve those self-given ends? One famous, but certainly not universal view, is that prudence is purely instrumental: it consists merely in conformity to some (more or less effective) means-ends calculus, but that there are absolutely no non-self-given aims – at least none that are given in the name of prudence. (Bertrand Russell is an adherent of this view: “‘Reason’,” he writes, “signifies the choice of the right means to an end that you wish to achieve. It has nothing whatever to do with the choice of ends.”14 Herbert Simon, too: “Reason is wholly instrumental. It cannot tell us where to go; at best it can tell us how to get there. It is a gun for hire that can be employed in the service

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of any goals we have, good or bad.”15 ) According to this view, the prudent individual may, if moved by certain passions or fancies, aim to achieve true belief, but is not required to do so. However, if true belief (or some close cousin) concerning some subject matter, is the most efficient means to achieving a certain self-given end, then evidently prudence would require pursuit of these beliefs. Another famous view, at the opposite extreme, is that there exist imperatives of reason to pursue true belief (or, even better, knowledge) either for its own sake or for the sake of rationality itself. Plato is perhaps the most unself-conscious about making this proclamation, but Nozick in a recent study of the subject writes: “What the rational person cares about is the truth. He uses the net balance among the reasons he has or knows of to estimate or predict this truth.”16 There are, to be sure, undeniable propositions in the immediate vicinity of each of these views. Dretske17 and Clarke,18 for example, agree that true belief (hence knowledge?) is a “biological imperative”, being the extraordinarily useful commodity it is. By and large, true belief confers survival advantage over false belief. This proposition, which is so unsurprising, does not settle our question: in what way should truth (or knowledge) be a quarry of the prudent individual, among whatever others are self-chosen? The question we wish to answer concerns identifying the source of the imperative Bernard Williams called to attention when he wrote that “beliefs aim at truth.”19 There are, then, two apparently self-evident propositions: (1) prudence consists in effective choice of means to self-given aims; and (2) the prudent individual aims to achieve knowledge. Should we, upon being presented with these two propositions, find both attractive, we shall be faced with the difficulty of reconciling them. For what does pursuit of knowledge have to do with achieving self-given aims effectively, that both are simultaneously demanded in the name of prudence or rationality? One response, so obvious it seems hardly worth the trouble of stating, is that one’s aims, no matter what they are, are more effectively achieved if one acquires relevant beliefs in an impartial or objective fashion. In other words, action-taking for the sake of self-given aims is well served by belief, so long as the process of belief formation is not itself a slave to passions: belief formation serves self-given aims when the unit conducting belief acquisition is not influenced by the passions. Thus action-taking and belief-acquisition must be conducted independently of one another. Believing and desiring/achieving must come apart in the psyche of the prudent individual. This answer is, I think, strictly speaking false. But it contains the germ of a truth, the extracting of which will reveal the falsehood.

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The first proposition, according to which prudence calls us to be effective pursuers of self-given aims, is concerned with the achievement of goals. The second proposition, according to which prudence calls us to pursue truth, is concerned with true opinion, or better yet knowledge. Which of these two concerns is the more essential to prudence? According to the view we are examining – the view according to which action-taking and belief-acquisition must be conducted independently – the more central to prudence is the first. For how could anyone who cares about their true, self-given aims, refuse to aim at pursuing them effectively, and still name the name of prudence? Whereas there is nothing particularly irrational or imprudent about refusing to chase after knowledge or truth – particularly if one is tired, or prefers (at least momentarily) to achieve some other, incompatible goal instead. According to the view under consideration, therefore, prudence is by its essence a conception that concerns the effective achievement of goals. And belief – if it is insisted upon in the name of prudence or rationality – can be insisted upon only for the sake of goals already aspired to. This is the kernel of truth which, I believe, must be preserved, which survives the view according to which the activities of belief-acquisition and goal-achievement must be conducted independently: that prudence consists in pursuing self-given aims effectively, and that this objective is in ordinary circumstances served by formation of beliefs, which can be marked as approved by prudence by being called ‘prudent’ or ‘beliefs of convenience’. So we might say that the dog of rationality wags prudent belief as its tail. Reconciling the two apparently self-evident propositions concerning prudence consists in answering the question: is prudence like a Swiss army knife – an instrument with many, possibly unrelated functions, each achieved by a different and independent component part of reason that is loosely connected to the others? Or is it an instrument whose products are the result of co-operations among all the potentially separable component parts? In other words, do the two apparently different cognitive functions of a cogitating individual – the belief-framer on the one hand and the efficient achiever on the other – operate independently, or do they cooperate?20 Only the Swiss army knife response admits of an easy reconciliation of the two propositions we are contemplating, as will become more clear. The days of faculty psychology are behind us. Even so, the Swiss army knife answer to the question concerning the nature of dependence among the functions of reason is still the apparent favorite. I will call it the modularity view of reason. Modularity of reason divides the functions or systems of reason. There is the belief-forming system, and there is the actiontaking system, among other systems of reason. And certain relations of

