Abstract

This ninth volume in the Library of Exact Philosophy series is a development of the author’s 1971 McGill University dissertation written under the guidance of Mario Bunge. The thesis of the book is that the objectivity of mathematics does not require that there be any mathematical objects. The objectivity of mathematics is the widespread agreement among working mathematicians on what is provable, i.e., on what entailments hold between mathematical constructs. Castonguay gives precise definitions of several terms; but, unfortunately, "construct" is not one of them. He has set himself the task of arguing that we can account for community recognition and acceptance of proofs without assuming that working mathematicians have had to inspect some special mathematical objects to verify that things are in the mathematical realm as they are said to be in the proved propositions. He does concede that many mathematicians, for heuristic reasons, may need to speak as if there were a mind-independent mathematical realm.