The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability.

1 Knowledge and Justification This book is an investigation of one central problem which arises in the attempt to give a philosophical account of empirical ...

Probabilistic models have much to offer to philosophy. We continually receive information from a variety of sources: from our senses, from witnesses, from scientific instruments. When considering whether we should believe this information, we assess whether the sources are independent, how reliable they are, and how plausible and coherent the information is. Bovens and Hartmann provide a systematic Bayesian account of these features of reasoning. Simple Bayesian Networks allow us to model alternative assumptions about the nature of the information sources. (...) Measurement of the coherence of information is a controversial matter: arguably, the more coherent a set of information is, the more confident we may be that its content is true, other things being equal. The authors offer a new treatment of coherence which respects this claim and shows its relevance to scientific theory choice. Bovens and Hartmann apply this methodology to a wide range of much discussed issues regarding evidence, testimony, scientific theories, and voting. Bayesian Epistemology is an essential tool for anyone working on probabilistic methods in philosophy, and has broad implications for many other disciplines. (shrink)

Let E be a set of n propositions E1, ..., En. We seek a probabilistic measure C(E) of the ‘degree of coherence’ of E. Intuitively, we want C to be a quantitative, probabilistic generalization of the (deductive) logical coherence of E. So, in particular, we require C to satisfy the following..

This study uses techniques from economics to illuminate fundamental questions in ethics, particularly in the foundations of utilitarianism. Topics considered include the nature of teleological ethics, the foundations of decision theory, the value of equality and the moral significance of a person's continuing identity through time.

Scientific reasoning is—and ought to be—conducted in accordance with the axioms of probability. This Bayesian view—so called because of the central role it accords to a theorem first proved by Thomas Bayes in the late eighteenth ...

Value is either additive or else it is subject to organic unity. In general we have organic unity where a complex whole is not simply the sum of its parts. Value exhibits organic unity if the value of a complex, whether a complex state or complex quality, is greater or less than the sum of the values of its components or parts. Whether or not value is additive might be thought to be of purely metaphysical interest, but it is also (...) connected with important aspects of evaluative reasoning. Additivity is closely connected with principles of bare difference and separability which are often tacitly assumed in value theory. The author spells out these principles and trace their connections with additivity and organic unity. The author then develops an unpleasant paradox of additivity. Additivity apparently entails nihilism: that nothing is more valuable than anything else. Additivity involves a kind of axiological atomism -- that complexes decompose into components or factors; that these factors possess value independently of their role in valuable complexes; and that the factors do not interact in their production of overall value. In order to avoid the paradox it seems as though the factors have to be akin to the metaphysically privileged states of logical atomism -- a doctrine that does not enjoy widespread support. The paradox poses a problem not only for the notions of organic unity and additivity, but also for the closely related bare-difference principles which lie at the heart of value theory and of its application. The author proposes a way of eliminating the paradox, and thereby saving additivity and separability, without presupposing an unpalatable variant of logical atomism. The author closes with the proposal to treat principles of additivity as regulative ideals in our search for intrinsic values. (shrink)

The coherentist theory of justification provides a response to the sceptical challenge: even though the independent processes by which we gather information about the world may be of dubious quality, the internal coherence of the information provides the justification for our empirical beliefs. This central canon of the coherence theory of justification is tested within the framework of Bayesian networks, which is a theory of probabilistic reasoning in artificial intelligence. We interpret the independence of the information gathering processes (IGPs) in (...) terms of conditional independences, construct a minimal sufficient condition for a coherence ranking of information sets and assess whether the confidence boost that results from receiving information through independent IGPs is indeed a positive function of the coherence of the information set. There are multiple interpretations of what constitute IGPs of dubious quality. Do we know our IGPs to be no better than randomization processes? Or, do we know them to be better than randomization processes but not quite fully reliable, and if so, what is the nature of this lack of full reliability? Or, do we not know whether they are fully reliable or not? Within the latter interpretation, does learning something about the quality of some IGPs teach us anything about the quality of the other IGPs? The Bayesian-network models demonstrate that the success of the coherentist canon is contingent on what interpretation one endorses of the claim that our IGPs are of dubious quality. (shrink)

This vital study offers a new interpretation of Hume's famous "Of Miracles," which notoriously argues against the possibility of miracles. By situating Hume's popular argument in the context of the 18th century debate on miracles, Earman shows Hume's argument to be largely unoriginal and chiefly without merit where it is original. Yet Earman constructively conceives how progress can be made on the issues that Hume's essay so provocatively posed about the ability of eyewitness testimony to establish the credibility of marvelous (...) and miraculous events. (shrink)

If you believe more things you thereby run a greater risk of being in error than if you believe fewer things. From the point of view of avoiding error, it is best not to believe anything at all, or to have very uncommitted beliefs. But considering the fact that we all in fact do entertain many specific beliefs, this recommendation is obviously in flagrant dissonance with our actual epistemic practice. Let us call the problem raised by this apparent conflict the (...) Addition Problem. In this paper we will find reasons to reject a particular premise used in the formulation of the Addition Problem, namely, the fundamental premise according to which believing more things increases the risk of error. As we will see, acquiring more beliefs need not decrease the probability of the whole, and hence need not increase the risk of error. In fact, more beliefs can mean an increase in the probability of the whole and a corresponding decrease in the risk of error. We will consider the Addition Problem as it arises in the context of the coherence theory of epistemic justification, while keeping firmly in mind that the point we wish to make is of epistemological importance also outside the specific coherentist dispute. The problem of determining exactly how the probability of the whole system depends on such factors as coherence, reliability and independence will be seen to open up an interesting area of research in which the theory of conditional independence structures is a helpful tool. (shrink)

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An attractive admirer of George Bernard Shaw once wrote to him with a not-so modest proposal: ``You have the greatest brain in the world, and I have the most beautiful body; so we ought to produce the most perfect child.'' Shaw replied: ``What if the child inherits my body and your brains?''What if, indeed? Shaw's retort is interesting not because it revealsa grasp of elementary genetics, but rather because it suggests his grasp of an interesting and important principle of axiology. (...) Since the brainy but ugly Shaw and his beautiful but apparently dim admirer both fall short of the ideal, she suggests that the best thing would be to genetically recombine his intelligence with her beauty. But what then would be the value of another genetic possibility: that of recombining his ugliness with her stupidity? Underlining the prompted inference is a fundamental principle of the theory of value which, perhaps surprisingly, has so far gone largely unnoticed in the ethical literature. I will call it the principle of recombinant values. (shrink)