The Greek noun apodeixis (G585) means demonstration, proof, or conclusive evidence. It is derived from apodeiknymi (G584, to demonstrate/show forth) — the kind of proof that compels assent, not merely suggests a possibility. The word appears once in the New Testament, in 1 Corinthians 2:4, where Paul contrasts human rhetorical proof with Spirit-empowered demonstration.
Paul's use of apodeixis in 1 Corinthians 2:4 is one of the most important statements on the nature of Christian proclamation. He writes: 'My message and my preaching were not with wise and persuasive words, but with a demonstration (apodeixis) of the Spirit's power.' The contrast is between the rhetorical proof of Greek philosophy (which could produce intellectual assent but not transformed lives) and the apodeixis of the Spirit — a demonstration that bypasses the intellect's defenses and produces genuine faith, repentance, and new birth. True gospel proof is not an argument won but a life changed by the power of God.