SUMMARIES OF ARTICLES.
LOGIC AND METAPHYSICS.
The present address aims to explain what scientific interests are common to the work of philosophers and mathematicians. In general, all the sciences of the normative division are concerned with ideal as distinct from physical truth. Pure mathematics is concerned with the investigation of the logical consequences of certain exactly statable postulates, freely chosen, and not necessarily bearing on practical life, though never trivial or capricious. Philosophy, on the other hand, seeks to unify our knowledge, to comprehend its sources, meaning, and relation to the whole of human life. The two are not sharply contrasted, however; the mathematician deals only with significant postulates, and the philosopher, in reflecting on the significance of fundamental ideas, must inquire into their logical consequences. The value or significance of an idea or theory depends on its place in the whole organized system of human ideas. Hence arises the problem of the categories: On what group of concepts do the other concepts of human science logically depend? In the comparatively new field of modern logic, through the joint work of mathematicians and philosophers, a flood of new light on this problem has been obtained. On the mathematical side, the reëxamination of fundamental postulates and axioms has shown how few and how simple are the conceptions and postulates on which the actual edifice of exact science rests, and has exhibited them in a new light. On the philosophical side, modern logic, including symbolic logic and the logic of scientific method, is rapidly approaching new solutions of the problem of the fundamental nature and the logic of relations. These researches of modern logic, abstract though they seem, are already developing the most interesting and unexpected relations to widely divergent fields. Thus the formal nature of the self is seen to be related to the
