An Objective Theory of Probability (Routledge Revivals)

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Routledge, Jul 26, 2012 - Mathematics - 262 pages
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This reissue of D. A. Gillies highly influential work, first published in 1973, is a philosophical theory of probability which seeks to develop von Mises’ views on the subject. In agreement with von Mises, the author regards probability theory as a mathematical science like mechanics or electrodynamics, and probability as an objective, measurable concept like force, mass or charge. On the other hand, Dr Gillies rejects von Mises’ definition of probability in terms of limiting frequency and claims that probability should be taken as a primitive or undefined term in accordance with modern axiomatic approaches.

This of course raises the problem of how the abstract calculus of probability should be connected with the ‘actual world of experiments’. It is suggested that this link should be established, not by a definition of probability, but by an application of Popper’s concept of falsifiability. In addition to formulating his own interesting theory, Dr Gillies gives a detailed criticism of the generally accepted Neyman Pearson theory of testing, as well as of alternative philosophical approaches to probability theory. The reissue will be of interest both to philosophers with no previous knowledge of probability theory and to mathematicians interested in the foundations of probability theory and statistics.

 

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Contents

Preface
THE SPECIAL SCIENCES IN GENERAL
Its Machian Origins
The concepts of force and mass before Newton How Newton introduced
theory of conceptual innovation How our theory of conceptual innovation avoids
Probability and Frequency
Three views on the relations between probability and frequency Randomness
Mises and Kolmogorov on the relations between probability and frequency
Deduction of the law of excluded gambling systems Independence and gambling
The Falsification Problem for Probability Statements
Formulation ofa Falsifying Rule
statement Braithwaites theory of probability
Outline of the NeymanPearson theory The NeymanPearson theory without
Explanation of Technical Terminology
References
General Index

The Role

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