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Prove base case, then assume n and show for n+1.
P(0) ∧ (P(k) → P(k+1)) → ∀n: P(n)Every aspect of his life demonstrates prophetic qualities.
Base: Prophetic(worship). Step: ∀n: Prophetic(aspectₙ) → Prophetic(aspectₙ₊₁). ∴ ∀aspects: PropheticBase case: His worship was exemplary—praying until his feet swelled, fasting frequently. Inductive step: Every additional aspect maintains the same prophetic quality: (1) Ethics—flawless character acknowledged by enemies. (2) Knowledge—miraculous awareness of past and future. (3) Predictions—all fulfilled. (4) Leadership—united fractured tribes into civilization. (5) Teaching—produced the greatest generation of Muslims. The pattern holds universally across his life.
This is an inductive argument: we establish prophetic quality in one aspect (worship), show the pattern continues (every domain of life), and conclude prophethood. Unlike humans who excel in some areas and fail in others, his perfection spans every dimension.
This proof demonstrates the logical foundations of Islamic beliefs through rigorous philosophical methodology.