' The scholastic writers of the Middle Ages, especially St.

This all men speak of as God.'Īs Struik writes in Concise History of Mathematics: Therefore we cannot but postulate the existence of some being having of itself its own necessity, and not receiving it from another, but rather causing in others their necessity. Now it is impossible to go on to infinity in necessary things which have their necessity caused by another, as has been already proved in regard to efficient causes. But every necessary thing either has its necessity caused by another, or not. ' Therefore, not all beings are merely possible, but there must exist something the existence of which is necessary. It does come into play in the later part of Aquinas's argument as well, but concerning necessary things: Aristotle himself uses this as a prohibition on infinite regress in multiple places, particularly in his argument for the unmoved mover, a protoype of the cosmological argument. Aristotle's thesis on this was coined into a Latin maxim, infinitum actu non datur, there is no actual infinity. Not that it matters here, but Aquinas would deny an infinite chain of contingent beings causing each other as well. Note that it is very different from the modern term in modal logic, see What do necessity and possibility mean in Aquinas' Third Way argument for the existence of God? Thomist 'possibility' comes from Aristotle's potentiality in actual time, not from detached possible worlds unto themselves. One may object to such compositional treatment of 'contingency' (the totality of 'contingencies' is itself 'contingent'), but it is more understandable given the Aristotelian 'contingency' he worked with. Therefore, if everything is possible not to be, then at one time there could have been nothing in existence'Īquinas seems to argue about the totality of everything 'contingent', not about 'contingent' things one by one. But it is impossible for these always to exist, for that which is possible not to be at some time is not. ' We find in nature things that are possible to be and not to be, since they are found to be generated, and to corrupt, and consequently, they are possible to be and not to be. The argument doesn't seem prove a time in which nothing existed, he states in premise 5, 'Therefore there could have been a time when no things existed.' Notice Aquinas uses the word 'could', implying the possibility of this not occurring.įrom the original argument, Summa Theologica Part I, Question 2, Article 3: Premise 3 states, 'For each contingent being, there is a time it does not exist.' This doesn't negate the possibility of an infinite regress, as each contingent thing would, at one point, not have existed in an infinite chain of causation.

Receive its existence from another being, but rather causes them. Therefore some being exists of its own necessity, and does not Therefore not every being is a contingent being.Ĭ. We have reached an absurd result from assuming that every being is a

Therefore, nothing would be in existence now. Therefore at that time there would have been nothing to bring theĬurrently existing contingent beings into existence. Therefore there could have been a time when no things existed. Therefore it is impossible for these always to exist. We find in nature things that are possible to be and not to be, thatĬome into being and go out of being i.e., contingent beings.Īssume that every being is a contingent being.įor each contingent being, there is a time it does not exist. The Third Way: Argument from Possibility and Necessity (Reductio argument)

Infinte regress