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independence govern their operations. The action-taking system is benefitor outcome-directed – its products (when all goes well) are actions that promote the advantage (utility) of the individual taking action; while the belief-forming system is knowledge-directed – its products (when all goes well) are true and well-founded beliefs. The aim of the belief-forming system is, according to this view, strictly a private, but nonetheless an epistemological one: to furnish information, true to the best of the available evidence, making such information available to the action-taking system so that the latter may plot a suitable course of action. Modularity of reason, as I will use the term, is the hypothesis according to which belief formation is directed to operate independently of the system responsible for achieving self-given ends. (In contrast with Jerry Fodor’s empirical hypothesis, after which it is named, modularity of reason is not an empirical hypothesis, but a normative one. And its subject is not the entire information processing capabilities of the human system, but a small aspect of the voluntary and semi-voluntary operations of this system.) Thus on the modularity of reason hypothesis, belief formation is to the prudent individual what the screwdriver is to the Swiss army knife: the more it functions as if it were an independent entity, without becoming unduly hindered by its mates, by coming under their influence, the better it achieves its purpose. What’s more, screwdriver and knife may operate on the same object, but the effects of the one will always be clearly discernible from the effects of the other.21 The criticisms of Lewis, Levi, Nozick and Kyburg, while they do not explicitly adhere to modularity of reason, do not challenge it. These authors for the most part share with radical probabilism the view that the action of the belief-forming system is knowledge-directed, thus that the belief-forming system subserves a private (albeit epistemological) function, which is better achieved if conducted independently of the operations of other systems. This assumption, which has the consequence that the goal of belief formation is knowledge, and which urges a categorial division of the operations of reason, is the assumption I want to challenge. 4. T HE MERITS AND DEMERITS OF PRAGMATISM

Having agreed with the probabilists, that prudence consists in chasing after belief when it would further achievement of self-given aims, we turn next to the question: does belief serve the purpose for which it is sought, in the name of prudence, at least in part by being true? (Put slightly differently, does a belief serve a prudent person’s purposes through qualifying as knowledge?) And the undeniable answer to this question is: Not always. Belief serves its host in a wide and heterogenous range of capacities

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and offices, many of which have nothing whatever to do with truth or knowledge. It is of course the pragmatists who have made this point in a large number of ways. And they have argued, furthermore, that aiming at truth will sometimes conflict with certain self-given aims, for example with high aims, such as salvation, self-preservation or even with the aim to avoid error. (Pascal and the pragmatist James and Dewey are famous for bringing these points to philosophical attention.) But far more lowly aims are liable to conflict with the aim of knowledge. For example, it is well known that individuals who overestimate their personal capacities are far more likely to succeed in their endeavors (however lowly) than those with more realistic estimates of their abilities. This is a prominent example in which a true belief does not serve the individual well, and a false belief on the same subject does considerably better. Another aim known to conflict with the aim of knowledge is the aim to reduce certain types of psychological distress; when I switch off the evening news so as not to become apprised of political developments I suspect will enrage me, I fail to pursue knowledge, and pursue instead my self-given aim to reduce distress, where I cannot achieve both aims simultaneously. When the aim of truth (not selfgiven) conflicts with a self-given aim, how can we demand, in the name of prudence, that the individual abandon the self-given aim, however lowly that might happen to be? For how could pursuing aims not one’s own, not self-given, when one could pursue one’s own instead, qualify as a specimen of prudence? The pragmatists wisely recommend that, where possible, we not issue directives, in the name of prudence, that will give individuals conflicting aims, since conflicting aims cannot be achieved together.22 Richard Jeffrey writes that the pragmatist’s focus is deliberation, not opinion: “Opinion and valuation come together in the matrix of deliberation, from which action emerges.”23 Consequently truth is not, as a matter of prudence, sought as a form of relief from agnosticism, but as a means to achievement of self-given ends. According to some pragmatists, this means that belief may aspire to knowledge precisely when it serves the passions well enough.24 Knowledge – not simply prudent belief – is the tail, wagged by the dog of prudence. This, however, is the unpalatable aspect of pragmatist epistemology, since knowledge has nothing whatever to do with the achievement of aims, however noble they may happen to be. To paraphrase Williams, knowledge is directed at truth, and truth is every bit as much aimer-independent as it is believer-independent. Thus those who oppose pragmatist epistemology have their very good reasons for demanding that a knowledge system, as such, be forbidden to serve other systems. For how could belief aspire to

