Ontological belief in God: the idea that God exists because he exists
An ontological belief is an argument someone makes about reality: what exists simply because it exists. Due to God existing as an idea in the mind, and we cannot imagine a being greater than the greatest possible being that can be imagined (ie. God), it can therefore be concluded that God exists.
"Ontological arguments are arguments, for the conclusion that God exists, from premises which are supposed to derive from some source other than observation of the world—e.g., from reason alone. In other words, ontological arguments are arguments from nothing but analytic, a priori and necessary premises to the conclusion that God exists" (Stanford Encyclopedia of Philosophy).
"The first, and best-known, ontological argument was proposed by St. Anselm of Canterbury in the 11th. century C.E. In his Proslogion, St. Anselm claims to derive the existence of God from the concept of a being than which no greater can be conceived. St. Anselm reasoned that, if such a being fails to exist, then a greater being—namely, a being than which no greater can be conceived, and which exists—can be conceived. But this would be absurd: nothing can be greater than a being than which no greater can be conceived. So a being than which no greater can be conceived—i.e., God—exists. In the seventeenth century, René Descartes defended a family of similar arguments. For instance, in the Fifth Meditation, Descartes claims to provide a proof demonstrating the existence of God from the idea of a supremely perfect being. Descartes argues that there is no less contradiction in conceiving a supremely perfect being who lacks existence than there is in conceiving a triangle whose interior angles do not sum to 180 degrees. Hence, he supposes, since we do conceive a supremely perfect being—we do have the idea of a supremely perfect being—we must conclude that a supremely perfect being exists. In the early eighteenth century, Gottfried Leibniz attempted to fill what he took to be a shortcoming in Descartes’ view. According to Leibniz, Descartes’ arguments fail unless one first shows that the idea of a supremely perfect being is coherent, or that it is possible for there to be a supremely perfect being. Leibniz argued that, since perfections are unanalysable, it is impossible to demonstrate that perfections are incompatible—and he concluded from this that all perfections can co-exist together in a single entity. In more recent times, Kurt Gödel, Charles Hartshorne, Norman Malcolm and Alvin Plantinga have all presented much-discussed ontological arguments which bear interesting connections to the earlier arguments of St. Anselm, Descartes and Leibniz. Of these, the most interesting are those of Gödel and Plantinga; in these cases, however, it is unclear whether we should really say that these authors claim that the arguments are proofs of the existence of God" (Stanford Encyclopedia of Philosophy).
"Critiques of ontological arguments begin with Gaunilo, a contemporary of St. Anselm who used reductio ad absurdum arguments to show that the reasoning behind the ontological argument could be used to reach ludicrous conclusions. Perhaps the best known criticisms of ontological arguments are due to Immanuel Kant, in his Critique of Pure Reason. Most famously, Kant claims that ontological arguments are vitiated by their reliance upon the implicit assumption that “existence” is a predicate. However, as Bertrand Russell observed, it is much easier to be persuaded that ontological arguments are no good than it is to say exactly what is wrong with them. This helps to explain why ontological arguments have fascinated philosophers for almost a thousand years. Colin McGinn sides with Russell's opinion, at the expense of Kant's refutation" (Stanford Encyclopedia of Philosophy).
[P1] It is a conceptual truth (or, so to speak, true by definition) that God is a being than which none greater can be imagined (that is, the greatest possible being that can be imagined). [P2] God exists as an idea in the mind. [P3] A being that exists as an idea in the mind and in reality is, other things being equal, greater than a being that exists only as an idea in the mind. [P4] Thus, if God exists only as an idea in the mind, then we can imagine something that is greater than God (that is, a greatest possible being that does exist). [P5] But we cannot imagine something that is greater than God (for it is a contradiction to suppose that we can imagine a being greater than the greatest possible being that can be imagined.) [P6] Therefore, God exists.
Rejecting the premises
[Rejecting P3] The third premise adds existence to the definition of God given in P1. In other words, the concept of "greatest conceivable being" is axiomatically defined as something which actually exists, which just begs the question. The truth of the conclusion requires assuming the conclusion first.