Outline the Cosmological Argument for the existence of God (with reference to Thomas Aquinas’ Third Way)

The Cosmological Argument is an a posteriori and inductive argument for the existence of God. It has been formulated in various ways, both in the works of the Christian apologist Thomas Aquinas and the Enlightenment philosopher Gottfried Wilhelm Leibniz, while it has gained renewed interest in contemporary literature thanks to its kalām formulation by William Lane Craig. Broadly speaking, the Cosmological Argument contains two major premises: first, the existence of all contingent entities requires an explanation, i.e. the Principle of Sufficient Reason, and second, the universe is itself a contingent entity. Therefore, God must exist as the explanation of the existence of the universe.
First, consider the claim that the existence of all contingent entities requires an explanation. In Summa Theologica, Aquinas’ Third Way (the argument from contingency and necessity) begins with a distinction between necessary and contingent beings. A contingent being is one which comes into and out of existence, i.e. its existence is not necessary. Pens, cats, and stars are all contingent because they are caused to come into being in time. They are therefore not necessary because they require causes: without manufacturing, evolution or the Big Bang, neither pens, cats, or stars would come into being. These do not come into being out of nothing. By contrast, a necessary being is one for which there can be no external explanation. Abstract objects such as numbers are necessary because they are neither caused to exist nor cease to exist, so they cannot have explanations external to themselves. Likewise, upon Aquinas’ conception of God, God is wholly simple and timeless, so the very notion of God beginning to exist is incoherent, as God does not exist in time. Hence necessary beings are self-existent and do not need an external cause. Contingent beings by contrast must be subject to some explanation external to themselves, otherwise they could not exist at all.
Second, it is argued that the universe is itself contingent. Aquinas argues this by a reductio ad absurdum: given both that time can be infinite and that the universe is the totality of all contingent phenomena, in an infinite duration of time all possible arrangements of contingent phenomena will come into being. But because all contingent phenomena can come out of existence, it is possible that the totality of contingent entities should come out of existence altogether, i.e. that nothing should exist. But then, once this has occurred, it is inexplicable how anything should exist at all, because out of nothing, nothing can come (ex nihilo, nihil fit). But if the universe is eternal in the past, this must have already happened. From which it follows that the universe must have a cause which is itself a necessary being, or else nothing would exist. The being in question must be necessary because a contingent explanation for the universe would only continue an infinite regress of explanation, which Aquinas takes to be absurd. Therefore, the cause of the universe must have the property of aseity, a property ascribed to God which means that God exists by his own nature. Thus, by invoking the existence of God as the explanation for the existence of the universe, the Cosmological Argument entails the conclusion that God exists.