Philosophy of Religion
Arguments for and against God's existence
Know the classic proofs: ontological (Anselm, Descartes: a greatest conceivable being must exist), cosmological (Aquinas' first cause; Leibniz's principle of sufficient reason), teleological (design; Paley's watchmaker), and moral arguments. Know the critiques: Kant's claim that existence is not a predicate, Hume's objections to causation and design, and the problem of evil (logical vs. evidential forms; theodicies such as free will, soul-making).
Faith and reason
Distinguish fideism (faith independent of reason) from rational theology; know Aquinas' harmony of faith and reason, Pascal's wager, and Kierkegaard's leap. Understand agnosticism (suspension of judgement) as distinct from atheism (denial of God).
Religious language
Know analogy (Aquinas), via negativa, verificationist critiques (Ayer: religious statements are neither analytic nor empirically verifiable), and Wittgensteinian accounts of religious language games.
Traps
(a) Treating the ontological argument as an empirical argument; (b) confusing the logical problem of evil (contradiction) with the evidential one (probability); (c) equating agnosticism with atheism; (d) assuming the verificationist critique settles the truth of religious claims rather than their meaningfulness.
Rule of thumb
For any argument for God, identify its type (a priori or a posteriori) and the premise most likely to be challenged; then state the standard objection.
Worked example: The ontological argument is a priori - it moves from the concept of God to existence. Kant's objection targets the inference: existence adds no property to a concept. State the objection precisely.