Abstract: How is law possible in a heterogeneous society, composed of people who sharply disagree about basic values? Such disagreements involve the most important issues of social life: the distribution of wealth, the role of race and gender, the nature of free speech and private property. Much of the answer to this puzzle lies in an appreciation of how people who disagree on fundamental issues can achieve incompletely theorized agreements on particular cases. Lecture I sets out the basic idea of incompletely theorized agreements and argues that such agreements have many virtues. It offers analogical thinking as a case in point - this is the way that ordinary lawyers and indeed ordinary people often try to solve legal and ethical problems. For a system of law, analogical thinking, as a basis for incompletely theorized agreements, can be desirable because it is so much less sectarian, hubristic, and demanding than deep theories about (for example) equality, or liberty, or economic efficiency. Society is sometimes too sharply divided or confused about such theories to permit them to be foundations for judge-made law, which requires agreements among people who have little time and limited capacities, who must find a way to live together, who believe that values are plural and diverse, and who should show respect to one another’s most defining commitments. Hence incompletely theorized agreements play a large role in interpretation of both statutes and the Constitution itself; many of our basic rights are a product of such agreements. Lecture II opposes rules to rulelessness. Its principal goal is to point the way toward a more refined understanding of the ideal of the rule of law, one that sees a degree of particularity, and a degree of lawmaking at the point of application, as an important part of that ideal. It defends a form of casuistry and describes the potentially democratic foundations of the casuistical enterprise in law. The lecture begins by describing the distinctive advantages of rules and law via rules, especially as a means for providing a consensus on what the law is from people who disagree on so much else. It also discusses two attacks on decisions according to rule: the view that controversial political and moral claims always play a role in the interpretation of rules, and thus that rules are not what they appear to be; and the view that rules are obtuse, because they are too crude to cover diverse human affairs, and because people should not decide cases without closely inspecting the details of disputes. Giving special attention to the death penalty and broadcasting regulation, it offers two ways out of the dilemmas posed by rules and rulelessness: (a) a presumption in favor of privately adaptable rules, that is, rules that allocate entitlements without specifying outcomes, in an effort to promote goals associated with free markets; and (b) highly contextualized assessments of the virtues and pathologies of both options, in an effort to promote democratic goals of responsiveness and open participation. The lectures end with the suggestion that incompletely theorized agreements on particular outcomes play a large role not only in law, but also in many other sectors of social life, prominently including democratic discussion.