Anselm’s ontological argument refers to Psalm 14:1 ‘the fool says in his heart, ‘there is no god’.” Since the fool can conceive of God as the greatest being, it would be contradictory to think God doesn’t exist since then God wouldn’t be the greatest being.
Anselm argues that since God is that than which nothing greater can be conceived, it is incoherent to think that God exists in the mind alone because then we could conceive of something greater, i.e., that thing also existing in reality.
A weakness of the ontological argument is that Gaunilo raises an objection to P3; the premise that the greatest conceivable being exists in the mind/understanding, as an idea.
Necessary existence is a predicate of God, but contingent existence of things like cats and coins is not a predicate, since their reason for existence is something else.
Kant’s first criticism of the ontological argument might still succeed: Even if necessary existence were a predicate of God, that only shows that if God exists, then God necessarily exists.
Kierkegaard's argument is successful because it explains the reason the debate about God has been so persistent, as it cannot actually be solved through reason.
Religious belief involves a personal relationship with God such that faith in God is not only a matter of "belief-that" God exists, but also involves evaluative "belief-in".
Aquinas, Paley and Anselm only claim that their natural theology supports faith in God, but they each acknowledge that belief in God is ultimately founded on faith, not reason or philosophical argument.