Proof [Lat. probare, to prove, through Fr.; it translates Lat. probatio]: Ger. Probe; Fr. preuve; Ital. prova. An argument which suffices to remove all real doubt from a mind that apprehends it.

It is either mathematical demonstration; a probable deduction of so high probability that no real doubt remains; or an inductive, i.e., experimental, proof. No presumption can amount to proof. Upon the nature of proof see Lange, Logische Studien, who maintains that deductive proof must be mathematical; that is, must depend upon observation of diagrammatic images or schemata. Mathematical proof is probably accomplished by appeal to experiment upon images or other signs, just as inductive proof appeals to outward experiment.