Scales as challenging objects. From the theory of proportions to the quantitative interpretation in mechanics

In the connotation given by Jürgen Renn to historical epistemology, a change of paradigm does not consist solely in the breaking and replacement of an old paradigm with a new one, but in the production of new knowledge from accumulated knowledge, thereby eliciting cognitive potential. According to Renn, to understand the evolutionary history of scientific knowledge, we can study the so-called “challenging objects”. Challenging objects are phenomena or artefacts, such as scales and projectiles, concerning which the reflection on the cognitive content goes beyond the practical application, presenting a theoretical challenge. Following this perspective, the science of proportions, typical of Renaissance science, played a fundamental role in the evolution of knowledge, as it paved the way for quantitative physics. This paper aims to discuss the epistemological scope of the scale as a “challenging object” and to examine the concept of weight in the context of the theory of proportions applied to the case of the scale.