This important book by a major American philosopher brings together eleven essays treating problems in logic and the philosophy of mathematics.

The author examines three fundamental concepts: existence, a priori knowledge, and value. These concepts have been recurrent concerns of western philosophy and also reveal important similarities and differences between the movements from which the author takes his departure.

NOWADAYS, even schoolchildren babble about "null sets" and "singletons" and "one-one correspondences," as if they knew what they were talking about. But if they understand even less than their teachers, which seems likely, they must be using the technical jargon with only an illusion of understanding. Beginners are taught that a set having three members is a single thing, wholly constituted by its members but distinct from them. After this, the theological doctrine of the Trinity as "three in one" should (...) be child's play. (shrink)

The main goal of this paper is to urge that the normal platonistic account of mathematical truth is unsatisfactory even if pure abstract entities are assumed to exist (in a non-Question-Begging way). It is argued that the task of delineating an interpretation of a formal mathematical theory among pure abstract entities is not one that can be accomplished. An important effect of this conclusion on the question of the ontological commitments of informal mathematical theories is discussed. The paper concludes with (...) a sketch of a non-Platonistic theory of mathematical truth which utilizes an unanalyzed notion of logical possibility. (shrink)

This book develops arithmetic without the induction principle, working in theories that are interpretable in Raphael Robinson's theory Q. Certain inductive formulas, the bounded ones, are interpretable in Q. A mathematically strong, but logically very weak, predicative arithmetic is constructed. Originally published in 1986. 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 paperback editions preserve the original texts of these important books while presenting (...) them in durable paperback 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)

This paper assesses those features of Lesniewski's Ontology which make it difficult to understand for logicians accustomed to more orthodox systems of logic. It is seen that certain general features of presentation and content can, by selective acceptance or modification, be accommodated with a fairly orthodox viewpoint. The chief difficulty lies in the interpretation of Le?niewski's names, and the constant ???. Four interpretations are suggested in turn: Le?niewski's names as monadic predicates; as class terms; as common nouns; and as empty, (...) singular or plural terms. This last and least orthodox interpretation is argued to be the most suitable, but it is shown how it can be made to live in harmony with either the common noun or the class interpretation. (shrink)