Development of the Concept of Space up to Newton

Development of the Concept of Space up to Newton: Comparison

Please note this is a comparison between Version 2 by Rita Xu and Version 1 by Danilo Capecchi.

The concept of space, ubiquitous among all humans from birth, has changed profoundly in the course of the history of Western civilization, the only one to be considered here. An important contribution to this change was the theoretical elaborations of the philosophers of nature and mathematicians, started in Ancient Greece. Here, the process is considered up to Newton, when the concept of space for physicists, who then replaced the traditional philosophers of nature, took on a connotation that remained substantially undisputed for two centuries—that of absolute space.

space
mathematics
natural philosophy
void
atomists
Patrizi
Gassendi

There are countless studies on the history of the concept of space (see, for instance, the following monographs on the general characteristics [1,2,3,4,5,6,7,8,9]^{[1][2][3][4][5][6][7][8][9]}). This notwithstanding, here, I attempt to offer a new contribution. The present work is not, strictly speaking, historical research, in the sense that there is no attempt to search for documents not yet known among modern historians of science. The aim is rather to present a new point of view on the meaning of already published documents and the role that they have played in the ideas of modern physicists and mathematicians, especially regarding the study of motion. This paper is a substantial historical survey of prominent views, although primary sources are generally used.

Space is a term that today has many meanings ^[10] (pp. 1–3), and it can be considered from different perspectives ^[11]. In this entry, the points of view of natural philosophy and mathematics are mainly considered; abstraction is made, as far as possible, from epistemological, anthropological, psychological/sociological or theological aspects, always present in elaborations of ancient times.

The first conceptions of space were intuitive ones that even a modern child could describe: an environment outside of ours, populated by gods, ghosts, and material objects, and one has vague notions of their amplitude, depth, distance, and direction. The first mathematicians, particularly the first Greek mathematicians, had only an intuitive idea of space, as far as is known from existing written records, most of which have not reached us. However, they understood the operations of space by means of solid geometry. In fact, even architects in designing their buildings, and soldiers with their weapons, had an intuitive idea of ambient space that was sufficient for their purposes, and astronomers operated in space; even if they did not pose, perhaps, ontological and epistemological questions about space, they raised at least the question of the finitude of the universe and the substance of which it is constituted: vacuum or plenum.

Natural philosophers and mathematicians—both considered in a broad sense, to include most people that today would be classified as scientists—saw space in different ways. The natural philosopher had to answer general questions concerning the existence of material and immaterial beings, creation, and the presence of God; the mathematician, at least until the 18th century, was essentially interested in space as an environment in which to build geometric figures and study the motion of bodies.

A precise notion of space was not a pressing need for the mathematicians before Newton. All considered space was not of interest in itself; the role that it played in the motion of bodies was relevant. The pioneers of early modern science, such as Galileo, for example, did not need to go beyond the intuitive idea of space to study the motion of bodies in a terrestrial environment. It was sufficient to possess a metric and a reference frame, and the Earth was enough for this, even if it was known that it moved within the ‘space’. This notwithstanding, the study of the analyses that the philosophers of nature carried forward through two millennia of history is very important for the understanding of how mathematicians have utilized this concept since the early modern era.

The purpose of this entry is not only to show how the concept of space developed in history in the reflection of natural philosophers, which is certainly interesting in itself, but mainly to show that it was fundamental in the development of classical mechanics and the entirety of modern physics.

First, the various conceptions of space in Greek antiquity are presented, comparing them with the intuitive idea of space;
Then, the harmonization during the Renaissance of the notions of scholasticism and the rediscovered Ancient Greek sources are considered;
Finally, the vision of absolute space in the modern era is presented, successfully overcoming the intuitive idea of space, made necessary for the development of a science of motion with cosmic significance, with Newton and Gassendi.

References

Jammer, M. Concepts of Space: The history of Theories of Space in Physics, 3rd ed.; Dover: New York, NY, USA, 1993.
Grant, E. Much Ado about Nothing: Theories of Space and Vacuum from the Middle Ages to the Scientific Revolution; Cambridge University Press: Cambridge, MA, USA, 1981.
Sklar, L. Space, Time, and Spacetime; University of California Press: Berkeley, CA, USA, 1974.
Cornford, F. The invention of space. In The Concepts of Space and Time: Their Structure and Their Development; Čapek, M., Ed.; Springer: Dordrecht, The Netherlands, 1976; pp. 3–16.
Friedman, M. Foundation od Space-Time Theories; Princeton University Press: Princeton, NJ, USA, 1983.
Duhem, P. Le Système du Monde (10 Vols); Hermann: Paris, France, 1913.
Koyré, A. From the Closed World to the Infinite Universe; John Hopkins: Baltimore, MD, USA, 1957.
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Bakker, F.A.; Bellis, D.; Palmerino, C.R. (Eds.) Space, Imagination and the Cosmos from Antiquity to the Early Modern Period; Springer: Cham, Switzerland, 2018.
Lucas, J. Euclides ab omni naevo vindicatus. Br. J. Philos. Sci. 1969, 20, 1–11.
Schemmel, M. Historical Epistemology of Space; Springer: Dordrecht, The Netherlands, 2016.