One may discuss the role played by mechanical science in the history of scientific ideas, particularly in physics, focusing on the significance of the relationship between physics and mathematics in describing mathematical laws in the context of a scientific theory. In the second Newtonian law of motion, space and time are crucial physical magnitudes in mechanics, but they are also mathematical magnitudes as involved in derivative operations. Above all, if we fail to acknowledge their mathematical meaning, we fail to comprehend (...) the whole Newtonian mechanical apparatus. For instance, let us think about velocity and acceleration. In this case, the approach to conceive and define foundational mechanical objects and their mathematical interpretations changes. Generally speaking, one could prioritize mathematical solutions for Lagrange’s equations, rather than the crucial role played by collisions and geometric motion in Lazare Carnot’s operative mechanics, or Faraday’s experimental science with respect to Ampère’s mechanical approach in the electric current domain, or physico-mathematical choices in Maxwell’s electromagnetic theory. In this paper, we will focus on the historical emergence of mechanical science from a physico-mathematical standpoint and emphasize significant similarities and/or differences in mathematical approaches by some key authors of the 18th century. Attention is paid to the role of mathematical interpretation for physical objects. (shrink)

In 1824 Sadi Carnot published Réflexions sur la Puissance Motrice du Feu in which he founded almost the entire thermodynamics theory. Two years after his death, his friend Clapeyron introduced the famous diagram PV for analytically representing the famous Carnot’s cycle: one of the main and crucial ideas presented by Carnot in his booklet. Twenty-five years later, in order to achieve the modern version of the theory, Kelvin and Clausius had to reject the caloric hypothesis, which had influenced a few (...) of Carnot’s arguments. Relying on the possibility of studying the history of science by means of logical investigation, in this paper I shall propose an historical/epistemological research on Sadi Carnot’s original thermodynamics theory in which the French scientist presents more than two principles, all of which are expressed by double negated sentences (generally speaking) within non-classical logic. (shrink)

This paper is divided into two parts, this being the first one. The second is entitled ‘Historical and Epistemological Reflections on the Culture of Machines around Renaissance: Machines, Machineries and Perpetual Motion’ and will be published in Acta Baltica Historiae et Philosophiae Scientiarum in 2015. Based on our recent studies, we provide here a historical and epistemological feature on the role played by machines and machineries. Ours is an epistemological thesis based on a series of historical examples to show that (...) the relations between theoretical science and the construction of machines cannot be taken for granted, a priori. Our analysis is mainly based on the culture of machines around 15th and 17th centuries, namely the epoch of Late Renaissance and Early Modern Age. For this is the period of scientific revolution and this age offers abundant interesting material for researches into the relations of theoretical science/construction of machines as well. However, to prove our epistemological thesis, we will also exploit examples of machines built in other historical periods. Particularly, a discussion concerning the relationship between science theory and the development of science art crafts produced by non-recognized scientists in a certain historical time is presented. The main questions are: when and why did the tension between science give rise to a new scientific approach to applied discipline such as studies on machines and machineries? What kind of science was used for projecting machines and machineries? Was science at the time a necessary precondition to build a machine? In the first part we will focus on the difference between Aristotelian-Euclidean and Archimedean approaches and we will outline the heritage of these two different approaches in late medieval and Renaissance science. In the second part, we will apply our reconstructions to some historical and epistemological problems concerning the relations of science/technology/constructions of machines. The problem of perpetual motion will play an important role in this context. (shrink)