By a `denoting phrase' I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the present King of France, the center of mass of the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. Thus a phrase is denoting solely in virtue of its form. We may distinguish (...) three cases: (1) A phrase may be denoting, and yet not denote anything; e.g., `the present King of France'. (2) A phrase may denote one definite object; e.g., `the present King of England' denotes a certain man. (3) A phrase may denote ambiguously; e.g. `a man' denotes not many men, but an ambiguous man. The interpretation of such phrases is a matter of considerably difficulty; indeed, it is very hard to frame any theory not susceptible of formal refutation. All the difficulties with which I am acquainted are met, so far as I can discover, by the theory which I am about to explain. (shrink)

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

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)