Formalizing Lagrangian Mechanics and the Invariance of Lagrange Equations

According to the logical empiricists, the received view, a scientific theory is a set of propositions formalized in first-order logic. According to the rival view, semantic or non-propositional view, it is a set of models. In this article, I will argue that the received view cannot suggest an acceptable model for identifying the generalized forces in classical mechanics. In the second section, the invariance of Lagrange equations and its consequences are discussed. Besides, I show that the invariance implies that alike physical magnitudes will be different dimensionally. The third section firstly introduces the last version of the received view. After that, it is argued that Lagrangian mechanics formalized in this view cannot identify alike physical magnitudes similarly. In the last section, the semantic view of Suppes-Sneed and Lagrangian mechanics in this view are introduced. Finally, I show that this view can identify alike physical magnitudes similarly.