Cosmological Argument
The Cosmological Argument is the family of arguments that move from the existence of the contingent universe to the existence of a Necessary Being. The family is large enough that any short statement is misleading, but the canonical members share a common shape: there is something rather than nothing; the something is the kind of thing that could have failed to be; the explanation of its existence cannot be infinitely deferred or self-contained; therefore there must exist something whose existence is not contingent in this way, and that something is what theists mean by God.
The argument has medieval and modern forms. The medieval form is sharpest in Thomas Aquinas‘s Five Ways in the Summa Theologiae: arguments from motion, efficient causation, contingency, gradation, and final causation. The modern form is sharpest in Gottfried Wilhelm Leibniz‘s argument from the principle of sufficient reason in the Monadology: that for any contingent fact there must be a sufficient reason, and that the sufficient reason for the totality of contingent facts cannot itself be contingent.
The most influential modern critic is David Hume in the Dialogues Concerning Natural Religion, who attacked the principle of sufficient reason and pressed the question why an explanation must terminate in a single necessary being rather than in a brute fact at the level of the universe itself. Among contemporaries, Richard Swinburne defends a probabilistic version, while J. L. Mackie in The Miracle of Theism argues that the principle of sufficient reason is question-begging and that the argument fails.
What is true of the cosmological argument is true of most of the great philosophical arguments: it has been refuted often, and it has not gone away.