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Philosophies of probability: objective Bayesianism and its challenges
 Handbook of the philosophy of mathematics. Elsevier, Amsterdam. Handbook of the Philosophy of Science
, 2004
"... This chapter presents an overview of the major interpretations of probability followed by an outline of the objective Bayesian interpretation and a discussion of the key challenges it faces. ..."
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Cited by 7 (4 self)
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This chapter presents an overview of the major interpretations of probability followed by an outline of the objective Bayesian interpretation and a discussion of the key challenges it faces.
Against conditionalization
 Synthese
, 1990
"... The central focus of this paper is conditionalization, but we also address related principles such as that of reflection. It is argued that dutch book theorems do not show what they are intended to show in the ordinary (static) case, and that they are even less persuasive in the dynamic case to whic ..."
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Cited by 5 (1 self)
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The central focus of this paper is conditionalization, but we also address related principles such as that of reflection. It is argued that dutch book theorems do not show what they are intended to show in the ordinary (static) case, and that they are even less persuasive in the dynamic case to which conuitionalization applies. The first point is that to be forced to post odds and meet the bets of all comers reveals something about one's rationality, bu t nothing about one's degrees of belief. Adding conditional bets to the requirements of posting adds nothing to the rational constraints. We consider the argument of Paul Teller, which does address the genuinely dynamic consideration of changes of belief in the face of evidence. We argue that Teller's principle P is not a principle of rationality. This claim is relevant to the controversy concerning scientific change and its relation to anomalies in scientific theory. The principle of reflection introduced by van Fraassen fares no better. Finally, it is shown that suggestions of Carnap himself lead to the violation of conditionalization. Carnap may not have been infallible, but his intuitions concerning inductive relations were surely good enough to take into account. Overall, we find no compelling argument in favor of conditionalization as a genera.l principle, however important it may be in special circumstances.
Philosophies of probability
 Handbook of the Philosophy of Mathematics, Volume 4 of the Handbook of the Philosophy of Science
"... This chapter presents an overview of the major interpretations of probability followed by an outline of the objective Bayesian interpretation and a discussion of the key challenges it faces. I discuss the ramifications of interpretations of probability and objective Bayesianism for the philosophy of ..."
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Cited by 3 (2 self)
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This chapter presents an overview of the major interpretations of probability followed by an outline of the objective Bayesian interpretation and a discussion of the key challenges it faces. I discuss the ramifications of interpretations of probability and objective Bayesianism for the philosophy of mathematics in general.
Dynamic models of deliberation and the theory of games
 In Proceedings of the Theoretical Aspects of Rationality and Knowledge
, 1990
"... Deliberation can be modeled as a dynamic process. Where deliberation generates new information relevant to the decision under consideration, a rational decision maker will (processing costs permitting) feed back that information and reconsider. A firm decision is reached at a fixed point of this pro ..."
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Deliberation can be modeled as a dynamic process. Where deliberation generates new information relevant to the decision under consideration, a rational decision maker will (processing costs permitting) feed back that information and reconsider. A firm decision is reached at a fixed point of this process a deliberational equilibrium. Although there may be many situations in which informational feedback may be neglected and an essentially static theory of deliberation will suffice, there are others in which informational feedback plays a crucial role. From the point of view of procedural rationality, computation itself generates new information. Taking this point of view seriously leads to dynamic models of deliberation within which one can embed the theory of noncooperative games. In the sort of strategic situations considered by the theory of games, each player's optimal act depends on the acts selected by the other players. Thus each player must not only calculate expected utilities according to her current probabilities, but must also think about such calculations that other players are making and the effect on the probabilities of their
On the Emergence of Reasons in Inductive Logic
 Journal of the IGPL
, 2001
"... We apply methods of abduction derived from propositional probabilistic reasoning to predicate probabilistic reasoning, in particular inductive logic, by treating nite predicate knowledge bases as potentially in nite propositional knowledge bases. It is shown that for a range of predicate knowledg ..."
