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

This volume consists of the first of the John Dewey Lectures delivered under the auspices of Columbia University's Philosophy Department as well as other essays by the author. Intended to clarify the meaning of the philosophical doctrines propounded by Professor Quine in 'Word and Objects', the essays included herein both support and expand those doctrines.

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)

The main aim of this paper is to propose an appropriate logical system that is suitable to describe the notion of IS-A link as well as is-a link. The most important point to be realized is that those relations are not set thoretical ones. They connect two `general names' to construct a proposition, so that what is needed for proper descriptions of the relations in question is a theory of general names. It will be shown that is-a is a logical (...) unit of axiomatically determined behaviour. The axiom concerning is-a relation was established by S. Lesniewski who named his theory of general names ontology. Today `ontology' has also become a common term for AI researchers. I intend to make it clear that there is a close connection between `ontology' used by Lesniewski and by AI researchers, even though they developed quite independently. I wish to stress that ontology created by Lesniewski is a system of syllogistic equipped with singular propositions and the theory of quantification. To make this point clear, I proposed a fragment of syllogism that I called MO(minimal ontology). This paper includes comments and examples articulating the logical power of ontology. (shrink)