The body of this book is 100% errorfree. This seems especially evident if our belief-attributing practice turns out to be sensitive to contextually determined conversational saliencies. So perhaps the argument will be that although this level of confidence seems quite compatible with binary belief, the large reductio of P6 shows that P6 is not really belief-worthy. Thus, although the moral ideal might be attainable for no one, it might yet play a crucial role in grounding the moral obligations of each agent, obligations that were conditioned by particular facts about what that person could achieve. The same holds for probabilistic formal constraints on degrees of belief that have been advanced by many writers. Rationalist Epistemic Probabilism In the classical rationalist tradition, the laws of deductive logic are taken to apply to states of binary all-or-nothing belief. It is intended merely to point out that examples of arguments whose effects cannot be accommodated by graded-belief-based mechanisms are going to resemble the strikingly counterintuitive applications of cogency in some respects—respects that are likely to make them counterintuitive as well.
Obviously, talking about dogs in this way is extremely useful in everyday contexts. Suppose that beliefs are individuated—with respect to degree as well as content—by their causal roles. One might naturally imagine that the various events could somehow have been timed by relations to external events e. Nevertheless, it furnishes a compelling way of understanding a key dimension of epistemic rationality. As the first introductory textbook on formal epistemology, A Critical Introduction to Formal Epistemology is an invaluable resource for students and scholars of contemporary epistemology. For example, suppose that the general practice has been for Sophie to wash the dinner dishes. Alston 1985, 1988 divides deontological accounts of justification into two sorts.
Most of these workers—male and female, young and old—remain strongly committed to their jobs, but wish to combine work with other activities they value just as highly. She could then easily entertain the conjunction of 1 and the third claim in her book. Nevertheless, it furnishes a compelling way of understanding a key dimension of epistemic rationality. But this latter project has often involved defining graded beliefs in terms of preferences, which may seem to change the subject away from epistemic rationality. To look at just one example, consider goodness of chess play. In doing so, we try to abstract from a certain kind of luck, or accidentalness. Still, this leaves open a number of possible approaches to the objects of epistemic rationality.
Non-rationalists about deductive logic will find it less compelling. Maher 1993, 9 This approach toward defining degrees of belief by preferences need not be fleshed out by any naive commitment to operationalism, or to seeing the relevant definition as analytic or a priori. Indeed, in many different situations, the Immodest Preface Proposition will combine with background beliefs to result in all manner of strange beliefs. If a simple agent has a degree of belief of, e. It is the inconsistency, not the example in the text; 3 : 1 odds are the same as 0. The price or payoff of one bet may be such that it would alter the value of the price or payoff of a second bet. If the standard deductive consistency and closure constraints apply to rational binary belief, then it cannot be rational to believe that a given large lottery will have a winning ticket, while simultaneously believing of each ticket that it will not win.
Again, however, our being disturbed in such cases can be explained in degree-of-belief terms. But it seems obvious that claims made in a book by a respected authority may meet the standards for rational belief. I know this will come in handy when, as will inevitably occur, errors are found in this book. Moreover, it turns out that the arguments both for and against the imposition of the formal constraints are quite different for binary and graded belief. For neither one of these more reasonable metaphysical views of belief can support Representation Accuracy.
We might call the conception of rationality from which this argument springs the deontological concept of rationality. Given this background, it is not surprising that whenever a new book comes out—even a book written by a scholar he believes to be more meticulous than he himself is—Professor X believes that the new book will be found to contain errors. A less popular picture sees belief as a graded phenomenon. But various philosophers have devised conditions on justification, warrant, acceptability, etc. But it may also idealize in the way in which countless purely descriptive models idealize: it may assign a number to a quantity whose application to real instances is not completely precise. The graded model sees belief as coming in degrees.
And the notions invoked in such an account will naturally be notions of degree—e. If degrees of belief are, at bottom, defined in terms of preferences, the inconsistency involved in having probabilistically incoherent degrees of belief turns out to be an inconsistency of preference. This is where the tension comes in. We might substitute for an academic historian a more humble sort of researcher: one who looks up telephone numbers, say, for a political campaign. And evaluating the second component incurs obvious regress problems, since the epistemic credentials of the related beliefs will depend on their structural relations to still other beliefs, whose own epistemic credentials then become relevant; and so on. This general intuition may easily be applied to a simple agent in a straightforward way: since the simple agent cares solely and positively about money, a set of bets that is guaranteed to cost him money is guaranteed to leave him worse off, by his own lights.
For the affected agent, the epistemic difficulties are quite severe. One might insist, for example, that closure would not require any second-order belief about the first-order beliefs expressed in the book. It turns out, then, that thinking about the sorts of binary beliefs required by cogency in some quite ordinary circumstances reveals strong reasons for doubting the importance of cogency-respecting binary belief. This picture explored more by decision-theorists and philosophers of science thatn by mainstream epistemologists invites the use of probabilistic coherence to constrain rational belief. We thus arrive at intuitively reasonable probabilities of 0. Diachronic rationality constrains the way beliefs are changed or maintained across time. After all, one can imagine a variant on the Pascal example in which the rewards for the counter-evidential belief were purely epistemic.
The constraints that any version of probability theory places on degrees of belief flow from exactly these patterns. But none of these observations about binary belief turn out to provide a sound motivation for a cogency requirement on binary belief. The second task the traditional arguments have sought to accomplish is a normative one: to show that graded beliefs, so defined, should be probabilistically coherent. Let us begin, then, by examining formal constraints that apply to the whole set of beliefs an agent has at a given time, and asking whether such constraints can provide a model for ideal epistemic rationality. Both of these proposals are, of course, for synchronic constraints on rationality.
Such a view would, of course, divorce the two kinds of belief in a fundamental way. In that case, one would naturally see discrete belief as a trinary notion, encompassing three distinct attitudes one might take toward a proposition: belief, disbelief, and withholding judgment. Some have 12 Maher 1993 argues along these lines; his views on theory acceptance will be discussed in Chapter 4. But whether or not this is true an issue that will be examined in detail in the next chapter , it seems clear that the unequal treatment demanded by deductive cogency presents an acute intuitive difficulty. It has been pointed out, for example, that there are no clever bookies who know my degrees of belief and can compel me to wager with them. Thus the importance of synchronic constraints is perfectly compatible with conceptions of epistemic rationality according to which it has important dynamic dimensions. Unfortunately, as Maher 2002 has pointed out, there are other accuracy measures that do not support this result, and the arguments in Joyce 1998 that would rule out these measures are not fully convincing.