 A mathematical context in which PEM is valid, Brouwer points out, is that of the question whether a given construction of finite character is possible in a given finite domain. In such a context there are only finitely many possible attempts at that construction, and each will succeed or fail in finitely many steps (for clarity, the phrasing here is not that of Brouwer 1908C but that of Brouwer 1955). So on these grounds \(A \vee \neg A\) holds, where \(A\) is the proposition stating that the construction exists.