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knowledge if the system producing it is (say) a slave to certain passions? No belief can qualify as knowledge that is, for example, the result of wishful thinking, however serviceable that belief might happen otherwise to be; so belief-forming, according to the anti-pragmatist, cannot be a by-product of desiring or effective action-taking. I shall argue with the pragmatists that modularity of reason should be rejected. My reason, however, is that the product of the action-taking system ought in many circumstances to be full, rather than partial belief. I will show that sometimes a full belief achieves – and is the best route to achieving – a self-given aim, and does so simply through being a full rather than partial belief. Thus I will uphold the proposition that prudence sometimes demands full belief, in the name of self-given aims, and thereby affirm the first proposition, according to which prudence consists entirely in utilization of a means-end matrix. And since prudence sometimes directs an individual to full belief, the belief-forming system cannot be required, in the name of prudence, to operate independently of the system in charge of decision and its carriage. And this being so, belief formation cannot be directed in every instance at knowledge. Hence I will reject the second proposition, according to which the single aim of belief formation is truth or even knowledge. Thus I shall uphold the anti-pragmatist worries vis-à-vis knowledge, by rejecting that distinctively pragmatist presupposition – namely, that the products of rational belief formation aspire to knowledge – while nevertheless recognizing the merits of the pragmatists’ non-epistemological concerns. I shall thus uphold that practical considerations may sometimes intersect with epistemological considerations, but it will be an accident when they do. This is because the epistemological enterprise and the practical enterprise do not, except accidentally, share objectives. The objective of the epistemological enterprise is true (and perhaps also justified) belief, whereas the objective of rationality is whatever conduces to achievement of self-given aims. Belief, as sought by a well-functioning aim-serving system, is belief sought for the sake of aims. But belief, as sought by a knowledge system, is belief sought for the sake of knowledge or truth – for the sake of relief from ignorance. If these objectives ever come to the same thing – if, that is, the objectives in both cases are knowledge – it will be so only as a matter of accident. Knowledge is not the chief directive of prudent belief formation, and it is conceivable (if we are allowed to make up sufficiently artificial cases) that an individual be rational who never even once aims to achieve knowledge. To put it another way, knowledge is purely instrumental in a theory of prudence. Thus it is no more true that a theory of rationality can substitute for an epistemological theory, than is

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the reverse. And we cannot answer epistemological questions simply by appealing to what a rational or prudent person would believe. This is an important result.

5. T HE PUBLIC FUNCTION OF BELIEF

5.1. Binding I shall say that individual S is bound to a course of action A when A is, in S’s own estimation, the course of action most likely to promote S’s interests. Hence, I am now bound to a course of action A, when it is now in my own best interests, according to me, to perform A. Under such conditions I will also say that I have an incentive to perform A. If I wished to persuade you that I would not pay more than 75,000 for your property, which you know is worth 100,000 to me (possibly because you know I offered that figure to your next-door neighbor, whose property is similar to yours in every way), I can invoke a penalty on myself. I can draw up an irrevocable and enforceable agreement with a third party, according to which if I paid more than 75,000 for your property, I would forfeit 30,000 to that third party. Thereby I become bound not to pay more than 75,000 for your property. Moreover, now the fact that you know the property is worth 100,000 to me – a powerful piece of knowledge in circumstances in which I do not or cannot enter into side agreements – has null value to you. I have gained bargaining power merely by weakening my hand. For by rendering myself incapable of paying more than 75,000, I have gained bargaining advantage over you. This advantage I acquire by acquiring certain beliefs – in other words, by accepting certain propositions. This is one example of a situation in which weakness of a certain kind is strength of another. It was perhaps Thomas Schelling who taught us this profound truth:25 that when it comes to bargaining advantage, a wealth of ordinary capabilities – when their enjoyment is public knowledge – is rarely in the service of their possessor, and weakness is often better utilized to strategic advantage than strength. A weak or underdeveloped intelligence, for example, may function as a shield against threats. And an individual or government known to be incapable of controlling her resources might enjoy assistance that would be refused if the deficiency did not exist or were not recognized. I will show that the flexibilities of radical probabilism render an individual who embraces it strategically weak. Inflexibility can be to a person’s advantage, just as almost any limitation or weakness can be, under the right circumstances.

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5.2. The power to bind oneself The power to bind oneself to a particular course of action serves an important social function, among many that beliefs contribute to making possible. This power to bind allows us to coordinate and concert actions in the midst of negotiation, and moreover to swing negotiations in one particular direction rather than another. The binding of oneself is achieved through the acquisition of belief, since my state of being bound depends on my estimation of what is in my best interests. Now it does not matter at all to the question whether I am bound, that the belief by means of which I bind myself to a particular course of action is true. For example, it does not matter in the least that the third party (who figures in our real estate negotiations) will extract the penalty I have invoked because an institution of enforcing agreements exists. I am bound not to pay more than 75,000, whether that third party can extract the penalty or not, so long as I believe the third party will do so. My belief in the power of this third party to extract the penalty is enough to bind me, so long as I retain it. The belief in the third party’s powers serves my purposes, of directing your deliberations in a particular way, simply by being adhered to. In order to determine my incentives you need to examine my beliefs, since they, and only they, are the foundation of my incentives. And it is important to me for obvious reasons that you should recognize I have adopted this particular belief. For what matters is that, so long as I consider myself inescapably vulnerable to a third party for weakening to (say) 85,000 in our bargain, you cannot rationally expect me to weaken (since you know that I assess this weakening to bear a cost of 115,000 for a gain of only 100,000). You must come a longer way to meet me, if the bargain I make available is better in your estimation than no bargain at all. (Of course, if you prefer no bargain at all, then my gambit with the third party will be wholly unsuccessful.) We mortals utilize the power to bind ourselves to advantage in many such negotiations, formal and informal. But in the absence of a practice of acceptance to full belief, the power to bind oneself is significantly diminished. This is precisely because a relative-merit scheme of assessment admits of more refinement of judgment, and hence of more flexibility. You may perhaps try to convince me (if you think it worth the trouble) that my full belief, in the proposition that a penalty will be extracted upon my weakening, should be demoted to a degree of belief of say 0.9. You taunt that I am otherwise being irrational (or at least, less than fully rational). What should happen to my gambit if I succumb to the temptation to probabilize?

