Beth and Lorenzen on the History of Science

Evert Willem Beth (1908-1964) and Paul Lorenzen (1915-1994) are well-known for their contributions to philosophy of mathematics and to formal logic (e.g., semantic tableaux and the semantics of dialogue schemata, respectively). Less known are their “excursions” into the historiography of science, represented by several pertinent papers and a small Geschiedenis der Logica (1944, [2]1948) by Beth, and by Lorenzen’s Die Entstehung der exakten Wissenschaften (1960). The paper paradigmatically presents Beth’s reconstruction of Aristotle’s definition of a deductive science, as well as his formulation of “Aristotle’s Principle (of the Absolute)” and of “Plato’s Principle (of the Idea”. A survey of the contents of Lorenzen’s monograph is followed by an outline and discussion of the criticism put forward by three leading historians of mathematics against some of Lorenzen’s theses. Beth’s and Lorenzen’s concerns in their approaches to the history of logic and of science are expounded and scrutinized, and their merits for contemporary and future work in this field are highlighted.