Newton’s Conceptual Argument for Absolute Space

Abstract

While many take Newton’s argument for absolute space to be an inference to the best explanation, some argue that Newton is primarily concerned with the proper definition of true motion, rather than with independent existence of spatial points. To an extent the latter interpretation is correct. However, all prior interpretations are mistaken in thinking that ‘absolute motion’ is defined as motion with respect to absolute space. Newton is also using this notion to refer to the quantity of motion (momentum). This reading reveals a misunderstood argument for absolute space, according to which absolute space is necessary for a workable definition of momentum.

Acknowledgements

I would like to thank Arthur Fine, Marc Lange, Robert DiSalle, Sona Gosh, and two anonymous referees for providing comments on previous and current versions of the paper. I would also like to thank Walt Stevenson for his help in reading the scholium in Latin and clarifying the various uses of the word ‘situs’.

Notes

[1] Newton himself did not consider the possibility that remote bodies can provide a reference for the definition of motion. The reason could be that none of these other definitions of true motion were ever proposed by Newton’s contemporaries. I’m here of course ignoring Mach’s later objection that the bucket experiment doesn’t preclude the possibility that inertial effects could be correlated with the motion of the water relative to the universe as a whole.

[2] See Earman (1989, 64) for an explicit discussion of the two steps of the argument, which according to him amount to an inference to the best explanation.

[3] According to Mach, for example, Newton’s definition of inherent forces is ‘superfluous’, since the tendency to move in a straight line is included as an external case in the second law of motion (Mach 1893, 300). Mach devotes the majority of his powers to deny Newton his first inference, i.e., that non‐relative motion could not be reasonably correlated with inertial effects. But he also criticizes Newton for including unobservable entities such as absolute space and inherent forces which contribute nothing to our understanding of inertial effects. If Newton wanted to use a legitimate scientific inference, he could have discussed a medium that pervades the entire universe, which causally influences the behaviour of bodies (Mach 1893, 282). Nevertheless, such a full‐blown material medium is not Newton’s account of absolute space. Mach, therefore, takes Newton to be positing an absolute space which has no casual effect on any particular phenomenon. And it is this construction which he finds ‘metaphysical’ and ‘meaningless’. For a similar argument, see Einstein (1967 [1923], 13–17).

[4] For the history of this misreading of the argument, see Reichenbach (1927, 210–218), Burtt (1954, 244–255), Jammer (1994, 106), Lacey (1970), and Westfall (1971, 443).

[5] Newton explains why space is not a substance in the following passage: ‘Perhaps it may be expected that I should define extension as substance, or accident, or else nothing at all. But by no means, for it has its own manner of existing which is proper to it and which fits neither substances nor accidents. It is not a substance: on the one hand, because it is not absolute in itself, but as it were an emanative effect of God and an affection of every kind of being; on the other hand because it is not among the proper affections that denote substance, namely action, such as thoughts in minds and motions in body.’ (Newton 2004, 21)

[6] Laymon introduces a similar reading, although he takes the implicit definition of absolute rotation to provide some inductive support to the existence of absolute space: ‘the function of the [bucket] experiment clearly is to be an example of a case where it is possible to determine the state of absolute rotation, assuming the existence of absolute and relative space, and the truth of Newtonian mechanics. The function of the bucket experiment is not per se to show that absolute space exists. It shows this existence only indirectly in the sense that to show that a concept has application is to give inductive support to the claim that the entities presupposed by the concept do exist.’ (Laymon 1978, 403)

[7] This understanding of ‘place’ is quite in line with the commonplace use of ‘situs’ in Latin texts before the advent of modern science. The Oxford Latin Dictionary (OLD) (Glare 1996 [1983]) defines ‘situs’ as ‘the position (of a thing) in relation to its surroundings, situation.’ However, the quotations the OLD mentions in support of the definition actually use ‘situs’ with the connotation of a volume a body occupies within a larger volume that contains it. For example, in his discussion of the physical organs of speech as the ‘voice’ of the brain, Cicero tells us, ‘in ore sita lingua est finita dentibus; ea vocem immoderate profusam fingit et terminat atque sonos vocis distinctos et pressos efficit cum et dentes et alias partes pellit oris’ (‘the tongue is located within the mouth and confined by the teeth; it modulates and contains the inarticulate flow of the voice and renders its sounds distinct and clear by striking the teeth and other parts of the mouth’) (Cicero, 266, modified translation). Here the word ‘situs’ is used to indicate that the tongue has a designated place within the larger organ that contains it, the mouth. Another citation by the OLD also gives support to the meaning we attribute to ‘situs’: ‘superius autem umeri caput rotundius quam cetera ossa, de quibus adhuc dixi, parvo excessu vertici lati scapularum ossis inseritur, ac maiore parte extra situm nervis deligatur’ (’the upper head of the humerus is more rounded than any other bone hitherto described and is inserted by a small excrescence into the top of the wide bone of the shoulder‐blades, and the greater part of it is held fast by sinews outside its socket’) (Celsus 1935, 8.1.19, modified translation). As in Cicero, the word ‘situs’ is used to indicate the place of an organ created by the surrounding organs. The humerus joint is said to be held in its place by the ligaments within the shoulder‐blade bone.

[8] Newton’s account suggests that the distinction between space and bodies is that between penetrable and impenetrable places. However, there may also be another distinction at work in Newton’s thinking. Newton seems to follow More in distinguishing between mathematical and physical divisibility. While space is infinitely divisible, there seems to be a limit to divisibility in physical bodies and material bodies must comprise of indivisible atoms. See Janiak (2000) for an account of Newton’s views on mathematical and physical divisibility.

[9] In what follows I will mostly follow Garber (1992).

[10] Descartes’s initial claim is that that the quantity of motion of the whole universe is conserved. From this claim Descartes deduces that an isolated individual body continues to move in a straight line and that quantity of motion is conserved during collisions. However, the particular form in which the quantity of motion is conserved does not follow from the philosophical claim that quantity of motion is conserved throughout the universe as a whole.

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Notes on contributors

Ori Belkind

Ori Belkind is at the Department of Philosophy, University of Richmond.