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Cosmological argument
The cosmological argument is an a posteriori proof for God's existence that reasons from the observable fact that the universe exists and requires a cause to the conclusion that there must be a necessary, uncaused first cause. Versions by Aquinas, Leibniz, and the Islamic kalam tradition differ in detail but share the core claim that an infinite regress of contingent causes is impossible or explanatorily unsatisfying.
Metaphysics
Metaphysics is the branch of philosophy concerned with the fundamental nature of reality, including questions about existence, substance, causation, and the relationship between mind and body. Ayer argues that metaphysical statements are cognitively meaningless because they are neither analytic nor empirically verifiable.
Theological non-cognitivism
Theological non-cognitivism is the view that religious statements such as 'God exists' do not express propositions capable of being true or false. On Ayer's account, this is more radical than atheism, because the claim is not that God does not exist but that the sentence fails to say anything meaningful at all.