In spite of a powerful tradition, more than two thousand years old, that in a valid argument the premises must be relevant to the conclusion, twentieth-century logicians neglected the concept of relevance until the publication of Volume I of this monumental work. Since that time relevance logic has achieved an important place in the field of philosophy: Volume II of Entailment brings to a conclusion a powerful and authoritative presentation of the subject by most of the top people working in (...) the area. Originally the aim of Volume II was simply to cover certain topics not treated in the first volume--quantification, for example--or to extend the coverage of certain topics, such as semantics. However, because of the technical progress that has occurred since the publication of the first volume, Volume II now includes other material. The book contains the work of Alasdair Urquhart, who has shown that the principal sentential systems of relevance logic are undecidable, and of Kit Fine, who has demonstrated that, although the first-order systems are incomplete with respect to the conjectured constant domain semantics, they are still complete with respect to a semantics based on "arbitrary objects." Also presented is important work by the other contributing authors, who are Daniel Cohen, Steven Giambrone, Dorothy L. Grover, Anil Gupta, Glen Helman, Errol P. Martin, Michael A. McRobbie, and Stuart Shapiro. Robert G. Wolf's bibliography of 3000 items is a valuable addition to the volume. (shrink)

In spite of a powerful tradition, more than two thousand years old, that in a valid argument the premises must be relevant to the conclusion, twentieth-century logicians neglected the concept of relevance until the publication of Volume I of this monumental work. Since that time relevance logic has achieved an important place in the field of philosophy: Volume II of Entailment brings to a conclusion a powerful and authoritative presentation of the subject by most of the top people working in (...) the area. Originally the aim of Volume II was simply to cover certain topics not treated in the first volume--quantification, for example--or to extend the coverage of certain topics, such as semantics. However, because of the technical progress that has occurred since the publication of the first volume, Volume II now includes other material. The book contains the work of Alasdair Urquhart, who has shown that the principal sentential systems of relevance logic are undecidable, and of Kit Fine, who has demonstrated that, although the first-order systems are incomplete with respect to the conjectured constant domain semantics, they are still complete with respect to a semantics based on "arbitrary objects." Also presented is important work by the other contributing authors, who are Daniel Cohen, Steven Giambrone, Dorothy L. Grover, Anil Gupta, Glen Helman, Errol P. Martin, Michael A. McRobbie, and Stuart Shapiro. Robert G. Wolf's bibliography of 3000 items is a valuable addition to the volume. Originally published in 1992. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)

Metaphysics and language: Quine, W. V. O. On the individuation of attributes. Körner, S. On some relations between logic and metaphysics. Marcus, R. B. Does the principle of substitutivity rest on a mistake? Van Fraassen, B. C. Platonism's pyrrhic victory. Martin, R. M. On some prepositional relations. Kearns, J. T. Sentences and propositions.--Basic and combinatorial logic: Orgass, R. J. Extended basic logic and ordinal numbers. Curry, H. B. Representation of Markov algorithms by combinators.--Implication and consistency: Anderson, A. R. Fitch on (...) consistency. Belnap, N. D., Jr. Grammatical propaedeutic. Thomason, R. H. Decidability in the logic of conditionals. Myhill, J. Levels of implication.--Deontic, epistemic, and erotetic logic: Bacon, J. Belief as relative knowledge. Wu, K. J. Believing and disbelieving. Kordig, C. R. Relativized deontic modalities. Harrah, D. A system for erotetic sentences. (shrink)

What is new here is the detailed discussion of several important results in the classical foundations of mathematics and of the relation of logic to mathematics. As regards logical questions, the central thesis of Wittgenstein's later philosophy is well known, both from the earlier posthumous volume and from the writings of his many disciples. In the Investigations the thesis is applied to the "logic of our expressions" in everyday contexts; here he discusses in the same spirit the more specialized language (...) used in talking about the foundations of mathematics. (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).

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)

The dispute between nominalists and Platonic realists has been with us for a long time — long enough to have assumed many forms. I don't want to rehearse the history of these various debates, or even to look at the matter from a historical point of view. But I would like to begin by distinguishing two quite different skirmishes in the general battle, one of which is new, and one of which is very old. We begin with the new one, (...) which is the clearest. (shrink)

The practical moral problems, which really give substance to our ethical and moral talk, have been handed over to lawyers. Detailed studies of actual cases, where problems of remedy or redress are involved, are discussed in law journals. Most contemporary philosophers have just about given up on such matters.