 The condition of necessity on logical consequence obtains a new interpretation in the proof-centered approach. The condition can be reformulated thus: in a valid argument, the truth of the conclusion follows from the truth of the premises by necessity of thought (Prawitz 2005). Let us parse this formulation. Truth is understood constructively: sentences are true in virtue of potential evidence for them, and the facts described by true sentences are thus conceived as constructed in terms of potential evidence. (Note that one can completely forgo reference to truth, and instead speak of assertibility or acceptance of sentences.) Now, the necessity of thought by which an argument is valid is explained by the meaning of the terms involved, which compels us to accept the truth of the conclusion given the truth of the premises. Meanings of expressions, in turn, are understood through the rules governing their use: the usual truth conditions give their way to proof conditions of formulas containing an expression.