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5.3. The power to bind oneself is weakened without full belief One of the radical probabilist’s strongest arguments against a categorial division of propositions is the argument that whatever functions a categorial division of propositions will serve or explain can be served or explained equally well, if not better, by a noncategorial appraisal of propositions. Can the radical probabilist offer us the same power to bind ourselves by a noncategorial appraisal of propositions? No. For if, rather than fully believing that I shall have to pay a 30,000 penalty to a third party upon weakening to your urging of (say) 85,000, I merely assessed my chances of having to pay the penalty at 3 in 4, or 4 in 5 or even 9 in 10, my power to bind myself is weakened proportionally. For, upon learning of my estimates of having to pay the penalty, you will estimate the chances that I will weaken at perhaps 1 in 4 or 1 in 5 or 1 in 10, and persist in your demands rather than simply acting on a recognition that I cannot be moved. It might be replied that if, rather than fully believing, I instead assign a conditional probability of 0.9 to the third party’s penalizing me by 30,000 if I agree to pay more than 75,000 for your property, then the expected cost to me of giving in to your demands will be increased by 27,000; so there is no chance that I will make the concessions you seek. So a person in my bargaining situation can do just as well by publicizing those degrees of belief as by publicizing full belief. To this challenge I reply that by believing fully in the proposition that on weakening I shall have to pay a penalty of 30,000, I create a situation whereby each of us acknowledges that my weakening bears a price tag of 30,000, not just 27,000. However the difference between 30,000 and 27,000 is not a negligible one. In some cases, a high enough assignment of probability will do the job. But sometimes only full belief will achieve the desired outcome. There is a market value on full belief, and a different one on partial belief. The difference in many circumstances may not be very great, nevertheless it is there. And this is precisely the point I wish to make: that the strategic possibilities for someone who brandishes full belief are different for someone who brandishes only the partial variety. To achieve precisely the same effect through degrees of belief, I should have to wager more than 30,000 with the third party. But what if this higher wager is not available to me? What I may be able to achieve with degrees of belief under one set of circumstances, I may not be able to achieve under another, but may be able to do with full belief. Suppose your property is worth 103,000 to me. I can draw up a contract with a third party, but only in the amount of 30,000, and only if I specify that it shall go into effect on condition that I weaken to more than 75,000. Suppose now that the highest probability that evidence will permit me to

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assign the proposition that the third party will collect a 30,000 penalty, is 0.9. Then the expected cost to me of weakening to, say 76,000, is 102,000, which is less than the value (mutually known) of your property to me. So you might very well insist on 78,000, and force me to breach the contract with the third party and take the risk of paying the penalty. While if I am able fully to believe, I cannot be expected rationally to weaken, since you must accept that I estimate weakening to cost $105,000. So, while the third-party contract I have entered into still puts you at some very significant bargaining disadvantage, it can do little or nothing for me, if (as presumed) you know how much your property is worth to me. The contract with the third party in our concern does not have the power it could, given the circumstances, if I do not, on the basis of it, come to embrace the proposition that I shall have to pay 30,000 for weakening. You might say that this is a very artificial example, that life in the real world is not filled with these arbitrary constraints. And you would be right. But it does not matter. The (almost trivial) point they serve to illustrate, and quite handsomely, is simply that an individual who employs a categorial assessment of propositions is within reach of certain strategies, in certain circumstances, that cannot present themselves to one who massages a distribution of probabilities. Furthermore, these strategy potentials can put those in a position to employ them at great advantage, under the right circumstances. What follows from this? Precisely the denial of the radical probabilist’s contention, namely that not everything which can be accomplished by a system of full belief can be accomplished by a system of degrees of belief. And even if the strategy potentials of the two systems of appraisal were identical, this would be merely a matter of accident. And even under such circumstances, it does not follow that we can explain the course of events by positing that agents employ either form of assessment. What can be accomplished by a third-party contract to pay a penalty of M if I exceed my self-imposed limit, on the condition that I fully believe the proposition that I shall have to pay that penalty, can be accomplished only by a third-party contract to pay a larger penalty of M + K, under conditions in which I apply probability assignments. More interestingly, it also follows that whether an achievement can be accomplished or explained in terms of either full or partial belief, depends on normally unacknowledged details of the circumstances under which it is to take place. We can distinguish whether a partial belief will accomplish what is accomplished in the artificial example just described, or if only a full belief can do it. And thus we might be able to tease out whether agents utilize full belief or partial belief, by making a careful study of the circumstances in which their gambits are successful. Thus the radical probabilist is perhaps right that we

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can do everything with partial belief that we can do with full belief, but this (finally) would be beside the point, for we cannot always accomplish what we can with full belief under the same circumstances as we can accomplish it with partial belief. A noncategorial appraisal of propositions, under the right circumstances, can give me the strategic advantages of a categorial appraisal, only if it allows me to boost very high my confidence, perhaps artificially, in the third party’s power to extract the penalty. This artificial boosting will be possible only if the belief-forming system is allowed to take certain direction from either the action-taking system or the desire-forming system. But this is precisely what the modularity view of reason is supposed to prohibit. And if it did not, the distinction between categorial assessment and noncategorial assessment, which directs belief formation to be conducted independently of other systems of reason, would be a distinction without a difference.

