Abstract
For those philosophers of space and time inclined towards a structuralist, third-way approach to ontology, Newton’s defense of the immobility of the parts of space is often regarded as a powerful historical precedent, prompting a host of structuralist-leaning commentary over the past several decades. Newton’s arguments, which appear in his early De grav and the Principia’s scholium on space and time, have been analyzed by Stein, DiSalle, Healey, Torretti, and many others committed to a more nuanced spatial ontology than traditional substantivalism and relationism offer. Recently, however, there have appeared two important assessments, by Nerlich and Huggett, that question whether Newton’s structuralist or holistic conception of the identity of spatial parts ultimately undermines his overall conception of space, a problem that, interestingly, does not appear to be a connected with his espoused absolutism or alleged substantivalism. Since Newton bases the identity of the parts of space on their structural relationships, and since all the parts of his infinite Euclidean space manifest the same structural relationships with one another, do these parts thereby lack the necessary identity criterion for a coherent theory of space? In order to better grasp Newton’s arguments and his general conception of these issues, this chapter will explore the background of, and the possible sources of influence on, Newton’s theory of the identity of spatial parts, as well as critique several important interpretations and arguments put forward by commentators. Yet, this chapter is not limited to an historical examination of seventeenth century theories alone, since a contemporary analogue of the problems associated with Newton’s treatment of the identity of spatial parts finds a home in contemporary spacetime debates. The goal of this chapter, consequently, is two-fold: first, we will rebut the problems raised by both Nerlich and Huggett by means of a more intricate historical and philosophical analysis of the spatial holism intrinsic to Newton’s theory; second, we will argue that modern debates on the ontology of spacetime, some of which have been motivated by similar puzzles, have either unwittingly followed, or could benefit from, Newton’s holistic conception of spatial ontology.
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Notes
- 1.
- 2.
As Koyré and Cohen point out (1962, 91), most modern translations incorrectly use the term “indiscernible” in place of “indiscerpible”, the latter being the term actually used in Clarke’s original reply but mistranslated in the published versions of the correspondence.
- 3.
It is also interesting that the main published works that link the ontology of God and space do not appear until the General Scholium of the second edition of the Principia (1713), although this would seem consistent with Newton’s general avoidance of God’s role in his published natural philosophy prior to his later years (post 1700). Incidentally, another means of establishing God’s immobility in the Scholastic period is to emphasize the connection with God’s infinity (omnipresence): Vasquez reasons that, if God is infinite, then there is literally no place for God to move (see, Grant 1981, 369, n.125), a view that Locke accepts in the Essay as well (E II.xxiii.21).
- 4.
Monism and holism, as used in this monograph, will refer to an entity’s “oneness”, and is thus equivalent to the notion of oneness used by More and Newton. Therefore, to employ the term “monism” or “holism” with respect to, say, the metric field of GR is to claim that its topology or other structures are not independent of the metric, rather they are all parts of a single entity, g. Presumably, there is a difference between holism and monism, since monism implies the holism of that entity, but it would seem that an entity could be holistic but retain an ontological independence of its parts. In what follows, consequently, our use of holism will reject the ontological independence of the parts of an entity (in keeping with the demand for the oneness and simple nature of space advocated by both More and Newton).
- 5.
If one interprets our holistic maneuver as the view (ii), that metrical relations are primary, with the identity of points dependent on these relation, what then accounts for the identity of metrical relations? This new version of the collapse problem (for metric relations) fails, however: given any two metric relations among points, say, g1 and g2, their identity will be secured via a larger metrical relation, g3, which includes both g1 and g2 within its scope, and so on for any extent of space (to infinity). Internal relations are employed in (iii), where internal relations are sometimes described as the relational equivalent of an essential or monadic property: i.e., the relation, R, that a point, p, bears with another point, q, is viewed as an internal relation of p if p bears R to q in all possible worlds. Unlike an external relation among points, therefore, an internal relation R incorporates the identity of the point p, and thereby does not violate the PII and is not subject to the collapse argument. (This strategy was suggested by a referee with respect to an earlier version of this chapter.) Since (iii) refers to individual points and their properties, it exhibits a somewhat non-holistic appearance, but it leads to the same interconnected holism of space as in (i) and (ii). A further investigation of strategies (i), (ii), and (iii), and all of the other possible constructions, is clearly required, however.
- 6.
Some material thing would seem to be required to serve as a coordinating basis to resolve these epistemological worries. Moreover, references to the “whole” of space include, unless otherwise noted, all structures in space along with lesser (non-three) dimensional structures and the ℜ 3 point manifold.
- 7.
Stein provides the following comment on (Aii): “This can be taken, in rather modern terms, as saying that space is a structure, or “relational system”, which can be conceived of independently of anything else [i.e., it is not simply a relation among existents, contra strict relationism]; its constituents are individuated just be their relations to one another, as elements of this relational system” (Stein 2002, 272).
