The American Cyclopædia (1879)/Transcendental

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TRANSCENDENTAL (Latin transcendere, to go beyond), in metaphysics, a term applied in general to ideas and doctrines that are not suggested or limited by experience. In the scholastic philosophy, transcendens and transcendentalis designated anything that was not prædicamentalis, that is, anything that rose above, was not comprehended in, and could not be defined by, either of the ten summa genera or categories of Aristotle. Thus, being was transcendental, and only some category of being was prædicamental. Kant gave new and distinct significations to transcendens and transcendentalis. The former designated what is wholly beyond experience, is conceivable neither a priori nor a posteriori, and thus lies beyond every category of thought. The latter designated a priori conceptions and judgments, which are necessary and universal, and which transcend the sphere, while affording the conditions, of the contingent knowledge furnished by experience. Thus by the transcendental, formal, or critical philosophy of Kant is meant his system of the principles of the pure reason, which occupies itself not with the objects or matter of knowledge, but with the subjective ideas or forms, as time, space, substance, and causality, through which objects are represented to us as phenomena. Objects in themselves (Dinge an sich) he deemed transcendent. — In mathematics, transcendental quantities are those which cannot be expressed by a finite number of algebraic terms, but are represented by means either of logarithms, or variable exponents, or some of the trigonometrical functions. Transcendental curves, as the logarithmic spiral, are those whose equation is transcendental, i. e., expresses a relation between transcendental quantities.