# Term Paper On Bayesian Reasoning

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

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That is to say, what reason is there to believe that they do anything more than extend the laws of deductive logic from beliefs to degrees of belief?

It should be mentioned, however, that even if Bayesian epistemology only extended the laws of deductive logic to degrees of belief, that alone would represent an extremely important advance in epistemology.

For example, no matter what one's degree of belief in the proposition that all human life will be destroyed within the next ten years, it would be not be rational to offer to buy a bet on its truth.

Williamson extends de Finetti's Dutch Book Argument for a finite additivity constraint on rational degrees of belief to produce an argument for a countable additivity constraint on degrees of belief, but the argument is better interpreted as a reductio of the literal-minded interpretation of Dutch Book Arguments than as an argument for the rationality of a countable additivity constraint.

Many arguments have been given for regarding the probability laws as coherence conditions on degrees of belief and for taking some principle of conditionalization to be a rule of probabilistic inference.

The most distinctively Bayesian are those referred to as .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.Dutch Book Arguments are a truly distinctive contribution made by Bayesians to the methodology of epistemology.It should also be mentioned that some Bayesians have defended their principles more directly, with non-pragmatic arguments.Deductive inconsistency so defined determines one kind of incoherence in belief, which I refer to as — in both cases, to apply not to beliefs, but degrees of belief (degrees of confidence).For Bayesians, the most important standards of probabilistic coherence are the laws of probability.Dutch Book Arguments represent the possibility of a new kind of justification for epistemological principles.A Dutch Book Argument relies on some descriptive or normative assumptions to connect degrees of belief with willingness to wager — for example, a person with degree of belief is a Dutch Book combination of wagers that one will be motivated to enter into at different times.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.

## Comments Term Paper On Bayesian Reasoning

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