In this contribution I argue that Brouwer’s legal positivism suffers from an internal tension that is not easily solved. This tension stems from the combination of two strands in Brouwer’s thought. The first is that Brouwer wants to stick to the legal positivist view that the law is fixed by convention. The second is that there can be exceptions to the application of legal rules, based on legal principles. The combination of these two strands is, I argue, problematic, because the conventional basis for legal principles will usually be lacking in hard cases. One may then argue, as Brouwer does, that where conventions are lacking there is no law and the judge is not bound by the law. But then exceptions to rules are also allowed where there are no conventional principles to justify these exceptions. This contradicts Brouwer’s starting point that exceptions to the application of rules are possible on the basis of legal principles.