Newton’s Mathematical Principles of Natural Philosophy
appeared in 1687 (Principia
for short). It comprises three books. Book I analyzes motions of bodies in the absence of resisting media. Book II treats motions of bodies in resisting media. Book III assimilates observational data on comets, planets, the moon, and tides. The second edition issued in 1713, the third in 1726, the year before Newton’s death. Kant was born in 1724. At his death in 1804, Kant's personal library included a copy of the second edition of Principia
From 1732 to 1740, Kant attended Konigsberg’s Collegium Fredericum
, which prepared its students for the clergy or high civil office. It was a Pietistic institution. Pietism was a genre of Lutheranism. Kant excelled in Latin. Like any student being prepared to perhaps become a Lutheran minister, he was taught Hebrew and Greek. (Those were still required for Lutheran seminarians in America when I was a young man.) He learned to read French, but English was not offered. Latin and French would later give him access to Newton and his expositors. He was introduced to the basic principles of arithmetic, geometry, and trigonometry at the Collegium
From 1740 to 1744 steadily, from 1744 to 1748 intermittently, Kant attended the University of Konigsberg. There he was exposed to experiments in electricity and fire through Prof. Johann Teske. Kant was introduced to Newton’s physics through Prof. Martin Knutzen. It is reported that from his personal library Knutzen lent Newton to Kant. It is thought that Knutzen had some general understanding of Principia
, but did not understand Newton’s physics in mathematical detail.
Kant’s first published treatise was in 1747. That was “Thoughts on the True Estimation of Living Forces, and Criticism of the Proofs Propounded by Herr von Leibniz and Other Mechanists in Their Treatment of This Controversial Subject, Together with Some Remarks Bearing upon Force in Bodies in General.” The thesis of Section 9 is: “If the substances had no force whereby they can act outside themselves, there would be no extension, and consequently no space.” This is so because “without a force of this kind there is no connection, without this connection no order, and without this order no space.” (Leibnizian heritage is evident.) The young Kant then ponders the question of why space has three dimensions. In Section 10 he proposes “that the threefold dimension of space is due to the law according to which the forces in substances act upon one another.” Substances “have essential forces of such a kind that in union with one another they extend the sphere of their actions according to the inverse square of their distances.” Furthermore, “owing to this law the whole which thence arises has the property of threefold dimension.” (These translations are by John Handyside 1929.)
Recall the ultimate problem of the preceding post. That is the fine problem that had emerged for the planetary orbits: Given that a planet revolves around the sun in an elliptical path, with the sun at one of the two foci of the ellipse, what is the mathematical form of the attractive force responsible for such an orbit? Newton found the demonstration of the answer.
Kant is asking a question parallel in form: Given that space is three-dimensional, what can be said of the mathematical form of the force responsible for this fact? I think Kant inclines to connect the three-dimensionality of space to inverse-square separation dependencies of force strength because of a “schoolboy” argument to this dependency for gravity that had been circulating since the seventeenth century (and continues to this very day). An analogy is drawn between the intensity of gravity away from its source and the intensity of light away from its source. Light spreads out in a sphere in three-dimensional space. The surface area of that sphere is proportional to the radius of the sphere squared. Therefore the intensity of light diminishes by the inverse of the radius squared. Likewise for gravity.
If that were a correct reasoning to inverse-square separation dependence of gravitational attraction, it would apply no matter what the shape of the orbits resulting from an attractive force. But Newton had demonstrated in Book I that that is false. Various shapes of orbit imply various, different formulas of separation dependencies in the attractive force.
Kant continues his Pre-Critical constitution of space by inverse-square force in 1755 in “A New Elucidation of the First Principles of Metaphysical Cognition” (1:415) and in 1756 in “The Employment in Natural Philosophy of Metaphysics Combined with Geometry, of Which Sample 1 Contains the Physical Monadology” (1:476, 483–85). In his 1786 Metaphysical Foundations of Natural Science
, a work integral with his Critical project, Kant infers the inverse-square separation dependence of gravity from analogy with the spherical diffusion of light (4:519–21).Further Resources
“Part 3 – Kant” (1997) of my “Space, Rotation, Relativity” in Objectivity
Pertinent among the references cited there are Friedman 1992 and Polonoff 1973.The Kantian Philosophy of Space
(1966) by Christopher Browne Garnett.Kant and the Sciences
(OUP 2001) edited by Eric Watkins.Kant’s Transcendental Proof of Realism
(CUP 2005) by Kenneth Westphal.
Edited by Stephen Boydstun, 03 February 2008 - 07:51 AM.