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Saint Thomas Aquinas holds that scientific knowledge is attained when observable phenomena and their properties are accounted for in terms of their relations to their causes. On establishing the divisions of the sciences, Aquinas follows the threefold division of the speculative sciences as proposed by Aristotle and handed on to the Middle Ages by Boethius: natural philosophy, mathematics, and theology. Each science is defined by its subject matter and by its method of procedure.
While Aquinas followed the teachings of Boethius on this point, he makes significant additions and alterations. Thus in his analysis Aquinas focuses his attention on the role played by the intellect in the determination of the formal perspective (ratio) from which the intellect considers the various matters of science.
For Aquinas the intellect performs two operations: apprehension and judgment. Here we shall be concerned with the operation of apprehension. This operation of the intellect is capable of two distinct kinds of abstraction. First, there is the abstraction of form from sensible matter. Second, there is the abstraction by which a universal is abstracted from its particular. The objects of the operation called abstraction of form are the objects of mathematics, and the objects of the abstraction of the universal are the objects of science. Hence, the intellect by means of its powers of abstraction plays a fundamental role in establishing the division of the sciences.