Proof (truth)

A proof is sufficient evidence or an argument for the truth of a proposition.

The concept is applied in a variety of disciplines, with both the nature of the evidence or justification and the criteria for sufficiency being area-dependent. In the area of oral and written communication such as conversation, dialog, rhetoric, etc., a proof is a persuasive perlocutionary speech act, which demonstrates the truth of a proposition. In any area of mathematics defined by its assumptions or axioms, a proof is an argument establishing a theorem of that area via accepted rules of inference starting from those axioms and other previously established theorems. The subject of logic, in particular proof theory, formalizes and studies the notion of formal proof. In the areas of epistemology and theology, the notion of justification plays approximately the role of proof, while in jurisprudence the corresponding term is evidence, with burden of proof as a concept common to both philosophy and law.