 Brouwer’s proof of the bar theorem is remarkable in that it uses well-ordering properties of hypothetical proofs. It is based on the assumption that any proof that a property A on sequences is a bar can be decomposed into a canonical proof that is well-ordered. Although it is classically valid, Brouwer’s proof of the principle shows that the reason for accepting it as a valid principle in intuitionism differs fundamentally from the argument supporting its acceptability in classical mathematics.