5.4. Alternatives to belief: the power of reason Now the proposition that beliefs serve a function in the economy of life, for the likes of us, is not exactly newsworthy. The pragmatists have known it for some time now. Still, it takes a bit of philosophical argument to explain how full belief can confer an advantage over partial belief, under the right circumstances (however artificial), and this is what has been provided thus far, through the account of self-binding through belief adoption. We mortals, just as a matter of fact, utilize this power to advantage in situations calling for strategy, whether we recognize it as such or not. But while the act of accepting a certain proposition, as a route to binding oneself, might be one means to bringing about a certain end, I have not shown that it is the best means to that end, for the likes of ourselves. And this is precisely what I shall be required to do, if I am to be allowed to promote my account as an explanation of why in fact we believe, and all the more so if I am to be allowed to commend full over partial belief, to the prudent. However I cannot argue – nor should I be required to – that full belief is or should be calculated to achieve a strategic goal. For if it were so calculated, chances are it would not be as effective in achieving the goal, particularly if the chances are high of those beliefs being found out as purely beliefs of convenience. Even if it is prudent to hold a certain belief which promote one’s aims, it is not by the very same token prudent to hold also a belief to the effect that one holds the certain belief, simply for the sake of creating favorable conditions for oneself. This is a self-defeating pair of beliefs. For if belief in the pair comes to light, it might be even

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worse for the belief holder than if neither were held. So we should neither commend nor expect universal dissembling. Even so I am faced with a problem, which concerns all beliefs of convenience. If dispositions to believe or probabilize were biologically determined, then perhaps my account could be accepted without further question. But the fact is, that where there is the power of reason, there is, at least sometimes, the potential for casting out beliefs that fail to survive a certain amount of examination and comparison with the evidence. And if there should happen to be (as undeniably there is) some palpable grounds for being in the least uncertain about the truth of contingent propositions, then should not a prudent person hesitate to believe in full, if only out of fear of being taken advantage of? True: the utility of full belief is independent of the grounds of the belief. But even more advantageous than being a known believer, is to give the appearance of believing whilst not doing so, thereby acquiring via a different route the power to prescind from the evidence, and act directly in favor of one’s aims. So why shouldn’t hypocrisy, coupled with partial belief, be undertaken on the advice of prudence, rather than full belief? My view is that an account such as mine should recommend a certain amount of hypocrisy, but not a full measure. Here is why. Prudence should counsel hypocrisy only where its advantages are not outweighed by its costs. To assess the percentage of cases in which prudence counsels hypocrisy, we have to answer two sets of questions. The first have to do with human capabilities: are humans capable, psychologically and intellectually, of sustaining hypocrisy? Can they sustain in memory the propositions which they only purport to embrace whilst not doing so, and keep separate the probabilities, being careful always to appear to be believing? Can they remember to dissemble far enough in advance of the need to do so arising, as well as long enough afterwards, so as not to give themselves away? Are they averse to the risk of being found out, and good at covering up indiscretions? There is some reason to believe that normal human functioning does not admit very easily of hypocrisy. But there are sure to be some individuals who can pull it off quite well. For those individuals the stable position will be hypocrisy. For the rest, full belief will be the more stable position. (For the population overall, we might say that full belief is a local maximum, and hypocrisy merely the global maximum, effectively unattainable for a majority of those with the human psychological endowment.) The second set of questions concerns the balance of costs to benefits, of each course of action. Take full belief first. Belief is obviously not without its burdens. Someone who divides propositions into two castes, has always to be updating these decisions, to draw and withdraw acceptance.

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Chances are, this is less costly than massaging probability assignments, but it is nevertheless a cost. And, as we’ve seen, the full believer gains the advantages of full belief (when there are advantages) by foregoing a certain refinement to his judgments. Surely there is a cost to be attached to this (and we will come to it one section hence). All these costs have to be weighed against the benefits of full belief. Similarly with hypocrisy, which is likely to be more favorable overall, because a hypocrite incurs costs only when others are watching. But with hypocrisy the psychological and intellectual costs are considerably more burdensome. And thus we cannot without knowing exact details say which balance is the more favorable in any given episode. The question, as I have been insisting, is an empirical one. Still, my money’s on full belief, in the preponderance of cases (as most beliefs are positively not sought for academic reasons). 6. T HE FUNCTIONS OF RATIONALITY ARE NOT INDEPENDENT

