A typical exponent of this school is Moisant, who, in the _Revue Philosophique_ for January 1905, attacked what he considered to be the characteristic of modern philosophy and also its vice. It will be observed that at the outset he reverses the _rôles_ of philosophy and mathematics as we have apprehended them. Philosophy, he says, should expect to be inspired by mathematics, but should avoid its method. Next, he connects the modern movement with the theories of Leibniz, who aimed at substituting general formulæ for elementary forms of reason and calculation. These short cuts, which seem to the mathematician to liberate the mind from a burden which prevents it from employing its full activity, seem to the psychologist to tend to a mechanical method, in which the thinker is only aware of premises and results, and in which the mathematical concept tends to replace the real idea. Then he attacks the new definition of mathematics as the science of relations, asserting that it still contains notions of space.[13] Finally, he comes to the real question at issue, and enters into the comparison of a metaphysical and a mathematical problem. He takes as his subject the argument from the known to the unknown. Descartes had said that argument should lead from the known to the unknown, simple to complex, and had defined the first as that which could be known without the help of the second. This logical order of reasoning has been attributed to mathematics, but has been considered to be inapplicable to philosophy. Mathematics, in its recent development, by the argument from the Finite to the Infinite and back again, starts from two propositions, neither of which can be said to be axiomatic, because each in turn can be proved from the other, but in the course of argument from either mathematics makes use of the logical process. The real axiom, as has been shown, is that of _existence_ or _being_. A metaphysical argument has the same root--that of existence--but a metaphysical problem deals with paradoxes, with questions which are sometimes defined as having two answers, each equally correct, and sometimes as yielding no answer at all. The method of thesis, antithesis, and synthesis is in the Hegelian logic applied to their solution.