Term Paper On Bayesian Reasoning

Dutch Book Arguments are a truly distinctive contribution made by Bayesians to the methodology of epistemology.

It is the change in the probability of the evidence statement )).

Problems with the Simple Principle (to be discussed below) have led many Bayesians to qualify the Simple Principle by limiting its scope.

Putting it this way makes susceptibility to Dutch Books sound irrational.

But this standard of rationality would make it irrational not to recognize all the logical consequences of what one believes. If successful, Dutch Book Arguments would reduce the justification of the principles of Bayesian epistemology to two elements: (1) an account of the appropriate relationship between degrees of belief and choice; and (2) the laws of deductive logic.

In addition to reporting Lewis's Dutch Book Argument, Teller offers a non-pragmatic defense of Conditionalization.

There have been many proposed non-pragmatic defenses of the probability laws (e.g., van Fraassen; Shimony). All such defenses, whether pragmatic or non-pragmatic, produce a puzzle for Bayesian epistemology: The principles of Bayesian epistemology are typically proposed as principles of content?The Lewis/Teller argument depends on a further descriptive or normative assumption about conditional probabilities due to de Finetti: An agent with conditional probability , their significance is that they show that those whose degrees of belief violate the probability laws or those whose probabilistic inferences predictably violate a principle of conditionalization are liable to enter into wagers on which they are sure to lose.There is very little to be said for the literal-minded interpretation, because there is no basis for claiming that rationality requires that one be willing to wager in accordance with the behavioral assumptions described above.The formal apparatus itself has two main elements: the use of the laws of probability as coherence constraints on rational degrees of belief (or degrees of confidence) and the introduction of a rule of probabilistic inference, a rule or principle of , which is now the dominant theoretical model for both the descriptive and normative analysis of decisions.The combination of its precise formal apparatus and its novel pragmatic self-defeat test for justification makes Bayesian epistemology one of the most important developments in epistemology in the 20 There are two ways that the laws of deductive logic have been thought to provide rational constraints on belief: (1) Synchronically, the laws of deductive logic can be used to define the notion of deductive consistency and inconsistency.The problem is not that one who violates the Bayesian constraints is likely to enter into a combination of wagers that constitute a Dutch Book, but that, on any reasonable way of translating one's degrees of belief into action, there is a potential for one's degrees of belief to motivate one to act in ways that make things worse than they might have been, when, as a matter of logic alone, it can be determined that alternative actions would have made things better (on one's own evaluations of better and worse).Another way of understanding the problem of susceptibility to a Dutch Book is due to Ramsey: Someone who is susceptible to a Dutch Book evaluates identical bets differently based on how they are described.The rational response to offers to bet on the proposition that all life will be destroyed within the next ten years or to bet on a single possible outcome in a countably infinite set of equiprobable possible outcomes is simply not to.A more plausible interpretation of Dutch Book Arguments is that they are to be understood hypothetically, as symptomatic of what has been termed .Because it would seem that the truth about the appropriate relationship between the degrees of belief and choice is independent of epistemology, Dutch Book Arguments hold out the potential of justifying the principles of Bayesian epistemology in a way that requires no other epistemological resources than the laws of deductive logic.For this reason, it makes sense to think of Dutch Book Arguments as indirect, pragmatic arguments for according the principles of Bayesian epistemology much the same epistemological status as the laws of deductive logic.