Anselm of Canterbury, a Benedictine monk and Archbishop of Canterbury, is credited with first formulating the Ontological Argument in his book Proslogion in the 11th century.

The Ontological Argument is based on the idea that the concept of a perfect being, or God, implies that such a being must exist. This is because a perfect being would have all possible perfections, including existence.

The main objection to the Ontological Argument is that it relies on a circular argument. The argument assumes that the concept of a perfect being includes existence, and then uses this assumption to prove that a perfect being must exist. This is a circular argument because it assumes the very thing that it is trying to prove.

Immanuel Kant famously criticized the Ontological Argument as a "leap from thought to being" in his Critique of Pure Reason. Kant argued that the existence of God cannot be proven through pure reason alone, and that the Ontological Argument is therefore invalid.

The modal version of the Ontological Argument argues that the concept of a necessary being, or a being that exists by its own nature, implies that such a being must exist. This is because the concept of a necessary being includes existence as an essential property, and therefore a necessary being cannot not exist.

Kurt Gödel, a mathematician and logician, developed the modal version of the Ontological Argument in the 20th century. Gödel's version of the argument is based on the idea that the concept of a necessary being is a consistent concept, and therefore such a being must exist.

The main objection to the modal version of the Ontological Argument is that it relies on a circular argument. The argument assumes that the concept of a necessary being includes existence as an essential property, and then uses this assumption to prove that a necessary being must exist. This is a circular argument because it assumes the very thing that it is trying to prove.

Bertrand Russell famously criticized the modal version of the Ontological Argument as a "fallacy of existence" in his book Why I Am Not a Christian. Russell argued that the existence of a necessary being cannot be proven through pure reason alone, and that the modal version of the Ontological Argument is therefore invalid.

The cosmological argument for the existence of God argues that the existence of the universe proves the existence of God. This is because the universe is contingent, meaning that it could have not existed, and therefore there must be a necessary being, or God, who caused it to exist.

Thomas Aquinas famously formulated the cosmological argument in his Summa Theologica. Aquinas argued that the existence of the universe is evidence of the existence of a first cause, or God.

The main objection to the cosmological argument is that it relies on a circular argument. The argument assumes that the universe is contingent, and then uses this assumption to prove that there must be a necessary being, or God, who caused it to exist. This is a circular argument because it assumes the very thing that it is trying to prove.

Immanuel Kant famously criticized the cosmological argument as a "leap from being to thought" in his Critique of Pure Reason. Kant argued that the existence of God cannot be proven through pure reason alone, and that the cosmological argument is therefore invalid.

The teleological argument for the existence of God argues that the beauty and complexity of nature point to the existence of a creator. This is because the universe appears to be designed with a purpose, and therefore there must be a designer, or God, who created it.

Aristotle famously formulated the teleological argument in his Metaphysics. Aristotle argued that the universe is ordered and purposeful, and therefore there must be a divine mind that created it.

The main objection to the teleological argument is that it relies on a circular argument. The argument assumes that the universe is designed with a purpose, and then uses this assumption to prove that there must be a designer, or God, who created it. This is a circular argument because it assumes the very thing that it is trying to prove.