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Check all possible cases exhaustively.
P(x) is true for every possible xAll human philosophies fail to answer ultimate questions; revelation succeeds.
∀φ ∈ {human philosophies}: ¬Complete(φ) → Revelation is necessaryExamine every major human philosophy: (1) Materialism—provides no basis for meaning or morality. (2) Idealism—no grounding in reality. (3) Existentialism—no objective purpose. (4) Utilitarianism—cannot determine ultimate good. (5) Nihilism—self-defeating. All fail to answer: Where did we come from? Why are we here? Where are we going? What should we do? Only revelation answers all four comprehensively.
This is proof by exhaustion: we systematically examine every human philosophical system, demonstrate that each fails to provide complete answers to life's ultimate questions, and conclude that divine revelation—which succeeds where all human systems fail—is necessary.
This proof demonstrates the logical foundations of Islamic beliefs through rigorous philosophical methodology.