AbstractThe theoretical core of positivism is thought to consist of three theses about the nature of law. The separability thesis denies the existence of necessary moral constraints on the content of law. The pedigree thesis articulates necessary and sufficient conditions for legal validity having to do with how or by whom law is promulgated. The discretion thesis asserts that judges decide hard cases by making new law. While it is often assumed that these theses form a coherent theoretical whole, such an assumption is false. Construed as a claim about all possible legal systems, the discretion thesis is inconsistent with the pedigree thesis. Construed as a claim that is true in some, but not all, possible legal systems, the discretion thesis makes a fundamentally different kind of claim than those made by the pedigree and separability theses and hence should not be thought of as part of positivism's theory of law.