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 122 DEVELOPMENT OF CARTESIANISM. • suited for instruction since it shows the way by which the matter has been discovered. Spinoza, on*the other hand, rigorously carried out the geometrical method, even in externals. He begins with definitions, adds to these axi- oms (or postulates), follows with propositions or the- orems as the chief thing, finally with demonstrations or proofs, which derive the later propositions from the earlier, and these in turn from the self-evident axioms. To these four principal parts arc further added as less essential, deductions or corollaries immediately resulting from the theorems, and the more detailed expositions of the demonstrations or scholia. Besides these, some longer discussions are given in the form of remarks, introductions, and appendices. If everything is to be cognizable through mathematics, then everything must take place necessarily ; even the thoughts, resolutions, and actions of man cannot be free in the sense that they might have happened otherwise. Thus there is an evident methodological motive at work for the extension of mechanism to all becoming, even spiritual be- coming. But there are metaphysical reasons also. Des- cartes had naively solved the anthropological problem by the answer that the interaction of mind and body is incompre- hensible but actual. The occasionalists had hesitatingly questioned these conclusions a little, the incomprehen- sibility as well as the actuality, only at last to leave them intact. For the explanation that there is a real influence of body on mind and vice versa, though not an immediate but an occasional one, one mediated by the divine will, is scarcely more than a confession that the matter is inexpli- cable. Spinoza, who admits neither the incognizability of anything real, nor any supernatural interferences, roundly denies both. There is no intercourse between body and soul ; yet that which is erroneously considered such is both actually present and explicable. The assumed interaction is as unnecessary as it is impossible. Body and soul do not need to act on one another, because they are not two in kind at all, but constitute one being which may be looked at from two different sides. This is called body when con- sidered under its attribute of extension, and spirit when