Sociative Logics And Their Applications
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Sociative Logics and Their Applications
This title was first published in 2003. Richard Sylvan died in 1996, he had made contributions to many areas of philosophy, such as, relevant and paraconsistent logic, Meinongianism and metaphysics and environmental ethics. One of his "trademarks" was the taking up of unpopular views and defending them. To Richard Sylvan ideas were important, wether they were his or not. This is a book of ideas, based on a collection of work found after his death, a chance for readers to see his vision of his projects. This collected works represents material drafted between 1982 and 1996, and the theme is that a small band of logics, namely pararelevant logics, offer solutions to many problems, puzzles and paradoxes in the philosophy of science.
60 Years of Connexive Logic
This book provides deep insights into current research in the rapidly developing field of connexive logic and includes contributions from leading scholars in the field. Unlike the most well known systems of non-classical logic, systems of connexive logic are contra-classical in that they both reject certain classically valid principles and validate schemata that are not valid classically. The history of modern formal connexive logic may be seen to have started with Storrs McCall’s dissertation “Non-classical Propositional Calculi" (Oxford) 1963, thus roughly 60 years ago. While at the turn of the 21st century connexive logic was a virtually dead research programme, the situation has changed significantly after the inclusion of an entry on connexive logic in the Stanford Encyclopedia of Philosophy in 2006 and the beginning of a series of annual workshops on connexive logic in 2015. Nowadays, connexive logic is a vibrant area, and the present volume offers an exciting glimpse on recent work in connexive logic. The topics range from discussions of the notion of connexivity in logic, to conditional logic, relevance logic, and experimental philosophy. The volume contains an introduction that puts the various chapters into perspective and concludes with a list of open problems in connexive logic. The volume will be of interest to logicians and philosophers interested in non-classical logic. Chapters 1, 9 and 10, are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
The Many Valued and Nonmonotonic Turn in Logic
The present volume of the Handbook of the History of Logic brings together two of the most important developments in 20th century non-classical logic. These are many-valuedness and non-monotonicity. On the one approach, in deference to vagueness, temporal or quantum indeterminacy or reference-failure, sentences that are classically non-bivalent are allowed as inputs and outputs to consequence relations. Many-valued, dialetheic, fuzzy and quantum logics are, among other things, principled attempts to regulate the flow-through of sentences that are neither true nor false. On the second, or non-monotonic, approach, constraints are placed on inputs (and sometimes on outputs) of a classical consequence relation, with a view to producing a notion of consequence that serves in a more realistic way the requirements of real-life inference. Many-valued logics produce an interesting problem. Non-bivalent inputs produce classically valid consequence statements, for any choice of outputs. A major task of many-valued logics of all stripes is to fashion an appropriately non-classical relation of consequence.The chief preoccupation of non-monotonic (and default) logicians is how to constrain inputs and outputs of the consequence relation. In what is called "left non-monotonicity, it is forbidden to add new sentences to the inputs of true consequence-statements. The restriction takes notice of the fact that new information will sometimes override an antecedently (and reasonably) derived consequence. In what is called "right non-monotonicity, limitations are imposed on outputs of the consequence relation. Most notably, perhaps, is the requirement that the rule of or-introduction not be given free sway on outputs. Also prominent is the effort of paraconsistent logicians, both preservationist and dialetheic, to limit the outputs of inconsistent inputs, which in classical contexts are wholly unconstrained.In some instances, our two themes coincide. Dialetheic logics are a case in point. Dialetheic logics allow certain selected sentences to have, as a third truth value, the classical values of truth and falsity together. So such logics also admit classically inconsistent inputs. A central task is to construct a right non-monotonic consequence relation that allows for these many-valued, and inconsistent, inputs.The Many Valued and Non-Monotonic Turn in Logic is an indispensable research tool for anyone interested in the development of logic, including researchers, graduate and senior undergraduate students in logic, history of logic, mathematics, history of mathematics, computer science, AI, linguistics, cognitive science, argumentation theory, and the history of ideas. - Detailed and comprehensive chapters covering the entire range of modal logic. - Contains the latest scholarly discoveries and interprative insights that answers many questions in the field of logic.