This book is intended to be used as a textbook by students of mathematics, and also within limitations as a reference work.

This book is intended to be used as a textbook by students of mathematics, and also within limitations as a reference work.

Relevantism, as a matter of definition, rejects classical logic as incorrect and adopts instead a relevant logic as encapsulating correct inference. It rejects classical logic on the grounds that the rule of Material Detachment, from A and not A or B to infer B,, sometimes leads from truth to falsity. Relevantism — although promoted by some relevant logicians, and an integral part of ultralogic — has recently encountered heavy, but interesting, criticism from relevance logicians themselves.

The logician's central concern is with the validity of argument. A logical theory ought, therefore, to provide a general criterion of validity. This book sets out to find such a criterion, and to describe the philosophical basis and the formal theory of a logic in which the premises of a valid argument are relevant to its conclusion. The notion of relevance required for this theory is obtained by an analysis of the grounds for asserting a formula in a proof.

Relevance logics came of age with the one and only International Conference on relevant logics in 1974. They did not however become accepted, or easy to promulgate. In March 1981 we received most of the typescript of IN MEMORIAM: ALAN ROSS ANDERSON Proceedings of the International Conference of Relevant Logic from the original editors, Kenneth W. Collier, Ann Gasper and Robert G. Wolf of Southern Illinois University. 1 They had, most unfortunately, failed to find a publisher - not, it appears, (...) because of overall lack of merit of the essays, but because of the expense of producing the collection, lack of institutional subsidization, and doubts of publishers as to whether an expensive collection of essays on such an esoteric, not to say deviant, subject would sell. We thought that the collection of essays was still (even after more than six years in the publishing trade limbo) well worth publishing, that the subject would remain undeservedly esoteric in North America while work on it could not find publishers (it is not so esoteric in academic circles in Continental Europe, Latin America and the Antipodes) and, quite important, that we could get the collection published, and furthermore, by resorting to local means, published comparatively cheaply. It is indeed no ordinary collection. It contains work by pioneers of the main types of broadly relevant systems, and by several of the most innovative non-classical logicians of the present flourishing logical period. We have slowly re-edited and reorganised the collection and made it camera-ready. (shrink)

This paper reformulates and decides a certain conjecture in Dunn's 'Relevant Predication 1: The Formal Theory' (Journal of Philosophical Logic 16, 347-381, 1987). This conjecture of Dunn's relates his object-language characterisation of a property's being relevant in a variable x to certain grammatical characterisations of relevance, analogous to some given by Helman, in 'Relevant Implication and Relevant Functions' (to appear in Entailment: The Logic of Relevance and Necessity, vol. 2, by Alan Ross Anderson, Nuel Belnap, and J. Michael Dunn et (...) al.) In the course of the investigation this paper also investigates Kit Fine's semantics for quantified relevance logics, which appears in his appropriately titled 'Semantics for Quantified Relevance Logics'. (shrink)

First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.

This study provides a unified theory of properties, relations, and propositions (PRPs). Two conceptions of PRPs have emerged in the history of philosophy. The author explores both of these traditional conceptions and shows how they can be captured by a single theory.

Brand Blanshard has been among the most stubborn of contemporary philosophers in rejecting that mathematical analysis of “logic” which has most enchanted his contemporary mathematical practitioners of the trade. He has said repeatedly that the mathematically orthodox have simply got hold of the whole topic by the wrong handle, and cited many complaints about material and strict “implication” as evidence that something has gone gravely wrong. Most of the objections he raises coincide with those of students newly introduced to the (...) topic. But in the case of our students, it seems that the vast majority can be either brainwashed or browbeaten into ignoring the initial objections we all felt, on introduction, to principles like ⊃q, or p ⊃, or ☐ p ⊰. Blanshard has, however, continued to champion the cause of the “common man” against the mathematically precise, but allegedly misguided dogmas of orthodoxy. (shrink)

R-Dagger is the theory of relevant implication, Got from the calculus r (see belnap, Jsl, 32, 1-22), By adding machinery for propositional quantification. In r-Dagger define t as for some p, P, F as for all p, P. Then (t, F) is closed in r-Dagger under truth-Functions and relevant implication, Which, When confined to (t, F) acts just like material 'implication.' but r-Dagger admits of many propositions other than t, F. The article also contains polemics against extensionalism and nominalism. (edited).

First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.

F. H. Bradley was the foremost philosopher of the British Idealist school, which came to prominence in the second half of the nineteenth century. Bradley, who was a life fellow of Merton College, Oxford, was influenced by Hegel, and also reacted against utilitarianism. He was recognised during his lifetime as one of the greatest intellectuals of his generation and was the first philosopher to receive the Order of Merit, in 1924. His work is considered to have been important to the (...) formation of analytic philosophy. In metaphysics, he rejected pluralism and realism, and believed that English philosophy needed to deal systematically with first principles. This work, first published in 1893, is divided into two parts: 'Appearance' deals with exposing the contradictions that Bradley believed are hidden in our everyday conceptions of the world; and in 'Reality', he builds his positive account of reality and considers possible objections to it. (shrink)