Mechanics and natural philosophy are two locutions with completely different meanings today. Mechanics is normally understood as the science that studies the equilibrium and motion of bodies and is a highly formalized discipline; with this meaning, it is also labeled as “classical” in academic circles, so as to juxtapose it with relativistic and quantum mechanics. In the engineering world, the adjective “applied” is often juxtaposed with the noun “mechanics” to denote a discipline devoted to the investigation of technical applications of kinematics, dynamics, and statics of rigid and deformable bodies, and their encompassing fluids and gases. In this sense, mechanics is linked with the history of technicians and technology, starting from the ancient architects and manufacturers who also wrote about their techniques—one remarkable instance being the Latin architect Vitruvius.

Natural philosophy is a less common locution, and it is not possible, within the limits of this entry’s contribution, to describe all its meanings with enough detail; with some gross simplification, it can be said that, for some historians of science, it is an extinct discipline that took care of searching for explanations per causas of natural phenomena; for others, it is the name of a new branch of philosophy that studies nature as a whole, including mental states ^[1]. It is worth mentioning the existence of an important association of scientists named the Society for Natural Philosophy, founded by the mathematician Clifford Ambrose Truesdell in 1963, which “nourishes specific research aimed at the unity of mathematical and physical science” (from the by-laws of the society itself). The members of this society are scholars of exact sciences: mathematics, physics, biology, chemistry, meteorology, and so on. The name of the society is due, on the one hand, to historical continuity, since in English-speaking countries, the terms “physics” and “natural philosophy” were long exchangeable; on the other hand, it is meant to stress that the problems studied by the ancient natural philosophy are now the fields of investigation of exact sciences.

As a matter of fact, historically, the locutions mechanics and natural philosophy did not mean unrelated branches of knowledge. The following quotation gives a very good idea of how the two disciplines have been related in the past.

The quotation compares science and natural philosophy, but it is equally valid if science is intended to be limited to mechanics, and natural philosophy to the study of motion.

Before going further, as many of the terms in use in the past and still in use today have changed their meaning, a clarification is needed:

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Traditional natural philosophers: people trained in the investigation of nature by using the concepts of matter, causation, ethics. Examples are Aristotle, Plato, Descartes, and Leibniz, but not Newton and many of his successors.

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Mathematicians: people trained in theoretical mathematics and in practical activities.

Of course, one can envision a spectrum of intermediate figures ranging between canonical philosophers and mathematicians.