Multiple -conclusion logic extends formal logic by allowing arguments to have a set of conclusions instead of a single one, the truth lying somewhere among the conclusions if all the premises are true. The extension opens up interesting possibilities based on the symmetry between premises and conclusions, and can also be used to throw fresh light on the conventional logic and its limitations. This is a sustained study of the subject and is certain to stimulate further research. Part I reworks (...) the fundamental ideas of logic to take account of multiple conclusions, and investigates the connections between multiple - and single - conclusion calculi. Part II draws on graph theory to discuss the form and validity of arguments independently of particular logical systems. Part III contrasts the multiple - and the single - conclusion treatment of one and the same subject, using many-valued logic as the example; and Part IV shows how the methods of 'natural deduction' can be matched by direct proofs using multiple conclusions. (shrink)

Anti-realism is a doctrine about logic, language, and meaning that is based on the work of Wittgenstein and Frege. In this book, Professor Tennant clarifies and develops Dummett's arguments for anti-realism and ultimately advocates a radical reform of our logical practices.

Several of the so-called “fallacies” in Aristotle are not in fact mistaken inference-types, but mistakes or breaches of rules in the questioning games which were practiced in the Academy and in the Lyceum. Hence the entire Aristotelian theory of “fallacies” ought to be studied by reference to the author's interrogative model of inquiry, based on his theory of questions and answers, rather than as a part of the theory of inference. Most of the “fallacies” mentioned by Aristotle can in fact (...) be diagnosed by means of the interrogative model, including petitio principii, multiple questions, “babbling’, etc., and so can Aristotle's alleged anticipation of the fallacy of argumentum ad hominem. The entire Aristotelian conception of inquiry is an interrogative one. Deductive conclusions caught Aristotle's attention in the form of answers that every rational interlocutor must give, assuming only his own earlier answers. Several features of Aristotle's methodology can be understood by means of the interrogative model, including the role of endoxa in it. Theoretically, there is also considerable leeway as to whether “fallacies” are conceived of as mistakes in questioning or as breaches of the rules that govern questioning games. (shrink)

The main currently unsolved problem in the theory of argumentation concerns the function of logic in argumentation and reasoning. The traditional view simply identified logic with the theory of reasoning. This view is still being echoed in older textbooks of formal logic. In a different variant, the same view is even codified in the ordinary usage of words such as ‘logic’, ‘deduction’, ‘inference’, etc. For each actual occurrence of these terms in textbooks of formal logic, there are hundreds of uses (...) of the same idioms to describe the feats of real or fictional detectives. I have called the idea reflected by this usage the “Sherlock Holmes conception of logic and deduction.” In the history of science, we find no less a thinker than Sir Isaac Newton describing his experimental method as one of analysis or resolution and claiming to have “deduced” at least some of his laws from the “phenomena.”. (shrink)