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xxxiv PREFACE as such, whereas the concepts of metaphysics are abstractions from common intelligible matter and regulate the accord of concepts of reason to the modes of things according as being, one, true and good are present to the thing and the essence. Logic is a means between nature and metaphysics and only when so understood does it preserve its proper limitation and significance. Nature is an order of individuated things in which such things come to be and perish by a multiplication of formal act in matter consistent with the principle of one and many in material process. Substances are in nature simpliciter. But man in his finite and discursive capacity knows by virtue of analysis and only reaches synthesis after laborious efforts and even then only imperfectly. Man must know by division and composition or specially conditioned qualifying operations. The order of knowing is grounded in the order of existence through the continuity of abstraction, though the intellect must under- stand by means of its reflexive powers. The categories deal with the advention of accidents in sub- stance, corporeal substances which are delimited and hence limiting wholes. Hermann Weyl observes on page one, 30, of his Philosophic der Mathemati^ und Wissenschajt: "Auch die Aristotelische Logik war im wesentlichen abstrahiert aus der Mathematik"; and he might have observed that a natural sub- stance is like a finite magnitude or whole, though not neces- sarily quantitative as such. Genus, species, difference, property, and accident, the predicables, are fabrications of the intellect, but as analytic similitudes or analogues of substance they in- dicate discursively the necessary mode of a substance or the relative limitation of categoric accidents. A limited whole in the order of nature can be brought into commensuration with a limited whole in the order of reason, and thus Aristotle, and after him St. Thomas, affirm that nature divides readily into