# Term Paper On Bayesian Reasoning

For more on the laws of probability, see the following supplementary article: By itself, the definition of conditional probability is of little epistemological significance.

It acquires epistemological significance only in conjunction with a further epistemological assumption: (assumed to state the totality of one's new evidence and to have initial probability greater than zero), then rationality requires that one systematically transform one's initial probabilities to generate final or In epistemological terms, this Simple Principle of Conditionalization requires that the effects of evidence on rational degrees be analyzed in two stages: The first is non-inferential.

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.

In addition, some Bayesians follow Jeffrey in generalizing the Simple Principle to apply to cases in which one's new evidence is less than certain (also discussed below).

What unifies Bayesian epistemology is a conviction that conditionalizing (perhaps of a generalized sort) is rationally required in some important contexts — that is, that some sort of conditionalization principle is an important principle governing rational changes in degrees of belief.

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.

Ramsey and de Finetti first employed synchronic Dutch Book Arguments in support of the probability laws as standards of synchronic coherence for degrees of belief.

The first diachronic Dutch Book Argument in support of a principle of conditionalization was reported by Teller, who credited David Lewis.

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