APA PsycNET abstract: This is the first volume of a two-volume work on Probability and Induction. Because the writer holds that probability logic is identical with inductive logic, this work is devoted to philosophical problems concerning the nature of probability and inductive reasoning. The author rejects a statistical frequency basis for probability in favor of a logical relation between two statements or propositions. Probability "is the degree of confirmation of a hypothesis (or conclusion) on the basis of some given evidence (...) (or premises)." Furthermore, all principles and theorems of inductive logic are analytic, and the entire system is to be constructed by means of symbolic logic and semantic methods. This means that the author confines himself to the formalistic procedures of word and symbol systems. The resulting sentence or language structures are presumed to separate off logic from all subjectivist or psychological elements. Despite the abstractionism, the claim is made that if an inductive probability system of logic can be constructed it will have its practical application in mathematical statistics, and in various sciences. 16-page bibliography. (PsycINFO Database Record (c) 2016 APA, all rights reserved). (shrink)

Probability and inverse inference; Neyman-Pearson theory; Fisherian significance testing; The fiducial argument: one parameter; The fiducial argument: several parameters; Ian hacking's theory; Henry Kyburg's theory; Relevance and experimental design.

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At least one of these conceptions of probability underlies any theory of statistical inference (or, to use Neyman's phrase, 'inductive behavior'). ...

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It is argued that randomization has no role to play in the design or analysis of an experiment. If a Bayesian approach is adopted this conclusion is easily demonstrated. Outside that approach two principles, of conditionality and similarity, lead, via the likelihood principle, to the same conclusion. In the case of design, however, it is important to avoid confounding the effect of interest with an unexpected factor and this consideration leads to a principle of haphazardness that is clearly related to, (...) but not identical with, randomization. The role of exchangeability is discussed. (shrink)