Arguments for God

In plain terms

The arguments divide into three families, and each has a characteristic weakness.

Ontological arguments proceed from the concept alone: a being than which nothing greater can be conceived must exist, since existing is greater than not. They are valid, they require no observation, and almost nobody finds them convincing - which is itself a philosophical puzzle.

Cosmological arguments proceed from the existence of contingent things to a necessary being. They rely on the principle that everything has an explanation, which is exactly what a critic will decline to grant.

Teleological arguments proceed from apparent design. Darwin removed their best evidence and the fine-tuning of physical constants has supplied a new version.

None commands assent, and the interesting question is what that shows.

As a philosopher would put it

Anselm's argument in the Proslogion defines God as that than which nothing greater can be conceived and argues that such a being cannot exist in the understanding alone. Gaunilo's reply - the same reasoning would establish a perfect island - and Kant's objection that existence is not a predicate are the standard responses; Plantinga's modal reconstruction avoids the second and depends on granting that a maximally great being is possible.

Cosmological arguments come in contingency and temporal forms. Ibn Sīnā and Aquinas argue from what requires a cause to a necessary existent; the kalām version argues that an actual infinite regress of past events is impossible.

Teleological arguments were devastated as biology by natural selection and have re-emerged as fine-tuning. Hume's Dialogues anticipated most of the objections a century before Darwin.

Kant's critique is structural: the cosmological and physico-theological arguments both smuggle in the ontological, and reason overreaches when it applies the categories beyond experience.

What is actually disputed

Whether the arguments are supposed to convince.

One view is that they are proofs and should compel any rational person, which makes their persistent failure to do so a serious problem. Another is that they were never that: Anselm wrote his as a prayer, addressed to God, from a position of faith seeking understanding, and Aquinas presented the five ways in a work of theology for students already committed.

On that reading the arguments articulate a faith rather than establishing one, and asking them to convert an atheist is asking for something they were not built to do.

What is not disputed is the current state. Every classical argument has a serious objection, every objection has a serious reply, and the specialists on both sides regard the matter as open. That is unusual for a question so old, and it tells against the idea that either theism or atheism follows from reason alone.