1. the establishment of a proposition or theory as true, or the method by which it is so established. There is much debate as to whether propositions or theories can ever be truly proven. In logic and philosophy, even a valid argument can be untrue if its first premise is false. For example, it is a valid argument to say that All trees are pines: I have a tree in my garden: Therefore my tree is a pine. In empirical sciences such as psychology, both logical and methodological problems make it impossible to prove a theory or hypothesis true. Disciplines that rely on empirical science must settle for some type of probabilism based on empirical support of its theories and hypotheses. See also falsifiability.

2. in mathematics and logic, a sequence of steps formally establishing the truth of a theorem or the validity of a proposition.

3. in law, evidence that establishes and supports the truth of claims made by either party in a dispute. Only evidence presented at trial can constitute proof; the trier of fact must then decide whether such evidence constitutes adequate proof. In criminal cases, the standard of proof required to obtain a conviction is proof beyond reasonable doubt.