Suppose now that two philosophers, McX and I, differ over ontology. Suppose McX maintains there is something which I maintain there is not. McX can, quite consistently with his own point of view, describe our difference of opinion by saying that I refuse to recognize certain entities. I should protest of course that he is wrong in his formulation of our disagreement, for I maintain that there are no entities, of the kind which he alleges, for me to recognize; but (...) my finding him wrong in his formulation of our disagreement is unimportant, for I am committed to considering him wrong in his ontology anyway. When I try to formulate our difference of opinion, on the other hand, I seem to be in a predicament. I cannot admit that there are some things which McX countenances and I do not, for in admitting that there are such things I should be contradicting my own rejection of them. (shrink)

We have now provided an overall simple theoretical account of the structure of perceptual experience proto-philosophically examined in Part I. The next task is to find the proper logical machinery to formulatte those accounts rigorously.

INTRODUCTION MATHEMATICAL logic differs from the traditional formal logic so markedly in method, and so far surpasses it in power and subtlety, ...

The Fourth Edition of this long-established text retains all the key features of the previous editions, covering the basic topics of a solid first course in ...

Philosophy is the search for the large patterns of the world and of the large patterns of experience, perceptual, theoretical, . . . , aesthetic, and practical - the patterns that, regardless of specific contents, characterize the main types of experience. In this book I carry out my search for the large patterns of practical experience: the experience of deliberation, of recognition of duties and their conflicts, of attempts to guide other person's conduct, of deciding to act, of influencing the (...) physical world with one's doings, and the like. This is the experience that makes possible our social life, the formulation of plans for teamwork, the building of institutions, the development of nations, and the adoption of the ideal of morality. Here I develop a network of theories about the most fundamental aspects of practical thinking: what is thought in such thinking; what makes that thinking correct; what makes it practical; and the structure of the doings that accrue to the world when such thinking is effective. I have attempted to build each theory in sufficient detail, so that it il luminates its subject matter with a certain degree of fullness. But I have also aimed at producing an harmonious system of theories, so that the grand pattern of practical thinking can be admired, not only for the beauty of the separate structures of its parts, but also for its architectonic unity. Chapter 1 gives the details of the many facets of this project and discusses some methodological techniques. (shrink)

Hailed by the Bulletin of the American Mathematical Society as "undoubtedly a major addition to the literature of mathematical logic," this volume examines the essential topics and theorems of mathematical reasoning. No background in logic is assumed, and the examples are chosen from a variety of mathematical fields. Starting with an introduction to symbolic logic, the first eight chapters develop logic through the restricted predicate calculus. Topics include the statement calculus, the use of names, an axiomatic treatment of the statement (...) calculus, descriptions, and equality. Succeeding chapters explore abstract set theory—with examinations of class membership as well as relations and functions—cardinal and ordinal arithmetic, and the axiom of choice. An invaluable reference book for all mathematicians, this text is suitable for advanced undergraduates and graduate students. Numerous exercises make it particularly appropriate for classroom use. (shrink)

The author argues that the primary lesson of the so-Called logical and semantical paradoxes is that certain entities do not exist, Entities of which we mistakenly but firmly believe that they must exist. In particular, Russell's paradox teaches us that there is no such thing as the property which every property has if and only if it does not have itself. Why should anyone think that such a property must exist and, Hence, Conceive of russell's argument as a paradox rather (...) than a proof for the nonexistence of this property? the author traces this conviction to an uncritical acceptance of the so-Called principle of property abstraction and claims that this principle is false. It is simply not true, As one widely assumes, That propositional forms represent (complex) properties. Then it is argued, On independent grounds, That there are no complex properties, But only complex states of affairs. (shrink)

W. V. Quine’s systematic development of mathematical logic has been widely praised for the new material presented and for the clarity of its exposition. This revised edition, in which the minor inconsistencies observed since its first publication have been eliminated, will be welcomed by all students and teachers in mathematics and philosophy who are seriously concerned with modern logic. Max Black, in Mind, has said of this book, “It will serve the purpose of inculcating, by precept and example, standards of (...) clarity and precision which are, even in formal logic, more often pursued than achieved.”. (shrink)