In a ground-breaking essay Nagel contended that the controversy over impossible numbers influenced the development of modern logic. I maintain that Nagel was correct in outline only. He overlooked the fact that the controversy engendered a new account of reasoning, one in which the concept of a well-made language played a decisive role. Focusing on the new account of reasoning changes the story considerably and reveals important but unnoticed similarities between the development of algebraic logic and quantificational logic.

The ArgumentA scientific work presupposes a body of texts that are a condition for its intelligibility. This paper shows that the study of intertextual reference — of the ways a text indicates its relation to other texts — provides a fruitful perspective in the study of science that deserves more attention than it has hitherto received. The paper examines intertextual reference in early nineteenth-century mathematics, first surveying a variety of mathematical texts in the period and then examining in detail W.R. (...) Hamilton's work on quaternions.Three questions are addressed: (1) What forms of intertextual reference are employed? (2) What is the range of intertextual reference? (3) What are the functions of intertextual reference? The answers to the first two questions provide an unexplored perspective on the institutional changes in science during the period. The transitional status of the period in the development of later professional science is reflected in the relative openness in the forms of intertextual reference employed and the range of texts to which reference was made. In virtue of these features the period is particularly fruitful in the study of the functions of intertextual reference. With some major qualifications, the paper defends a Mertonian view that intertextual reference needs to be understood in terms of the claim to intellectual property rights. (shrink)