Larry Alexander has long been a leading proponent of the thesis that the meaning of a law is the meaning that the lawmaker intended it to communicate. He has argued frequently and powerfully against nonintentionalism, which denies either that a multimember lawmaker can have an intention, or that its intentions inform the meanings of its laws. In this chapter I say only a little about that debate, but enough to indicate why I agree with Alexander that nonintentionalism (thus defined) is implausible. Instead, I mainly discuss a disagreement within the intentionalist camp, between “strong” or “subjective” intentionalists – such as Alexander and Richard Kay – and “weak” or “objective” intentionalists – such as me. I treat Larry Solum’s public meaning originalism as a version of the latter position. I explain and assess the main arguments for and against these positions, and defend objective intentionalism and public meaning originalism against Alexander’s and Kay’s criticisms.