Various theories try to give accounts of how measures of this confidence do or ought to behave, both as far as the internal mental consistency of the agent as ...

Previous studies with adult participants have investigated reasoning from one or two uncertain premises with simple deductive arguments. Three exploratory experiments were designed to extend these results by investigating the evaluation of the plausibility of the conclusion of "combined" arguments, i.e. arguments constituted by two or more "atomic" standard arguments which each involved the same conclusion and one uncertain premise out of two. One example is "If she meets Nicolas it is very improbable she will go to the swimming pool; (...) if she meets Sophie it is very probable she will go to the swimming pool; she meets Nicolas; she meets Sophie". With two conflicting arguments, one supporting and one unfavourable, participants chose a compromise stance (Exp. 1), unless the thematic content of the premises allows one to consider one argument as more important than the other (Exp. 3). With two favourable arguments and rather unfamiliar materials, two typical behaviours appeared. One consisted in choosing a degree of plausibility of the conclusion that is intermediate between the modals asserted in the premises, and the other in choosing a more favourable degree than the most favourable modal (Exp. 1). The plausibility of the conclusion increased when the number of supporting atomic arguments increased from one to three, and decreased when the number of unfavourable arguments increased (Exp. 2). Theoretical implications are discussed and a model is sketched. (shrink)

In artificial intelligence (AI), a number of criticisms were raised against the use of probability for dealing with uncertainty. All these criticisms, except what in this article we call the non-adequacy claim, have been eventually confuted. The non-adequacy claim is an exception because, unlike the other criticisms, it is exquisitely philosophical and, possibly for this reason, it was not discussed in the technical literature. A lack of clarity and understanding of this claim had a major impact on AI. Indeed, mostly (...) leaning on this claim, some scientists developed an alternative research direction and, as a result, the AI community split in two schools: a probabilistic and an alternative one. In this article, we argue that the non-adequacy claim has a strongly metaphysical character and, as such, should not be accepted as a conclusive argument against the adequacy of probability. (shrink)

The object of this paper is to show why recent research in the psychology of deductive and probabilistic reasoning does not have.

The introduction has a brief statement, sufficient for the purpose of this paper, which describes in general terms the notion of probability logic on which the paper is based. Contributions made in the eighteenth century by Leibniz, Jacob Bernoulli and Lambert, and in the nineteenth century by Bolzano, De Morgan, Boole, Peirce and MacColl are critically examined from a contemporary point of view. Historicity is maintained by liberal quotations from the original sources accompanied by interpretive explanation. Concluding the paper is (...) a summary. (shrink)

In a recent monograph, I advocated a new theory—the theory of belief functions—as an alternative to the Bayesian theory of epistemic probability. In this paper I compare the two theories in the context of a simple but authentic example of assessing evidence.The Bayesian theory is ostensibly the theory that assessment of evidence should proceed by conditioning additive probability distributions; this theory dates from the work of Bayes and Laplace in the second half of the eighteenth century. It is indisputably the (...) dominant theory of epistemic probability today.The theory of belief functions differs from the Bayesian theory in that it uses certain non-additive set functions in the place of additive probability distributions and in that it generalizes the rule of conditioning to a general rule for combining evidence. As a mathematical theory its apparent origin is rather recent and abrupt; it first appears in work of A. P. Dempster, published in the 1960’s. (shrink)

The received model of degrees of belief represents them as probabilities. Over the last half century, many philosophers have been convinced that this model fails because it cannot make room for the idea that an agent’s degrees of belief should respect the available evidence. In its place they have advocated a model that represents degrees of belief using imprecise probabilities (sets of probability functions). This paper presents a model of degrees of belief based on Dempster–Shafer belief functions and then presents (...) arguments for belief functions over imprecise probabilities as a model of evidence-respecting degrees of belief. The arguments cover three kinds of issue: theoretical virtues (simplicity, interpretability and flexibility); motivations; and problem cases (dilation and belief inertia). (shrink)

