Principal Principle of David Lewis What roles does physical probability play in science? What are its properties? One central property of chance is that, when known, it constrains rational belief to take the same numerical value. David Lewis called this the Principal Principle,A Subjectivist's Guide to Objective Chance, Philosophical Papers of David Lewis, Volume 2, Oxford: Oxford University Press, 1986, pp. 83–132. a term that philosophers have mostly adopted. For   example, suppose you are certain that a particular biased coin has propensity 0.32 to land heads every time it is tossed. What is then the correct price for a gamble that pays $1 if the coin lands heads, and nothing otherwise ? According to the Principal Principle, the fair price is 32 cents. It is argued that Propensity Theories fail to meet the Principal Principle .
Principal Principle of David Lewis What roles does physical probability play in science? What are its properties? One central property of chance is that, when known, it constrains rational belief to take the same numerical value. David Lewis called this the Principal Principle,A Subjectivist's Guide to Objective Chance, Philosophical Papers of David Lewis, Volume 2, Oxford: Oxford University Press, 1986, pp. 83–132. a term that philosophers have mostly adopted. The principle states: The Principal Principle. Let C be any reasonable initial credence function. Let t be any time. Let x be any real number in the unit interval. Let X be the proposition that the chance, at time t, of A's holding equals x. Let E be any proposition compatible with X that is admissible at time t. Then C(AIXE) = x. Thus, for example, suppose you are certain that a particular biased coin has propensity 0.32 to land heads every time it is tossed. What is then the correct credence ? According to the Principal Principle, the correct credence is .32 .
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For
The principle states:
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The Principal Principle. Let C be any reasonable initial credence function. Let t be any time. Let x be any real number in the unit interval. Let X be the proposition that the chance, at time t, of A's holding equals x. Let E be any proposition compatible with X that is admissible at time t. Then C(AIXE) = x.
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Thus, for
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price for a gamble that pays $1 if the coin lands heads, and nothing otherwise
credence
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fair price is 32 cents. It is argued that Propensity Theories fail to meet the Principal Principle
correct credence is .32