It is quite true, and an article of faith on which even the argument here being presented rests, that the function of belief formation, full or partial, is to serve the interests of the individual. I am nevertheless suggesting that this proposition is not true in the way usually thought. Belief need not serve the individual merely by providing (true) information on which the action-taking system may plot its course. For beliefs are not, generally speaking, merely points on the compass by which an individual steers a course. Instead, beliefs play other crucial roles. Beliefs are also devices that serve us in situations calling for strategy. Among the services a belief can render is that of drawing attention to itself, in the process giving others (whether friends or competitors) evidence of certain incentives; thereby beliefs serve as evidence of intentions as well. Belief does not serve the merely private function of information or “intelligence”. The belief-forming system manufactures certain articles for public inspection, just as it manufactures certain others for private use. Where humans are concerned, rational processes cannot be required, in the name of rationality, to be conducted by independently operating systems. In the economy of rational processes, formation of belief must be responsive enough to the needs of the individual whom it serves, to render all the services that belief can render. To say that sometimes belief has a public function is not at all to say that my beliefs sometimes serve the interests of others, or of the community as a whole. Rather, it is to say that sometimes it is in my own best interests to form beliefs so that they will be publicly visible. In other words, beliefs are articles that can be placed in the landscape to be navigated by others,

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not merely points on the compass by which one steers a course through an antecedently fixed landscape that is mutable only through actions which do not involve “private” operations on propositions. And since beliefs can be so placed, they can also be placed strategically. Thus the theory of rational belief belongs, at least in part, to the study of strategy. Propositional attitudes become full-fledged articles in the landscape through adoption. The radical probabilist might perhaps wish to argue that degrees of belief are just as good candidates for articles in the landscape as beliefs are. However, even if degrees of belief are respectable candidates for placement in the landscape, they are items of a different caliber. What can be done with beliefs cannot always be done with degrees of belief. Since belief, as the result of a rational process, may serve purposes that are not private purposes, I conclude that belief formation should not, in a normative theory intended for consumption by humans living under the conditions with which we are familiar, always be directed at knowledge. For if the function of a belief may ultimately be simply its publicity, the fact that it can (for example under different circumstances) also function as a guide through the landscape to be navigated, is not sufficient evidence of truth-directedness. And belief formation is not knowledge directed if it is not truth directed. The belief-forming system, for the likes of us, is therefore not one whose sole directive is to manufacture knowledge. Hence the belief-forming system is not a purely epistemological system.26 (One may at this point question the wisdom of embracing the proposition according to which rationality is instrumental and dispensing with the proposition that belief is to aspire in every instance to knowledge. Why not, instead, do the opposite: dispense with the former and embrace the latter? This opposite course of action, of course, collapses the distinction between rationality and epistemology, vis-à-vis belief, while making it impossible to discuss belief as potentially the product of a means-ends calculus. So it does not even allow us to enter into the discussions we should have on the subject.) 7. N ORMATIVE BAYESIANISM

There is a compelling argument, made very persuasively by Richard Jeffrey – possibly the most vigorous champion of probabilism – that a policy of full belief in contingent propositions, since it can never be warranted by evidence, is at best reckless, if not downright irrational.27 He argues that the purpose of belief is to serve the deliberation process under numerous and dissimilar circumstances, where dissimilar things are at stake, from nickels to lives. Acceptance, according to Jeffrey, is commitment in

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the strongest possible terms. For to believe a proposition P fully is to be prepared to risk any amount of money on the truth of P, at any odds. And while ordinarily no serious harm comes from risking nickels at any odds, risking lives, on the other hand, is another story. And no one should be so imprudent as to undertake commitment of this sort, particularly when the stakes are very high. Partial belief, on the other hand, does not involve undertaking reckless commitments, since it is precisely and no more than what evidence warrants. Jeffrey recognizes that it is extraordinarily difficult to live the life of a true radical probabilist. But “the important question is whether it’s feasible and desirable for us to train ourselves to choose probabilities or odds or Bayes factors, etc., as occasions demand, for use in our practical and theoretical deliberations.”28 This line of argument, persuasive as it is, presupposes that partial belief involves no commitment of any kind, even when the precise partial beliefs are published. And this presupposition, as we have seen, is not correct. Bayesians will in fact be the first to point out that partial beliefs also entail a preparation to undertake certain risks at certain odds, though perhaps not at any odds. According to the official Bayesian line, these predispositions too are commitments. Every published belief, as we have argued independently, involves a commitment, as the price-negotiation case shows. And there is no guarantee that a reckless risk-taker will fare particularly badly, and more badly than a conservative one, in any particular circumstance. Jeffrey’s line of argument also presupposes that action is a strict function of belief, that once the beliefs are given, the course of action is a foregone conclusion.29 In other words, Jeffrey’s argument presupposes the falsity of voluntarism, according to which the will has a role to play in the formation of belief. Thus the Bayesian is not only conservative, but strategy-averse, on principle. However, even if Jeffrey’s argument in favor of conservatism were correct, it would prove only that full belief is inadvisable, as a policy, a proposition with which I am in full agreement. It would not prove that full belief is inadvisable universally – the proposition I am challenging. And it certainly does not prove that full belief is inadvisable under any given set of circumstances. So it does not establish the advisability of radical probabilism as a policy. Jeffrey’s brand of radical probabilism rests on a picture of belief painted early on by Bernard Williams.30 The first element of that picture is that belief is not entirely up to the believer – that the believer cannot choose how to believe at a given episode, and in particular cannot choose to go against what he takes the evidence to support. And the second, and more important

