This book is intended to be a survey of the most important results in mathematical logic for philosophers. It is a survey of results which have philosophical significance and it is intended to be accessible to philosophers. I have assumed the mathematical sophistication acquired· in an introductory logic course or in reading a basic logic text. In addition to proving the most philosophically significant results in mathematical logic, I have attempted to illustrate various methods of proof. For example, the completeness (...) of quantification theory is proved both constructively and non-constructively and relative ad vantages of each type of proof are discussed. Similarly, constructive and non-constructive versions of Godel's first incompleteness theorem are given. I hope that the reader· will develop facility with the methods of proof and also be caused by reflect on their differences. I assume familiarity with quantification theory both in under standing the notations and in finding object language proofs. Strictly speaking the presentation is self-contained, but it would be very difficult for someone without background in the subject to follow the material from the beginning. This is necessary if the notes are to be accessible to readers who have had diverse backgrounds at a more elementary level. However, to make them accessible to readers with no background would require writing yet another introductory logic text. Numerous exercises have been included and many of these are integral parts of the proofs. (shrink)

Ockham’s criticisms of earlier theories of universals depend on the fact that they are universals, that the supposed entities are essentially different in kind from particulars. Since modern theories which postulate the existence of senses or propositions as part of a semantic theory make no such claims about those entities it would seem that Ockham’s views are irrelevant to disputes over the value of those semantic theories. That is, for Frege, Church and others the senses or propositions postulated are not (...) claimed to be universal in the traditional medieval sense, but are rather abstract objects which in the theory are treated as particulars exactly on a par with rocks, tables and numbers. However, if one considers Ockham’s positive theory of language it becomes clear that his views are at odds with modern abstract semantic accounts just as much as they were with the traditional universalist semantic accounts. (shrink)

Motivations for systems of free logics are reviewed and systems are divided according as they are positive (asserting atomic truths with non-denoting terms) negative (denying all such sentences) or neutral. A positive theory is developed and defended. One of the major considerations in favor of the theory is that it allows (via translation) representation of the other points of view. Finally, the relation between free logic and truth theories is elaborated.

H.P. Grice is a distinguished philosopher predominantly known for his influential contributions to the philosophy of language, but that is only one strand in a rich tapestry of ideas bearing on the philosophy of mind, ethics, and metaphysics as well. Some of the essays in this collection of original papers by leading philosophers edited by Grandy and Warner develop Grice's earlier work in the philosophy of language, but most of them discuss or present his newer and less-known work. Together they (...) demonstrate the unified and powerful character of his thoughts on being, mind, meaning, and morals. An introductory essay provides some of the first overview of Grice's thought, and makes explicit some of the relations among the essays. Grice's substantial response is followed by nineteen contributed papers whose authors include Donald Davidson, Stephen Schiffer, John Searle, and P.F. Strawson. The Times Literary Supplement writes of Grice: 'the only leader of whom it is true that the level of the discipline would be raised if most philosophers took him as a model of how to think and write.' This paperback edition replaces the hardback, published March 1986. (shrink)