 A weak counterexample shows that we cannot at present prove some proposition, but it does not actually refute it; in that sense, it is not a counterexample proper. From 1928 on, Brouwer devised a number of strong counterexamples to classically valid propositions, that is, he showed that these propositions were contradictory. This should be understood as follows: if one keeps to the letter of the classical principle but in its interpretation substitutes intuitionistic notions for their classical counterparts, one arrives intuitionistically at a contradiction. So Brouwer’s strong counterexamples are no more counterexamples in the strict sense of the word than his weak counterexamples are (but for a different reason). One way of looking at strong counterexamples is that they are non-interpretability results.