Of the three views of theoretical knowledge which form the focus of this article, the first has its source in the work of Russell, the second in Ramsey, and the third in Carnap. Although very different, all three views subscribe to a principle I formulate as ‘the structuralist thesis’; they are also naturally expressed using the concept of a Ramsey sentence. This paper distinguishes the framework of assumptions which give rise to the structuralist thesis from an unproblematic emphasis on the importance of ‘structural’ differences for the analysis and interpretation of theories belonging to the exact sciences, and it reviews a number of logical properties of Ramsey sentences using very simple arithmetical theories and their models. It then develops a reconstruction of the views of Russell, Ramsey, and Carnap that clarifies the interrelationships among them by appealing to aspects of the arithmetical examples that inform the discussion of Ramsey sentences. The author concludes with an account of the philosophical basis of the structuralist thesis and the fundamental difficulty to which it leads.