Jaakko Hintikka is an internationally renowned philosopher known as the main architect of game-theoretical semantics and of the interrogative approach to inquiry, as well as one of the architects of distributive normal forms, possible-worlds semantics, tree methods, infinitely deep logics, and present-day-theory of inductive generalization. Currently a Professor of Philosophy at Boston University, he is the author of more than thirty books and has received a number of honors, most recently the Rolf Schock Prize for Logic and Philosophy, for his pioneering contributions to the logical analysis for modal concepts, in particular the concepts of knowledge and belief.

This book, written by one of philosophy's pre-eminent logicians, argues that many of the basic assumptions common to logic, philosophy of mathematics and metaphysics are in need of change. It is therefore a book of critical importance to logical theory. Jaakko Hintikka proposes a new basic first-order logic and uses it to explore the foundations of mathematics. This new logic enables logicians to express on the first-order level such concepts as equicardinality, infinity, and truth in the same language. The famous impossibility results by Godel and Tarski that have dominated the field for the last sixty years turn out to be much less significant than has been thought. All of ordinary mathematics can in principle be done on this first-order level, thus dispensing with the existence of sets and other higher-order entities.