Logic Without Gaps Or Gluts

Logic Without Gaps or Gluts

This book offers a defense against non-classical approaches to the paradoxes. The author argues that, despite appearances, the paradoxes give no reason at all to reject classical logic. In fact, he believes classical solutions fare better than non-classical ones with respect to key tests like Curry’s Paradox, a Liar-like paradox that dialetheists are forced to solve in a way totally disjoint from their solution to the Liar. Graham Priest’s In Contradiction was the first major work that advocated the use of non-classical approaches. Since then, these views have moved into the philosophical mainstream. Much of this movement is fueled by a widespread sense that these logically heterodox solutions get to the real nub of the issue. They lack the ad hoc feel of many other solutions to the paradoxes. The author believes that it's long past time for a response to these attacks against classical orthodoxy. He presents a non-logically-revisionary solution to the paradoxes. This title offers a literal way of cashing out the disquotation metaphor. While the details of the view are novel, the idea has a pre-history in the relevant literature. The author examines objections in detail. He rejects each in turn and concludes by comparing the virtues of his logically orthodox approach with those of the paraconsistent and paracomplete competition.

Logic Without Gaps Or Gluts

Paraconsistency: Logic and Applications

A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more "big picture" ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics.