The Logic of Conditionals


Book Description

Of the four chapters in this book, the first two discuss (albeit in consider ably modified form) matters previously discussed in my papers 'On the Logic of Conditionals' [1] and 'Probability and the Logic of Conditionals' [2], while the last two present essentially new material. Chapter I is relatively informal and roughly parallels the first of the above papers in discussing the basic ideas of a probabilistic approach to the logic of the indicative conditional, according to which these constructions do not have truth values, but they do have probabilities (equal to conditional probabilities), and the appropriate criterion of soundness for inferences involving them is that it should not be possible for all premises of the inference to be probable while the conclusion is improbable. Applying this criterion is shown to have radically different consequences from the orthodox 'material conditional' theory, not only in application to the standard 'fallacies' of the material conditional, but to many forms (e. g. , Contraposition) which have hitherto been regarded as above suspi cion. Many more applications are considered in Chapter I, as well as certain related theoretical matters. The chief of these, which is the most important new topic treated in Chapter I (i. e.







IFS


Book Description

With publication of the present volume, The University of Western Ontario Series in Philosophy of Science enters its second phase. The first fourteen volumes in the Series were produced under the managing editorship of Professor James J. Leach, with the cooperation of a local editorial board. Many of these volumes resulted from colloguia and workshops held in con nection with the University of Western Ontario Graduate Programme in Philosophy of Science. Throughout its seven year history, the Series has been devoted to publication of high quality work in philosophy of science con sidered in its widest extent, including work in philosophy of the special sciences and history of the conceptual development of science. In future, this general editorial emphasis will be maintained, and hopefully, broadened to include important works by scholars working outside the local context. Appointment of a new managing editor, together with an expanded editorial board, brings with it the hope of an enlarged international presence for the Series. Serving the publication needs of those working in the various subfields within philosophy of science is a many-faceted operation. Thus in future the Series will continue to produce edited proceedings of worthwhile scholarly meetings and edited collections of seminal background papers. How ever, the publication priorities will shift emphasis to favour production of monographs in the various fields covered by the scope of the Series. THE MANAGING EDITOR vii W. L. Harper, R. Stalnaker, and G. Pearce (eds.), lIs, vii.




Probability and Conditionals


Book Description

Essays on the state of research investigating the relationship between conditionals and conditional probabilities.




Conditionals


Book Description

A unified treatment of conditionals based on epistemological principles rather than the semantical principles in vogue over recent decades. This book by distinguished philosopher Nicholas Rescher seeks to clarify the idea of what a conditional says by elucidating the information that is normally transmitted by its utterance. The result is a unified treatment of conditionals based on epistemological principles rather than the semantical principles in vogue over recent decades. This approach, argues Rescher, makes it easier to understand how conditionals actually function in our thought and discourse. In its concern with what language theorists call pragmatics—the study of the norms and principles governing our use of language in conveying information—Conditionals steps beyond the limits of logic as traditionally understood and moves into the realm claimed by theorists of artificial intelligence as they try to simulate our actual information-processing practices. The book's treatment of counterfactuals essentially revives an epistemological approach proposed by F. P. Ramsey in the 1920s and developed by Rescher himself in the 1960s but since overshadowed by the now-dominant possible-worlds approach. Rescher argues that the increasingly evident liabilities of the possible-worlds strategy make a reappraisal of the older style of analysis both timely and desirable. As the book makes clear, an epistemological approach demonstrates that counterfactual reasoning, unlike inductive inference, is not a matter of abstract reasoning alone but one of good judgment and common sense.




Conditionals, Paradox, and Probability


Book Description

Conditionals, Paradox, and Probability comprises fifteen original essays on themes from the work of Dorothy Edgington, the first woman to hold a chair in philosophy at Oxford. Eminent contributors from philosophy and linguistics discuss a range of topics including conditionals, vagueness, knowledge, reasoning, and probability.




Counterfactuals and Probability


Book Description

Moritz Schulz explores counterfactual thought and language: what would have happened if things had gone a different way. Counterfactual questions may concern large scale derivations (what would have happened if Nixon had launched a nuclear attack) or small scale evaluations of minor derivations (what would have happened if I had decided to join a different profession). A common impression, which receives a thorough defence in the book, is that oftentimes we find it impossible to know what would have happened. However, this does not mean that we are completely at a loss: we are typically capable of evaluating counterfactual questions probabilistically: we can say what would have been likely or unlikely to happen. Schulz describes these probabilistic ways of evaluating counterfactual questions and turns the data into a novel account of the workings of counterfactual thought.




Probability Theory


Book Description

Probability theory




Logic and Conditional Probability


Book Description

This monograph develops an algebra of Boolean fractions, (ab) - ordered pairs of propositions or events - "a if b", "event a given event b". In nine chapters, the author shows that these conditional propositions (together with their associated instantiations or models): Provide logical elements that better represent and more faithfully facilitate manipulation of certain and uncertain conditional information Extend the Boole's algebra of 2-valued statements to a 3-valued system that includes "inapplicable statements" - those whose condition may be false in some or all instances (examples, cases, models...) Allow a definition of the probability of an arbitrary Boolean proposition Non-trivially combine Boolean logic with standard conditional probability theory Provide a complete and adequate development of the crucial 4th operation for Boolean logic, namely conditioning, including iterated conditioning Provide an expanded theory of deduction defined in terms of the extended operations on the Boolean fractions Admit a variety of deduction relations, and that the deductively closed sets generated by some initial set of conditionals can be calculated Extend the ordinary function operations of sum, difference, product & quotient to real-valued functions with possibly different or overlapping domains of definition Represent & simplify complex conditional statements in Bayesian expert systems used to calculate maximum information entropy solutions Explicate the logic of quantum measurements by better expressing the changing conditions in quantum mechanics




Probabilistic Knowledge


Book Description

Sarah Moss argues that in addition to full beliefs, credences can constitute knowledge. She introduces the notion of probabilistic content and shows how it plays a central role not only in epistemology, but in the philosophy of mind and language. Just you can believe and assert propositions, you can believe and assert probabilistic contents.