THE RIGOR OF THE ANCIENTS AND THE OPPORTUNISM OF THE MODERNS: THE CASE OF THE LEVER

ABSTRACT – We bring an argument favoring the perspective that modern science is different from ancient science as the former is less rigorous than the latter. To prove this thesis, we investigate how Archimedes and Galilei demonstrate the principle of the lever, i.e. the law according to which the equilibrium of the lever depends on the product of the loaded weight times the length of the arm. In explaining Archimedes’ proof, we follow Dijksterhuis’ presentation, defending its rigor from Mach’s attack. Concerning Galileo, on the other hand, we show how his proof of the lever principle is based on the thesis that continuum is constituted by an infinity of atoms. Moreover, we shed light on the fact that Galileo employs this notion of continuum despite knowing that it is not rigorous. We conclude by emphasizing the opportunism of Galileo’s methodology as contraposed to Archimedes’ rigor