In this chapter a broad overview will be given of atheological arguments, without any attempt to determine whether they ultimately succeed. The aim is to give us a feeling for these arguments and an appreciation for their positive role in bringing about important conceptual reforms in the way in which God's nature has been conceived of over time.
The aim of an atheological argument is to reveal a logical inconsistency in the theist's concept of God. Accordingly, it begins with an initial set of propositions each of which is accepted by the theist as a necessary conceptual truth. For example, from the initial set containing the sole premise that necessarily God is omnipotent, an attempt is made to deduce a contradiction, namely, that there is some task that an omnipotent being cannot do. Or, from the initial set containing the conceptual truth that God is benevolent in the sense of always choosing the best alternative, it is deduced that God both does and does not actualize some possible world, with appeal being made to the additional premise that necessarily there is no best of all possible worlds. In both of these atheological arguments, the initial set contains only propositions that the theist takes to be necessary truths.
It would seem that my definition of an “atheological argument” as a deduction of a contradiction from the theist's concept of God, with appeal to only necessarily true additional premises, is unduly restrictive; for some of the most important attempts to demonstrate the logical inconsistency of theism begin with an initial set of propositions that contain at least one proposition that is taken by the theist to be only contingently true, for instance, that there exists evil, created free persons, and so on. For example, the deductive argument from evil, in one of its versions, begins with an initial set containing two propositions:
1. There exists an omnipotent and benevolent God; and
2. Evil exists,
from which it is deduced that evil does not exist, with appeal being made to some extra premises that articulate conceptual truths about omnipotence and benevolence. Herein the initial set is not comprised solely of conceptual truths, the theist taking 2 to be only contingently true, and also 1, if God's existence is taken to be contingent.