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The book extends the development of probability logic_a logic using probability, not verity (true, false) as the basic semantic notion. The basic connectives 'not,' 'and,' and 'or' are described in depth to include quantified formulas. Also discussed is the notion of the suppositional, and resolution of the paradox of confirmation.

This volume represents a radical departure from the current philosophical duopoly in the area of foundations of probability, that is, the frequency and subjective theories. One of the main new ideas is a set of scientific laws of probability. The new laws are simple, intuitive and, last but not least, they agree well with the contents of current textbooks on probability. Another major new claim is that the “frequency statistics” has nothing in common with the “frequency philosophy of probability,” contrary to popular belief. Similarly, contrary to the general perception, the “Bayesian statistics” shares nothing in common with the “subjective philosophy of probability.”

Probability is increasingly important for our understanding of the world. What is probability? How do we model it, and how do we use it? Timothy Childers presents a lively introduction to the foundations of probability and to philosophical issues it raises. He keeps technicalities to a minimum, and assumes no prior knowledge of the subject.

If it was not obvious before, after reading McShane and Gal, the conclusion is that p-values should be proscribed. There are no good uses for them; indeed, every use either violates frequentist theory, is fallacious, or is based on a misunderstanding. A replacement for p-values is suggested, based on predictive models.

\"It is a commonplace that scientific inquiry makes extensive use of probabilities, many of which seem to be objective chances, describing features of reality that are independent of our minds. Such chances appear to have a number of paradoxical or puzzling features: they appear to be mind-independent facts, but they are intimately connected with rational psychology; they display a temporal asymmetry, but they are supposed to be grounded in physical laws that are time-symmetric; and chances are used to explain and predict frequencies of events, although they cannot be reduced to those frequencies. This book offers an accessible and non-technical introduction to these and other puzzles. Toby Handfield engages with traditional metaphysics and philosophy of science, drawing upon recent work in the foundations of quantum mechanics and thermodynamics to provide a novel account of objective probability that is empirically informed without requiring specialist scientific knowledge\"-- Provided by publisher.

The present study is an extension of the topic introduced in Dr. Hailperin's Sentential Probability Logic, where the usual true-false semantics for logic is replaced with one based more on probability, and where values ranging from 0 to 1 are subject to probability axioms. Moreover, as the word 'sentential' in the title of that work indicates, the language there under consideration was limited to sentences constructed from atomic (not inner logical components) sentences, by use of sentential connectives ('no,' 'and,' 'or,' etc.) but not including quantifiers ('for all,' 'there is'). An initial introduction presents an overview of the book. In chapter one, Halperin presents a summary of results from his earlier book, some of which extends into this work. It also contains a novel treatment of the problem of combining evidence: how does one combine two items of interest for a conclusion-each of which separately impart a probability for the conclusion-so as to have a probability for the conclusion based on taking both of the two items of interest as evidence? Chapter two enlarges the Probability Logic from the first chapter in two respects: the language now includes quantifiers ('for all,' and 'there is') whose variables range over atomic sentences, not entities as with standard quantifier logic. (Hence its designation: ontological neutral logic.) A set of axioms for this logic is presented. A new sentential notion-the suppositional-in essence due to Thomas Bayes, is adjoined to this logic that later becomes the basis for creating a conditional probability logic. Chapter three opens with a set of four postulates for probability on ontologically neutral quantifier language. Many properties are derived and a fundamental theorem is proved, namely, for any probability model (assignment of probability values to all atomic sentences of the language) there will be a unique extension of the probability values to all closed sentences of the language. The chapter concludes by showing the Borel's early denumerable probability concept (1909) can be justified by its being, in essence, close to Hailperin's probability result applied to denumerable language. The final chapter introduces the notion of conditional-probability to a language having quantifiers of the kind discussed in chapter two. A definition of probability for this type of language is defined and some of its properties characterized. The much discussed and written about Confirmation Paradox is presented and theorems involving conditional probability for this quantifier language with the conditional are derived. Using these results, Hailperin obtains a resolution of this paradox.