Possible it would be; we might have under the sciences of logical attitudes not only logic and mathematics but as a subdivision of these, again, the sciences which construct the logical system of a phenomenalistic world—­physics being in this sense merely mathematics with the conception of substance added.  And yet we must not forget that the teleological attitudes, to become a teleological science, must be also logically reconstructed, as they must be teleologically connected, and thus in this way the totality of purpose-sciences might be, too, logically subordinated to the science of logic.  Logic itself would thus become a subdivision of logic.  We should thus move in a circle, from which the only way out is to indicate the teleological character of all sciences by starting not with science but with the strictly teleological conception of life—­life as a system of purposes, felt in immediate experience, and not as the object of phenomenalistic knowledge.  Life as activity divides itself then into different purposes which we discriminate not by knowledge but by immediate feeling; one of them is knowledge, that is, the effort to make life, its attitudes, its means and ends a connected system of overindividual value.  In the service of this logical task we connect the real attitudes and thus come to the knowledge of purposes:  and we connect the means and ends—­by abstracting from our subjective attitudes, considering the objects of will as independent phenomena—­and thus come to phenomenalistic knowledge.  At this stage the phenomenalistic sciences are no longer dependent upon the teleological ones, but cooerdinated with them; physics, for instance, is a logical purpose of life, but not a branch of logic:  the only branch of logic in question is the philosophy of physics which examines the logical conditions under which physics is possible.

One point only may at once be mentioned in this connection.  While we have cooerdinated the knowledge of phenomena with the knowledge of purposes we have subordinated mathematics to the latter.  As a matter of course much can be said against such a decision, and the authority of most mathematicians would be opposed to it.  They would say that the mathematical objects are independent realities whose properties we study like those of nature, whose relations we ‘observe,’ whose existence we ‘discover’ and in which we are interested because they belong to the real world.  All that is true, and yet the objects of the mathematician are objects made by the will, by the logical will, only, and thus different from all phenomena into which sensation enters.  The mathematician, of course, does not reflect on the purely logical origin of the objects which he studies, but the system of knowledge must give to the study of the mathematical objects its place in the group where the functions and products of logical thought are classified.  The arithmetical or geometrical material is a free creation, and a creation not only as to the combination of elements—­that