An ontological argument attempts to deduce the existence of God from an analysis of the conception of God, thereby showing that it is necessary that God exists. From the mere logical possibility that this conception of God is instantiated, it is supposed to follow that it is necessarily instantiated. It has been dogmatically pronounced by a long line of philosophers from Hume up through the logical positivists that an ontological argument cannot work, since existence can never be a logical consequence of an entity's essence. This dogma is called into question by what appear to be perfectly legitimate ontological arguments for certain types of abstract entities, that is, entities that could not logically be located in either space and/or time, such as numbers, properties, and propositions. God, as conceived of by the great medieval theists, is such an abstract entity, though differing from these abstracta in having a life (an illimitable one at that, which is supposed to be had all at once!) and also having a causally efficacious will that can timelessly bring about effects in the universe. Given God's status as an abstract entity, the question naturally arises whether the same style of deductive reasoning from premises knowable a priori to an existential conclusion, such as figures so prominently in mathematics in which existential questions are internal to the system, being decidable by deductions from axioms and definitions, might not also apply to the existence of God. It certainly would be a blatant begging of the question to deny that it can. It is no accident that the ontological argument is the darling of the mathematically inclined theistic philosophers in the Platonic tradition, those who think that the mathematical method of reasoning is the pathway to true knowledge.

This chapter will consider many different types of ontological arguments. The first is based on a weak version of the principle of sufficient reason according to which everything has a possible explanation and argues that a contradiction follows from the assumption that God does not exist consisting in there both being and not being a possible explanation for this negative state of affairs. The second version, of which there are several variants, is based on some premise that is supposed to formulate a necessary truth about abstract entities in general, from which, in conjunction with other necessary premises, God's existence is supposed to follow.