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element of that picture, is that acceptance goes beyond mere assignment of a measure of support that evidence lends a hypothesis, and is posterior to it. By leaving out belief from the normative formula, Jeffrey has (mistakenly) assumed that he has left off commitment. And by embracing modularity, Jeffrey has given expression to the idea that acceptance is posterior to evaluation of a hypothesis in relation to available evidence. There is, however, no true sense in which acceptance goes beyond assessment of likelihood; it does not go beyond it in terms of commitment, for example. And there is even less truth to the proposal that assessment of a hypothesis, in relation to a certain body of evidence, must be made prior to a decision to accept, as I will now argue. Jeffrey might reply to my price-haggling example as follows. I say that, given a choice in a particular instance, between assigning probabilities exactly as the evidence warrants, and full acceptance, prudence permits a choice to accept, provided that acceptance promises better results. And that you can reevaluate your choice to accept at any time thereafter. Jeffrey might reply: but once I’ve assessed the evidence to warrant an assignment of 0.8 to P, how can I go on and accept P? How can I achieve belief, when I’m under the spell, cast upon me by the available evidence, that P only deserves a confidence of 0.8? My reply is that Jeffrey makes a decision whether or not to accept simultaneously with an assessment of P’s likelihood. If he chooses to make likelihood assessments, then ipso facto, he has chosen not to make a decision to accept with respect to a particular episode. In fact, I think that this is what the lottery example, with which I introduced this essay, teaches – that once the probabilities have been displayed, it is too late to make a decision to accept. Conversely, if he makes a decision to accept, then ipso facto, he has chosen not to make likelihood assignments. 8. T HE MARKET VALUE OF BELIEF

In opening remarks to his 1970 essay “Dracula Meets Wolfman: Acceptance vs. Partial Belief,”31 Jeffrey characterizes himself as a proponent of pragmatism, whose focus is deliberation, not opinion. It is there that he writes: “Opinion and valuation come together in the matrix of deliberation, from which action emerges.” Truth, he tells us, is not sought as a form of relief from agnosticism, but as a means to a practical, agent-centered end. But if my arguments have shown anything, they have shown that radical probabilism is not radical enough to serve the pragmatism Jeffrey esteems. That pragmatism is served better by the thesis that propositional attitudes have more uses than those which the intellectuals speak of in their forum.

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The moral of the story is that attitudes toward propositions have value in the marketplace. And that only a disengaged academic can refuse to recognize the market value of full belief, over against the partial scheme, at least sometimes. And that we can choose full belief over the partial scheme, possibly on a case-by-case basis, on grounds that one is more likely to prove advantageous, or to minimize risk, depending on which we care more about just then. Only a disengaged academic can urge that doxastic attitudes be formed as they might be on Mount Olympus, where belief is not required to sustain our economic being. Aiming at truth is a luxury that only a privileged few, at least in this world, can afford. And this is no less true as regards style of belief, than as regards lifestyle. William James, in the “Will to Believe,” wrote that “he who says, ‘Better go without belief forever than believe a lie!’ merely shows his own preponderant private horror of becoming a dupe.”32 But I say that he who says, “Better go without full belief than go beyond the evidence!” merely shows his own preponderant private horror of taking strategic action, via belief, in pursuit of self-given aims. But if belief has a market value, what does this mean for epistemology? Precisely that the directives of epistemology have nothing to do with the demands of prudence, and (in particular) are not founded on them. Hence that pragmatist epistemology should be rejected.

NOTES 1 Henry Kyburg, Jr., Probability and the Logic of Rational Belief (Middletown, Conn.: Wesleyan University Press, 1961), 196–99. 2 Henry Kyburg, Jr., “Conjunctivitis,” in Induction, Acceptance, and Rational Belief, ed. Marshall Swain (Dordrecht: Reidel, 1970), 55-82. Kyburg’s own resolution of this dilemma is to keep the threshold proposal but give up deductive closure, arguing there are independent reasons also for giving up closure. Richard Foley (Working Without a Net, New York: Oxford University Press, 1993, 143-45) also gives up closure, although the dilemma does not arise for him because he also surrenders acceptance – (1) above. 3 The term is due to Richard Jeffrey, Probability and the Art of Judgment (Cambridge: Cambridge University Press, 1992), essays 1, 4-6. However the first radical probabilist is probably Carnap, whose most explicit discussion of the view is “Inductive Logic and Inductive Intuition,” The Problem of Inductive Logic, Imre Lakatos, ed. (Amsterdam: North Holland, 1968). 4 Richard Jeffrey discusses L. Savage’s argument to this effect, and offers one of his own in “Dracula Meets Wolfman: Acceptance vs. Partial Belief” in Induction, Acceptance and Rational Belief, ed. M. Swain (Dordrecht: Reidel, 1970), 157-185. 5 While it is true that many Bayesians are radical probabilists, it is equally true that many are not, for example P. Horwich, Probability and Evidence (Cambridge, 1982); and many probabilists (Bayesian and not) are not particularly radical (in our sense), for example F.

