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Check all possible cases exhaustively.
P(x) is true for every possible xAll possible explanations of existence fail except the Creator.
∀x ∈ {naturalistic explanations}: ¬Valid(x) → Creator is only valid explanation(1) Eternal universe: violates the 2nd law of thermodynamics (entropy would reach maximum) and the BGV theorem proves any expanding universe must have a beginning. (2) Self-creation: logically impossible—a thing cannot cause itself before it exists. (3) Multiverse: merely pushes the question back—what caused the multiverse? (4) Spontaneous creation from nothing: "nothing" has no causal powers. All naturalistic options exhausted.
This is proof by exhaustion: we systematically examine every possible naturalistic explanation, demonstrate each one fails, and conclude by elimination that a transcendent Creator is the only coherent explanation.
This proof demonstrates the logical foundations of Islamic beliefs through rigorous philosophical methodology.