Abstract

When in 1950, the distinguished psychologist, Jean Piaget, published a book on the relation of logic and psychology, the book was severely criticized in the journal Methodos by the logician E. V. Beth. Piaget asked to get together with Beth to discuss the issues involved. The result, over 15 years later, is the present book. Beth is the author of the first half in which he defends the complete autonomy of logic in relation to psychology by means of a partly philosophical, partly historical treatment of logicist, formalist, and intuitionist philosophies of mathematics. Briefly put, Beth's thesis is the now familiar one in contemporary philosophy that logic and mathematics are normative sciences, psychology is a factual science. As a consequence, Beth argues that we must renounce all "psychologism" in logic and mathematics, and all "logicism" in psychology. Piaget has come to accept these main contentions of Beth and affirms them in the second half of the volume. But Piaget is impressed by the fact that a good deal of human conceptual development must go on before human beings recognize and state normative laws of logical thought. Piaget attempts to chart this conceptual development and explain how it takes place. He attempts to show that this genetic-psychological approach to the study of logical and mathematical thought is complementary to and fully compatible with the deductive approach of the formal logician, and hence compatible with Beth's thesis about the conceptual autonomy of logic and psychology. Logician and psychologist can thus deal with the same material although their approaches are conceptually autonomous. The book repays careful reading not only for the arguments defending these challenging claims but also for many other details in both parts.--R. H. K.