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Cited by 2 (2 self)
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We apply methods of abduction derived from propositional probabilistic reasoning to predicate probabilistic reasoning, in particular inductive logic, by treating nite predicate knowledge bases as potentially in nite propositional knowledge bases. It is shown that for a range of predicate knowledge bases (such as those typically associated with inductive reasoning) and several key propositional inference processes (in particular the Maximum Entropy Inference Process) this procedure is well de ned, and furthermore yields an explanation for the validity of the induction in terms of `reasons'. Keywords: Inductive Logic, Probabilistic Reasoning, Abduction, Maximum Entropy, Uncertain Reasoning. 1 Motivation Consider the following situation. I am sitting by a bend in a road and I start to wonder how likely it is that the next car which passes will skid on this bend. I have some knowledge which seems relevant, for example I know that if there is ice on the road then there is a good chance of a skid, and similarly if the bend is unsigned, the camber adverse, etc.. I possibly also have some knowledge of how likely it is that there is ice on the road, how likely it is that the bend is unsigned (possibly conditioned on the iciness of the road) etc.. Notice that this is generic knowledge which applies equally to any potential passing car.
On the Emergence of Reasons in
"... We apply methods of abduction derived from propositional probabilistic reasoning to predicate probabilistic reasoning, in particular inductive logic, by treating finite predicate knowledge bases as potentially infinite propositional knowledge bases. It is shown that for a range of predicate knowled ..."
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Cited by 2 (2 self)
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We apply methods of abduction derived from propositional probabilistic reasoning to predicate probabilistic reasoning, in particular inductive logic, by treating finite predicate knowledge bases as potentially infinite propositional knowledge bases. It is shown that for a range of predicate knowledge bases (such as those typically associated with inductive reasoning) and several key propositional inference processes (in particular the Maximum Entropy Inference Process) this procedure is well defined, and furthermore yields an explanation for the validity of the induction in terms of `reasons'. Keywords: Inductive Logic, Probabilistic Reasoning, Abduction, Maximum Entropy, Uncertain Reasoning. 1 Motivation Consider the following situation. I am sitting by a bend in a road and I start to wonder how likely it is that the next car which passes will skid on this bend. I have some knowledge which seems relevant, for example I know that if there is ice on the road then there is a good chance of a skid, and similarly if the bend is unsigned, the camber adverse, etc.. I possibly also have some knowledge of how likely it is that there is ice on the road, how likely it is that the bend is unsigned (possibly conditioned on the iciness of the road) etc.. Notice that this is generic knowledge which applies equally to any potential passing car.
Some Limit Theorems for ME, MD and ...
"... We apply methods of abduction derived from propositional probabilistic reasoning to predicate probabilistic reasoning, in particular inductive logic, by treating nite predicate knowledge bases as potentially innite propositional knowledge bases. Full and detailed proofs are given to show that for a ..."
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We apply methods of abduction derived from propositional probabilistic reasoning to predicate probabilistic reasoning, in particular inductive logic, by treating nite predicate knowledge bases as potentially innite propositional knowledge bases. Full and detailed proofs are given to show that for a range of predicate knowledge bases (such as those typically associated with inductive reasoning) and several key propositional inference processes (in particular the Maximum Entropy Inference Process) this procedure is well dened, and furthermore yields an explanation for the validity of the induction in terms of `reasons'. Motivation Consider the following situation. I am sitting by a bend in a road and I start to wonder how likely it is that the next car which passes will skid on this bend. I have some knowledge which seems relevant, for example I know that if there is ice on the road then there is a good chance of a skid, and similarly if the bend is unsigned, the camber adverse, etc.. I possibly also have some knowledge of how likely it is that there is ice on the road, how likely it is that the bend is unsigned (possibly conditioned on the iciness of the road) etc.. Notice that this is generic knowledge which applies equally to any potential passing car. Supported by a EPRSC Research Associateship y Supported by an Egyptian Government Scholarship, File No. 7083 1 Armed with this knowledge base I may now form some opinion as to the likely outcome when the next car passes. Subsequently several cars pass by. I note the results and in consequence possibly revise my opinion as to the likelihood of the next car through skidding. Clearly we are all capable of forming opinions, or beliefs, in this way, but is it possible to formalize this inductive process, this pro...
Lecture 7 Carnap’s Inductive Logic
"... Rudolf Carnap (1891–1970) worked on explicating inductive probability from the early 1940s until his death in 1970. His last and best explicatum was published posthumously in ..."
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Rudolf Carnap (1891–1970) worked on explicating inductive probability from the early 1940s until his death in 1970. His last and best explicatum was published posthumously in