ism and vitalism. The present evidence justifies the mechanistic interpretation. Psychology should assume the same attitude toward the phenomenon of choice. This interpretation changes the ethical concept of responsibility. Ethics should concern itself with the sense of responsibility which mankind actually possesses. The genesis and activity of purpose are explicable on mechanistic grounds. The difficulty has been that the philosopher, the biologist, and the common man have retained the anthropomorphic psychology of early times. Psychology has been too much dominated by introspective analysis. Introspection needs objective checking; such objective methods are essential to genetic investigation. Animal psychology is hindered rather than helped by introspection. We must study behavior. Behavior reveals the dynamic aspect best. Introspection also is a field for exact investigation. In this field modern psychology has yielded many worthy scientific results. The double aspect view would prefer to treat conscious processes and behavior processes as branches of one science. From this viewpoint, psychology might be defined as the science of the individual organism or consciousness as related to its environment.
Two fundamentally different conceptions of the logic of mathematics are represented in the treatments of B. Russell and C. S. Peirce respectively. The former proceeds in conformity with his idea of inference, which reduces all reasoning to deduction and views induction as merely a method of making plausible conjectures, and so views mathematics as purely objective. Peirce, on the other hand, finds room for the genetic phase, for mathematics as a mental activity as well as an existence. The present discussion is methodological, and is concerned with mathematics as a science of discovery, and in particular with the use of the "working hypothesis" in this field. A working hypothesis, or idée directrice is essentially a mediator between two terms in disaccord, which is also the final form of other logical problems and their solutions. Mathematicians have been reluctant to admit the working hypothesis in pure mathematics, to recognize that their science is in one aspect a science of observation. Hence the formal elements of problems,—terms in disaccord and mediating idea,—are not often recognized in mathematical discussions. These elements are always present, however, and their recognition is becoming more and more explicit. E. H. Moore was the first to give them clear expression. The mediating concept corresponds, too, to the leitende Idee of Grassmann. In general terms, the problem is that of the discovery of relations, and the various logical conceptions of the nature of relations in the works of thinkers generally shed light on the issues involved. There is always a close relation between the mediating idea and some value, a fact which has been especially emphasized by James and the pragmatists, though clearly stated by Mill. The method of mediation must depend in large
