Statistical and Inductive ProbabilitiesPrentice-Hall, 1962 - 148 pagina's This even-handed treatment addresses the decades-old dispute among probability theorists, asserting that both statistical and inductive probabilities may be treated as sentence-theoretic measurements, and that the latter qualify as estimates of the former. Discusses sentence theory, set theory, statistical probabilities, inductive probabilities, more. Illustrations and footnotes elucidate definitions, theorems, and technicalities. |
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a)-sample absolute probability actual outcomes belong Carnap Chapter closed sentence coin landing heads conditional probability constants of LN containing occurrences contains free occurrences defined estimate example false in LN finite hence i-th individual constant individual variable individuals designated inductive inferences instance John Doe Kemeny logically equivalent logically false logically implies logically true meets requirements open sentence Ɔ P Ɔ P₁ P₂ pair of closed Pi(P Pi¹ Pi¹(P PiN Q PiN(P PioN population possible outcomes prob probability in LN probability set probability theory Proof Ps(P Ps(Q Ps²(P Q in LN Q is logically real numbers reckoned relative frequency allotment s₁ sample Section sentence of L sentence of LN sentence Q sequences serially ordered state-descriptions of LN station wagon statistical probability subsets suburbanite theorems true in L true in LN truth-value universe of discourse variables of LN W₁ W₂ weight in LN