![]() ![]() Infinite frequency principles belong to a broader class of direct inference principles, which include the well-known principal principle and various actual frequency principles. This type of reasoning draws on an infinite frequency principle. Then it seems unreasonable to set one’s credence in drawing a blue ball to anything else but q. Suppose that all one knows is that the frequency of drawing a blue ball approaches q as more balls are drawn (with replacement). ![]() A different kind of reasoning could be applied if one has knowledge about hypothetical frequencies. If all one knows is that the frequency of blue balls in the urn is q, it seems unreasonable to set one’s credence in drawing a blue ball to anything else but q. A typical example involves finite frequencies: suppose one is drawing from an urn with blue and red balls, with replacement. Although one may adhere to such a principle, one is not irrational otherwise. ![]() If all that rationality requires is adherence to the probability axioms, then there are no principles of direct inference. Infinite frequency principles can be used for what is known as direct inference, the calibration of one’s credence using evidence of chances and frequencies. These principles play a prominent role in some philosophical theories of subjective probability, such as Howson and Urbach ( 2006) and Williamson ( 2010), as well as theories of objective probability (Mellor, 1995). Infinite frequency principles differ from each other concerning the conditions under which this holds. An infinite frequency principle prescribes that a rational agent should set her credence that an experiment has outcome a to the frequency of a’s if that experiment were repeated indefinitely, provided that she knows this frequency. ![]()
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