 In the 1908 paper, Brouwer draws a consequence of his general view on logic that he had overlooked in his dissertation: PEM, \(A \vee \neg A\), is not valid. Its constructive validity would mean that we have a method that, for any \(A\), either gives us a construction for \(A\), or shows that such a construction is impossible. But we do not have such a general decision method, and there are many open problems in mathematics. Brouwer states “Every number is finite or infinite” as an example of a general proposition for which so far no constructive proof has been found. As a consequence, he says, it is at present uncertain whether problems such as the following are solvable: