Philosophy: Here and Now Lewis Vaughn Chapter 2 Definitions 2.2

A posteriori argument

Radios from empirical facts about the world to the conclusion that God exists. Cosmological, teleological, and religious-experience arguments are of this kind.

A Priori argument

Logically derive the conclusion that God exists from concepts of God. Ontological arguments take this form.

Thomas Aquinas, Summa Theologica (famous five ways)

One: argument from motion.

Two: nature of the efficient cause.

Aquinas's argument from motion

It is obvious that some things in the universe are moving (that is, changing), and if they are moving, something else must have caused them to move. And this "something else" must also have been moving, set in motion by by yet another thing that was moving, and this thing set in motion by another moving thing, and so on. But this series of things-moving-other-things cannot go on forever, to infinity, because then there would not be something that started all the moving. There must therefore be an initial mover (a "first mover"), an extraordinary bring that started the universe moving but is not itself moving by anything else -- and this bring we call God.

Aquinas's first-cause argument:

He maintains that everything we can observe has a cause, and it is clear that nothing can cause itself. For something to cause itself, it would have to exist prior to itself, which is impossible. Neither can something be caused by an infinite regress of causes -- that is, a series of causes stretching to infinity. In any series of causes, Aquinas says, there must be a first cause which causes the second, which causes the third and so one. But in an infinite series of causes, there would be no first cause and thus no subsequent causes, including causes existing now. So infinite regresses make no sense. Therefore, there must be a first cause of everything, and this first cause we call God. (Here Aquinas is not thinking of a first cause of a temporal series of causes, as in a sequence of falling dominoes, but of a first cause that sustains the whole series of causes, like the bottom building block that holds up all the others in a stack.)

William Paley

Natural Theology: The watch against the ground story.

David Hume

Dialogues concerning Natural Religion