An Objective Theory of Probability
Author | : D. A. Gillies |
Publisher | : |
Total Pages | : |
Release | : 1978 |
Genre | : |
ISBN | : |
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Author | : D. A. Gillies |
Publisher | : |
Total Pages | : |
Release | : 1978 |
Genre | : |
ISBN | : |
Author | : Donald Gillies |
Publisher | : Routledge |
Total Pages | : 264 |
Release | : 2012-07-26 |
Genre | : Mathematics |
ISBN | : 1136810811 |
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.
Author | : Donald Gillies |
Publisher | : Routledge |
Total Pages | : 264 |
Release | : 2012-03-02 |
Genre | : Mathematics |
ISBN | : 0415618657 |
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.
Author | : Donald Gillies |
Publisher | : Psychology Press |
Total Pages | : 239 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 0415182751 |
The use of probability and statistics has increased dramatically in all fields of research. This book presents an account of the resultant philosophical theories of probability and explains how they relate to one another.
Author | : Richard Jeffrey |
Publisher | : Cambridge University Press |
Total Pages | : 144 |
Release | : 2004-04-12 |
Genre | : Mathematics |
ISBN | : 9780521536684 |
Sample Text
Author | : Vincent F. Hendricks |
Publisher | : Springer Science & Business Media |
Total Pages | : 222 |
Release | : 2001-06-30 |
Genre | : Mathematics |
ISBN | : 9780792369523 |
A collection of papers presented at the conference on Probability Theory - Philosophy, Recent History and Relations to Science, University of Roskilde, Denmark, September 16-18, 1998. Since the measure theoretical definition of probability was proposed by Kolmogorov, probability theory has developed into a mature mathematical theory. It is today a fruitful field of mathematics that has important applications in philosophy, science, engineering, and many other areas. The measure theoretical definition of probability and its axioms, however, are not without their problems; some of them even puzzled Kolmogorov. This book sheds light on some recent discussions of the problems in probability theory and their history, analysing their philosophical and mathematical significance, and the role pf mathematical probability theory in other sciences.
Author | : Patrick Maher |
Publisher | : Cambridge University Press |
Total Pages | : 336 |
Release | : 1993-02-26 |
Genre | : Education |
ISBN | : 052141850X |
This book is a major new contribution to decision theory, focusing on the question of when it is rational to accept scientific theories. The author examines both Bayesian decision theory and confirmation theory, refining and elaborating the views of Ramsey and Savage. He argues that the most solid foundation for confirmation theory is to be found in decision theory, and he provides a decision-theoretic derivation of principles for how many probabilities should be revised over time. Professor Maher defines a notion of accepting a hypothesis, and then shows that it is not reducible to probability and that it is needed to deal with some important questions in the philosophy of science. A Bayesian decision-theoretic account of rational acceptance is provided together with a proof of the foundations for this theory. A final chapter shows how this account can be used to cast light on such vexing issues as verisimilitude and scientific realism.
Author | : Donald Gillies |
Publisher | : Routledge |
Total Pages | : 238 |
Release | : 2012-09-10 |
Genre | : Philosophy |
ISBN | : 1134672462 |
The Twentieth Century has seen a dramatic rise in the use of probability and statistics in almost all fields of research. This has stimulated many new philosophical ideas on probability. Philosophical Theories of Probability is the first book to present a clear, comprehensive and systematic account of these various theories and to explain how they relate to one another. Gillies also offers a distinctive version of the propensity theory of probability, and the intersubjective interpretation, which develops the subjective theory.
Author | : Mauricio Suárez |
Publisher | : Cambridge University Press |
Total Pages | : |
Release | : 2021-01-21 |
Genre | : Philosophy |
ISBN | : 1108983847 |
This Element has two main aims. The first one (sections 1-7) is an historically informed review of the philosophy of probability. It describes recent historiography, lays out the distinction between subjective and objective notions, and concludes by applying the historical lessons to the main interpretations of probability. The second aim (sections 8-13) focuses entirely on objective probability, and advances a number of novel theses regarding its role in scientific practice. A distinction is drawn between traditional attempts to interpret chance, and a novel methodological study of its application. A radical form of pluralism is then introduced, advocating a tripartite distinction between propensities, probabilities and frequencies. Finally, a distinction is drawn between two different applications of chance in statistical modelling which, it is argued, vindicates the overall methodological approach. The ensuing conception of objective probability in practice is the 'complex nexus of chance'.
Author | : Henry Ely Kyburg |
Publisher | : |
Total Pages | : 278 |
Release | : 1980 |
Genre | : Mathematics |
ISBN | : |
Truth and probability; Foresight: its logical laws, its subjective sources; The bases of probability; Subjective probability as the measure of a non-measurable set; The elicitation of personal probabilities; Probability: beware of falsifications; Probable knowledge.