The Concept of the Infinite in the Philosophy of St. Thomas Aquinas

THE CONCEPT OF THE INFINITE IN THE PHILOSOPHY OF ST. THOMAS AQUINAS I N his Summa Theologiae, in discussing the Infinity of God, St. Thomas defines infinite thus: " a thing is said to be infinite by reason of the fact that it is not limited." 1 Substantially the same definition occurs in the Quaestiones Quodlibetales : " Infinity ... is predicated by reason of the fact that [something] is not limited"; 2 and in the De Potentia: "infinity is predicated by a negation of limit." 3 Infinity, then, is predicated by a contradiction of finiteness, per remotionem finis; it is said of that which is unending, unbounded, interminable. SL Thomas undertakes, in the De Veritate, in an article on the Divine Power, to analyze the concept of the infinite; he writes: ... infinite is distinguished in two ways. In one way, it is distinguished according to potency and act. The potential infinite is predicated of that which consists in an uninterrupted succession, for example: the generation ofbodie:; and the division of a continuum; in every such case there is a potency to infinity, one thing always following another. Actual infinity, on the other hand, would involve something like positing a line without end. In another way, the infinite is distinguished as necessary and contingent; the reason for this distinction may be shown in this wise: infinity, by its nature, is proper to the order of quantity, but quantity is predicated primarily of discrete quantity rather than of a continuum. Consequently , to determine the distinction of the necessary and the contingent infinite, it must be observed that a multitude may be either necessarily such, or it may be so only contingently. A multitude is a necessary multitude, if, as for example in a series of 1 ••• infinitum dicitur aliquid ex eo quod non est finitum (Summa Theol., I, q. 7, a. l c.). 2 Dicitur ... infinitum ex eo quod non finitur (Quodl. III, q. ~c.). • ... infinitum dicitur per remotionem finis (De Pot., q. 1, a. ~. ob. 8.). 31~ CONCEPT OF INFINITE IN PHILOSOPHY OF ST. THOMAS 318 subordinated causes and effects, each member has an essential dependence on another: thus, the soul moves the natural heat, by which are moved the nerves and muscles, which, in turn, move the hands, which move a stick, by which a stone is moved; in this series, each one of the subsequent members depends necessarily on one of the preceding. On the other hand, a multitude is ·said to be contingent when all the members contained in the multitude can be taken, as it were, as only one and are thus indifferently one, or many, or several; take, for example, a builder who constructs a house and uses up a number of saws successively in the process: a multitude of saws is not required for the construction of the house, except contingently by reason of the fact that no single saw can last forever. Nor does it make any difference in the construction how many saws are employed, wherefore no one of them has a dependence on any other, as was the case in the necessary multitude.4 We have here a double distinction: first, a distinction of actual and potential infinites, and then of necessary and contingent infinites (infinitum per se, per accidens) . An actual infinite is had when something is simply without limits, like a line with no terminal points, or an unlimited multitude whose members are co-existent: its characteristic is an esse totum simul. A potential infinite, on the other hand, occurs only in instances of a succession; it consists in a repetitive process of some kind-generation, for example, or division of a wholewhich does not come to an end. Its potentiality is grounded in the fact that each separate event, separately considered, could be initial or intermediate or final, or even unique; or it could be one in a series of similar events which is without beginning and without end. Characteristic of the potential infinite is its esse unum post aliud. St. Thomas introduces his second distinction, that between the infinite as necessary and the infinite as contingent, with the remark that infinity, by its nature, is proper to the order of quantity...