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Dretske, “Laws of Nature,” Philosophy of Science 44 (1977) 248-68, and B. van Fraassen, “Belief and the Will,” Journal of Philosophy 81 (1984) 235-256. 6 This is suggested by Richard Jeffrey, “Dracula Meets Wolfman,” op. cit., 161. 7 Laws and Symmetry (Oxford, 1989), 153. 8 Working Without a Net, op. cit., 140. 9 Analysis of Knowledge and Valuation (LaSalle: Open Court, 1946), 315 ff. 10 Change in View, Cambridge: MIT Press, 1986. 11 Isaac Levi, The Enterprise of Knowlege, 2-19 and passim, and Fixation of Belief and Its Undoing (Cambridge: Cambridge University Press, 1991) 57-62 and passim. 12 The Nature of Rationality (Princeton: Princeton University Press, 1993), 95. 13 “The Role of Detachment in Inductive Logic,” in The Problem of Inductive Logic, Imre Lakatos, ed., (Amsterdam: North Holland, 1968). Of course the probabilist may reply to Kyburg that the deductions he calls to attention belong to science insofar as they help to establish the analytic probability of statements which are never fully accepted. Or that science has room in it for more than merely the accepted propositions; there is room in science also for the partially embraced, as appropriately weighted. 14 Human Society in Ethics and Politics (London: Allen and Unwin) 1954, viii. 15 Reason in Human Affairs (Stanford: Stanford University Press) 1983, 7-8. 16 The Nature of Rationality (Princeton: Princeton University Press), 1993, 73. 17 Fred Dretske, “The Need to Know,” in M. Clay and K. Lehrer, eds., Knowledge and Skepticism (Boulder, Colorado: Westview Press, 1989) 89-100. 18 “Natural Selection and Indexical Representation,” in R. S. Cohen and M. Marion, eds., Quebec Studies in the Philosophy of Science II (Netherlands: Kluwer Academic Publishers, 1996) 53-62; and “Darwinian Algorithms and Indexical Representation,” Philosophy of Science (1996) 27–48. 19 “Deciding to Believe,” Problems of the Self (Cambridge University Press, 1973), 136-51. 20 Gilbert Ryle calls attention to a certain aspect of this question when he writes in A Rational Animal (London: Athlone Press, 1962), 5-6: [W]e feel some temptation to say, with august precedents to give us the courage to say it, that the Reason which distinguishes us who possess it from the brutes, infants and idiots that lack it is a dual Faculty. There is Theoretical Reason and there is Practical Reason. Theoretical Reason is our capacity, small or great, to think thoughts, that is, to operate from and with propositions. Practical Reason is our capacity, small or great, to conduct ourselves according to moral principles in the warm world of action. . . . Whether the Faculty of Practical Reason is to be thought of as the brother-officer of Theoretical Reason or as its sergeant-major is a question the interest of which has, by our de-mythologizing time, somewhat dwindled, without altogether disappearing. For we are now nearly, though not quite, immune from the temptation to picture our different abilities and liabilities as internal agencies or therefore as superior or subordinate agencies. 21 One prominent adherent of this Swiss army knife model is Jon Elster, Nuts and Bolts for the Social Sciences (Chicago: University of Chicago Press, 1989), who actually gives a diagrammatic representation of the dependence relations among the cognitive and semicognitive systems of the rational individual, p. 31. 22 William James thought that epistemic imperatives – truth-related imperatives – already conflict with each other (the aim to believe truth and shun error conflict). Hence certain matters of a certain moment may – in fact, must – be decided on practical, nontruth-related grounds. These momentous intellectual matters must be resolved by practical considerations.

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23 Richard Jeffrey, “Dracula Meets Wolfman: Acceptance vs. Partial Belief,” in Induction,

Acceptance and Rational Belief, ed. M. Swain (Dordrecht: Reidel, 1970) 157. 24 H. Simon (Administrative Behavior, New York: Free Press, 1945; Models of Man, New

York: Wiley, 1957; Models of Thought, New Haven: Yale University Press, 1979; Models of Bounded Rationality, Cambridge: MIT Press, 1983) has offered a “satisficing” model of human rationality (which he calls “bounded rationality”) on which epistemic considerations are decisions, just like any others, made by an individual with limited time and resources. 25 Strategy of Conflict (Harvard University Press, 1960. 26 Richard Foley (op. cit., chapter 6) makes the point that radical probabilism is appropriate only for ideal epistemological agents. They are epistemological engines, but we are not. 27 Probability and the Art of Judgment, op. cit., Essay 2. 28 ibid, 29. 29 Van Fraassen, “Belief and the Will,” op. cit, argues against this view, as does Bacchus, Kyburg and Thalos, “Against Conditionalization,” Synthese 85 (1990) 475-506. 30 op. cit. 31 Op. Cit., 157. 32 Essays in Pragmatism (New York: Hafner, 1940), 100. Department of Philosophy, Faculty of Social Sciences State University of New York at Buffalo 607 Baldy Hall, Box 601010 Buffalo, New York 14260–1010 USA