Author: Rudolf Carnap
Publisher:
ISBN:
Category : Probabilities
Languages : en
Pages : 613

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Book Description

Author: R. Chuaqui
Publisher: Elsevier
ISBN: 0080872778
Category : Mathematics
Languages : en
Pages : 505

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Book Description
Anyone involved in the philosophy of science is naturally drawn into the study of the foundations of probability. Different interpretations of probability, based on competing philosophical ideas, lead to different statistical techniques, and frequently to mutually contradictory consequences. This unique book presents a new interpretation of probability, rooted in the traditional interpretation that was current in the 17th and 18th centuries. Mathematical models are constructed based on this interpretation, and statistical inference and decision theory are applied, including some examples in artificial intelligence, solving the main foundational problems. Nonstandard analysis is extensively developed for the construction of the models and in some of the proofs. Many nonstandard theorems are proved, some of them new, in particular, a representation theorem that asserts that any stochastic process can be approximated by a process defined over a space with equiprobable outcomes.

Author: Rudolf Carnap (Philosopher, Germany, United States)
Publisher:
ISBN:
Category :
Languages : en
Pages : 607

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Book Description

Author: Henry E. Kyburg Jr.
Publisher: Springer Science & Business Media
ISBN: 9401021759
Category : Philosophy
Languages : en
Pages : 440

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Book Description
Everyone knows it is easy to lie with statistics. It is important then to be able to tell a statistical lie from a valid statistical inference. It is a relatively widely accepted commonplace that our scientific knowledge is not certain and incorrigible, but merely probable, subject to refinement, modifi cation, and even overthrow. The rankest beginner at a gambling table understands that his decisions must be based on mathematical ex pectations - that is, on utilities weighted by probabilities. It is widely held that the same principles apply almost all the time in the game of life. If we turn to philosophers, or to mathematical statisticians, or to probability theorists for criteria of validity in statistical inference, for the general principles that distinguish well grounded from ill grounded generalizations and laws, or for the interpretation of that probability we must, like the gambler, take as our guide in life, we find disagreement, confusion, and frustration. We might be prepared to find disagreements on a philosophical and theoretical level (although we do not find them in the case of deductive logic) but we do not expect, and we may be surprised to find, that these theoretical disagreements lead to differences in the conclusions that are regarded as 'acceptable' in the practice of science and public affairs, and in the conduct of business.

Author: William Dennis Coles
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Book Description

Author: Rudolf Carnap
Publisher: Univ of California Press
ISBN: 9780520038264
Category : Mathematics
Languages : en
Pages : 312

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Book Description
A basic system of inductive logic; An axiomatic foundation for the logic of inductive generalization; A survey of inductive systems; On the condition of partial exchangeability; Representation theorems of the de finetti type; De finetti's generalizations of excahngeability; The structure of probabilities defined on first-order languages; A subjectivit's guide to objective chance.

Author: John M. Vickers
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 264

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Book Description
Discussing the relations between logic and probability, this book compares classical 17th- and 18th-century theories of probability with contemporary theories, explores recent logical theories of probability, and offers a new account of probability as a part of logic.

Author: Rudolf Carnap
Publisher: [Chicago] : University of Chicago Press
ISBN:
Category : Probabilities
Languages : en
Pages : 613

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Book Description

Author:
Publisher: Allied Publishers
ISBN: 9788177644517
Category :
Languages : en
Pages : 436

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Book Description
Probability theory

Author: Louis Narens
Publisher: World Scientific
ISBN: 9812708014
Category : Mathematics
Languages : en
Pages : 230

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Book Description
Standard probability theory has been an enormously successful contribution to modern science. However, from many perspectives it is too narrow as a general theory of uncertainty, particularly for issues involving subjective uncertainty. This first-of-its-kind book is primarily based on qualitative approaches to probabilistic-like uncertainty, and includes qualitative theories for the standard theory as well as several of its generalizations.One of these generalizations produces a belief function composed of two functions: a probability function that measures the probabilistic strength of an uncertain event, and another function that measures the amount of ambiguity or vagueness of the event. Another unique approach of the book is to change the event space from a boolean algebra, which is closely linked to classical propositional logic, to a different event algebra that is closely linked to a well-studied generalization of classical propositional logic known as intuitionistic logic. Together, these new qualitative theories succeed where the standard probability theory fails by accounting for a number of puzzling empirical findings in the psychology of human probability judgments and decision making.