  “Intuitionist Reflections on Formalism” of 1928 identifies and discusses four key differences between formalism and intuitionism, all having to do either with the role of PEM or with the relation between mathematics and language. Brouwer emphasises, as he had done in his dissertation, that formalism presupposes contentual mathematics at the metalevel. He also here presents his first strong counterexample, a refutation of PEM in the form \(\forall x\in \mathbb{R}(Px \vee \neg Px)\), by showing that it is false that every real number is either rational or irrational. See the supplement on  Strong Counterexamples. 