Statistical and Inductive ProbabilitiesCourier Corporation, 27 jan 2012 - 160 pagina's Among probability theorists, a bitter controversy has raged for decades between the adherents of John Maynard Keynes' A Treatise on Probability (1921) and those of Richard von Mises' "Grundlagen der Wahrscheinlichkeitsrechnung" (1919). Keynes declared that probabilities measure the extent to which a so-called evidence proposition supports another sentence. Von Mises insisted that they measure the relative frequency with which the members of a so-called reference set belong to another set. Statistical and Inductive Probabilities offers an evenhanded treatment of this issue, asserting that both statistical and inductive probabilities may be treated as sentence-theoretic measurements, and that the latter qualify as estimates of the former. Beginning with a survey of the essentials of sentence theory and of set theory, author Hugues Leblanc examines statistical probabilities (which are allotted to sets by von Mises' followers), showing that statistical probabilities may be passed on to sentences, and thereby qualify as truth-values. Leblanc concludes with an exploration of inductive probabilities (which Keynes' followers allot to sentences), demonstrating their reinterpretation as estimates of truth-values. Each chapter is preceded by a summary of its contents. Illustrations accompany most definitions and theorems, and footnotes elucidate technicalities and bibliographical references. |
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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 denumerably infinite 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 population possible outcomes prob probability in LN probability set probability theory Proof Ps(P Ps(Q 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 tossed true in L true in LN truth-value universe of discourse variables of LN W₁ W₂