"A Survey of Ranking Theory": The paper gives an up-to-date survey of ranking theory. It carefully explains the basics. It elaborates on the ranking theoretic explication of reasons and their balance. It explains the dynamics of belief statable in ranking terms and indicates how the ranks can thereby be measured. It suggests how the theory of Bayesian nets can be carried over to ranking theory. It indicates what it might mean to objectify ranks. It discusses the formal and the philosophical (...) aspects of the tight relation and the complementarity of ranks and probabilities. It closes with comparative remarks on predecessors and other philosophical proposals as well as formal models developed in AI. (shrink)

L'idée d'associer probabilité et induction n'est pas propre au xxe siècle, mais elle a reçu un développement systématique lorsque les philosophes néo-positivistes s'en sont emparés. Dès les années 1940, le philosophe Rudolf Carnap s'est proposé de relever le «défi humien» en fondant une théorie de la confirmation par la construction d'une logique probabiliste dite «inductive». Ce projet avait été esquissé à Cambridge dans les années 1920 par l'économiste John M. Keynes. Examiner le programme de Carnap dans sa totalité, le situer (...) dans son contexte historique, suivre son évolution et les influences qu'il a eues, tels sont les buts de cet article. The idea of associating probability and induction is not a theme suitable for the xxth century but it has received a systematic development when the neo-positivist philosophers seized it. Beginning with the 1940's, the philosopher Rudolph Carnap proposed to affront the «Humian challenge» by founding a theory of confirmation through the construction of a probabilistic logic called «inductive». This project had been outlined in Cambridge during the 1920's by the economist John M. Keynes. To examine Carnap's program in its totality, to situate it in its historical context, to follow its evolution and the influences it has had, these are the aims of this article. (shrink)

This paper examines preferences among uncertain prospects when the decision maker is uneasy about his assignment of subjective probabilities. It proposes a two-stage lottery framework for the analysis of such prospects, where the first stage represents an assessment of the vagueness (ambiguity) in defining the problem's randomness and the second stage represents an assessment of the problem for each hypothesized randomness condition. Standard axioms of rationality are prescribed for each stage, including weak ordering, continuity, and strong independence. The ‘Reduction of (...) Compound Lotteries' axiom is weakened, however, so that the two lottery stages have consistent, but not collapsible, preference structures. The paper derives a representation theorem from the primitive preference axioms, and the theorem asserts that preference-consistent decisions are made as if the decision maker is maximizing a modified expected utility functional. This representation and its implications are compared to alternative decision models. Criteria for assigning the relative empirical power of the alternative models are suggested. (shrink)

In this article we analyze the claim that a probabilistic interpretation of the infinite epistemic regress problem leads to a unique solution, the so called “completion” of the regress. This claim is implicitly based on the assumption that the standard Kolmogorov axioms of probability theory are suitable for describing epistemic probability. This assumption, however, has been challenged in the literature, by various authors. One of the alternatives that have been suggested to replace the Kolmogorov axioms in case of an epistemic (...) interpretation of probability, are belief functions, introduced by Shafer in 1976. We show that when one uses belief functions to describe the infinite epistemic regress problem, it is no longer the case that the solution is unique. We also argue that this complies with common sense. (shrink)

Richard Jeffrey's generalization of Bayes' rule of conditioning follows, within the theory of belief functions, from Dempster's rule of combination and the rule of minimal extension. Both Jeffrey's rule and the theory of belief functions can and should be construed constructively, rather than normatively or descriptively. The theory of belief functions gives a more thorough analysis of how beliefs might be constructed than Jeffrey's rule does. The inadequacy of Bayesian conditioning is much more general than Jeffrey's examples of uncertain perception (...) might suggest. The ``parameter α '' that Hartry Field has introduced into Jeffrey's rule corresponds to the "weight of evidence" of the theory of belief functions. (shrink)