Aquinas on Infinite Multitudes
By Richard Cartwright
Medieval Philosophy and Theology, Vol. 6 (1997)
Introduction: To my knowledge, it is only in ST I, 7,4 that Aquinas considers quite on its own the question whether actually infinite multitudes are possible. There he declares, and claims to demonstrate, that it is impossible for there to be an actually infinite multitude (impossibile est . . . esse multitudinem infinitam in actu). But later, at ST I, 46, 2 ad 7, he says that it is not impossible to proceed to infinity per accidens in efficient causes (per accidens in infinitum procedere in causis agentibus non reputatur impossibile). The apparent inconsistency is the topic of this paper, and I shall begin by explaining in some detail how it arises.
The question under discussion in ST I, 46, 2 is whether it is a matter of faith that the world began. Aquinas holds that it is. But he must answer objections, of which the seventh is a purported demonstration that the world began. It reads:
If the world was eternal, generation was from eternity. Therefore one man was begotten of another to infinity. But the father is an efficient cause of the son, as is said in Physics II. Therefore in efficient causes there is an infinite series-which is disproved in Metaphysics II.
As it stands, the objection is silly: eternity of the world would hardly require an endless generation of human beings, as Aquinas points out elsewhere. Here, however, he responds in effect to a stronger version, which can be put succinctly with the help of a little technical apparatus.
Top Image: Saint Thomas Aquinas (1225-1274) stained glass window. Cathedral of Saint-Rombouts, Mechelen (Belgium). Photo by Eddy Van 3000 / Wikimedia Commons