About a century ago, Ernst Mach argued that Archimedes’s deduction of the principle of the lever is invalid, since its premises contain the conclusion to be demonstrated. Subsequently, many scholars defended Archimedes, mostly on historical grounds, by raising objections to Mach’s reconstruction of Archimedes’s deduction. In the debate, the Italian philosopher and historian of science Giovanni Vailati stood out. Vailati responded to Mach with an analysis of Archimedes’s deduction which was later quoted and praised by Mach himself. In this paper, (...) my objective is to show that the debate can be further advanced, as Mach indicated, by reframing it in terms of the empirical vs. the logical dimensions of mechanics. In this way, I will suggest, the debate about Archimedes’s deduction can be resolved in Mach’s favour.Keywords: Equilibrium; Experience; Thought experiment; Archimedes; Ernst Mach; Giovanni Vailati. (shrink)

Hermann Weyl succeeded in presenting a consistent overarching analysis that accounts for symmetry in material artifacts, natural phenomena, and physical theories. Weyl showed that group theory is the underlying mathematical structure for symmetry in all three domains. But in this study Weyl did not include appeals to symmetry arguments which, for example, Einstein expressed as “for reasons of symmetry”. An argument typically takes the form of a set of premises and rules of inference that lead to a conclusion. Symmetry may (...) enter an argument both in the premises and the rules of inference, and the resulting conclusion may also exhibit symmetrical properties. Taking our cue from Pierre Curie, we distinguish two categories of symmetry arguments, axiomatic and heuristic; they will be defined and then illustrated by historical cases. (shrink)

Lexical evidence reveals that ordinary notions of space underwent a dramatic change from the late seventeenth century into the first decades of the nineteenth century: the word’s core meaning metamorphosed from INTERVAL to DIMENSION, revolutionizing relations between ordinary conceptions of time and space. Analyzing instances of the word in French over the years 1330–1835 indicates this conceptual change of SPACE was concurrent with growing interest in metaphysics and natural philosophy and echoed debates—provoked by Newton’s Principia (1687)—over the precise nature of (...) space. Employing both quantitative and qualitative methodologies, I show how changes in philosophical and scientific theory reshaped the general lexicon. I argue that ordinary lexical mechanisms largely determine the manner of science’s dissemination into culture and propose a model accounting for such changes. (shrink)