While theology may take God's existence as absolutely necessary on the basis of authority, faith, or revelation, many philosophers -- and some theologians -- have thought it possible to demonstrate by reason that there must be a God.
St. Thomas Aquinas, in the thirteenth century, formulated the famous "five ways" by which God's existence can be demonstrated philosophically:
1. The "unmoved mover" argument. We know that there is a motion in the world; whatever is in motion is moved by another thing; this other thing also must be moved by something; to avoid an infinite regression, we must posit a "first mover," which is God.
2. The "nothing is caused by itself" argument. For example, a table is brought into being by a carpenter, who is caused by his parents. Again, we cannot go on to infinity, so there must be a first cause, which is God.
3. The cosmological argument. All physical things, even mountains, boulders, and rivers, come into being and go out of existence, no matter how low they last. Therefore, since time is infinite, there must be some time at which none of these things existed. But if there were nothing at that point in time, how could there be anything at all now, since nothing cannot cause anything? Thus, there must always have been at least one necessary thing that is eternal, which is God.
4. Objects in the world have differing degrees of qualities such as goodness. But speaking of more or less goodness makes sense only by comparison with what is the maximum goodness, which is God.
5. The teleological argument (argument from design). Things in the world move toward goals, just as the arrow does not move toward its goal except by the archer's directing it. Thus, there must be an intelligent designer who directs all things to their goals, and this is God.
Two other historically important "proofs" are the ontological argument and the moral argument. The former, made famous by St. Anselm in the eleventh century and defended in another form by Descartes, holds that it would be logically contradictory to deny God's existence. St. Anselm began by defining God as "that [being] than which nothing greater can be conceived." If God existed only in the mind, He then would not be the greatest conceivable being, for we could imagine another being that is greater because it would exist both in the mind and in reality, and that being would then be God. Therefore, to imagine God as existing only in the mind but not, in reality, leads to a logical contradiction; this proves the existence of God both in the mind and in reality.
Immanuel Kant rejected not only the ontological argument but the teleological and cosmological argument as well, based on his theory that reason is too limited to know anything beyond human experience. However, he did argue that religion could be established as presupposed by the workings of morality in the human mind ("practical reason"). God's existence is a necessary presupposition of there being any moral judgments that are objective, that go beyond mere relativistic moral preferences; such judgments require standards external to any human mind -- that is, they presume God's mind.
Arguments against God's existence have been given by philosophers, atheists, and agnostics. Some of these arguments find God's existence incompatible with observed facts; some are arguments that God does not exist because the concept of God is incoherent or confused. Others are criticisms of the proofs offered for God's existence.
One of the most influential and powerful "proofs" that there is no God proceeds from "The Problem from Evil." This argument claims that the following three statements cannot all be true: (a) evil exists; (b) God is omnipotent, and (c) God is all-loving. The argument is as follows:
Another argument claims that the existence of an all-knowing God is incompatible with the fact of free will -- that humans do make choices. If God is omniscient, He must know beforehand exactly what a person will do in a given situation. In that case, a person is not, in fact, free to do the alternative to what God knows he or she will do, and free will must be an illusion. To take this one step further, if one chooses to commit a sin, how can it then be said that one sinned freely?
Hume provided powerful critiques of the main arguments for God's existence. Against the cosmological argument (Aquinas's third argument), he argued that the idea of a necessarily existing being is absurd. Hume stated, "Whatever we can conceive as existent, we can also conceive as non-existent." He also asked why the ultimate source of the universe could not be the entire universe itself, eternal and uncaused, without a God?
Hume also criticized the argument from design (Aquinas's fifth argument). In particular, he emphasized that there is no legitimate way we can infer the properties of God as the creator of the world from the qualities of His creation. For instance, Hume questioned how we can be sure that the world was not created by a team; or that this is not one of many attempts at creations, the first few having been botched; or, on the other hand, that our world is not a poor first attempt "of an infant deity who afterwards abandoned it, ashamed of his lame performance."