- 8.
In correspondence, Nick Huggett has pointed out that a more adequate analogy would be to a set with the ordinal properties of the integers alone, without labels (such as 3), since every member of this set bears the same relation to some other member, and so this relationship would be preserved under the mapping.
- 9.
Concerning other aspects of Belkind’s (2007) innovative analysis: that a Cartesian body’s quantity of motion involves volume, or internal place (actually, the volume of its second and third elements; see, Slowik 2002, chapter 4) is not undermined by the fact that the constitutive parts of that body may have their own motions, and thus their own quantities of motion linked to their own volumes. This is no more a problem for Descartes than for Newton, especially given the latter’s Corollary 5 (the principle of Galilean relativity). Newton’s ship example is, ironically, Descartes’ own part-whole illustration: “on a ship, all motions are the same with respect to one another whether the ship is at rest or is moving uniformly straight forward” (N 78; cf. Descartes, Pr II 13). That is, if the scholium’s part-whole critique (above) is devised “to support the concept of momentum” (2007, 288), as opposed to a conceptual criticism of Cartesian motion, then Corollary 5 would undermine Newton’s own mechanics as well (since the true motion of the ship would need to be determined in order to calculate the momentum of any interactions on the ship). Furthermore, the rotating bucket and globes examples are probably best viewed as an inference to the best explanation in support of absolute space, since the non-inertial effects of rotation are not correlated with the relative motions of the bodies, contra relationism, and this is the only legitimate grounds that Newton can offer in support absolutism if the choice is confined to just absolutism and relationism—although Belkind’s point (290) may be that this constitutes a false dichotomy.
- 10.
McGuire (1982) and Koslow (1976, 254) attempt to make a case for a least spatial unit in Newton’s post-Questiones natural philosophy, or that Newton’s spatial ontology at least does not countenance dimensionless points. But, the passage quoted from TeL above (TeL 117) utterly refutes these readings, and, in fact, McGuire ultimately rejects the least distance interpretation in an endnote added later to his essay (McGuire 1982, 185).
- 11.
At length, Newton argues: “Now since it is impossible to pick out the place in which a motion began,…for this place no longer exists after the motion is completed, that traversed space, having no beginning, can have no length; and since velocity depends upon the length of the space passed over in a given time, it follows that the moving body can have no velocity” (N 20).
- 12.
Then again, if the hole argument is conceived employing a passive (coordinate) transformation, so that the original and mapped geometric structures (for instance, g and ğ, see Chap. 5) are merely alternative representations of the same reality, then maybe Newton’s (Ai) can indeed be seen as resolving this issue. Unlike active transformations, which purportedly describe a troubling physical underdeterminism involving two distinct states (or worlds), passive transformations do not pose any epistemological or ontological mysteries since they are trivial (coordinate) redescriptions of the same state (or world). The modern version of the hole argument is predicated on the active reading of transformations, of course; if not, it would fail to represent a problem for substantivalism or any other theory. Yet, since many text books on differential geometry and GR move happily between the active and passive use and interpretation of transformations, the hole argument is open to the objection that it is foisting a specific interpretation of geometric practice on substantivalists without argument. That is, while the active reading is the preferred basis for understanding many structures and models in contemporary physics, whether or not the hole argument poses a valid physics problem is precisely the issue at hand. Defenders of the passive interpretation of the hole argument can insist that isomorphic models, such as ğ, are the side effect of the geometric redundancies inherent in modern differential geometry, and hence not a true case of physical underdetermination at all. In fact, maybe a criterion should be invoked that confines legitimate ontological worries to only those underdetermination cases that arise under both the active and passive interpretations. At any rate, this assessment does not deny that the gauge-invariant interpretations of spacetime theories raise a host conceptual difficulties, such as the problem of frozen time and the status of “observables” in GR and quantum gravity (see, Belot and Earman 2001)—rather, our critique applies only to the issue of (unobservable) spacetime points apropos substantivalism. For an active interpretation of Einstein’s Hole argument for spacetime theories, see, Earman and Norton 1987.
- 13.
It should be added, here, that Huggett’s analysis, which examines the possibility of different spatial structures, is a very worthwhile exercise in its own right. His project is based on the idea that Newton’s theory allows counterfactual situations that require an account of the identity of points across such models. Overall, a modern theory based loosely on Newton’s views, and employing modern differential geometry, can benefit greatly from Huggett’s analysis. The intention of this chapter, however, is to make the historical case that Newton’s ideas do not, in fact, support the reality or possibility of these counterfactual states, as well as to make the philosophical point that modern spacetime debates prompted by contemporary versions of the identity argument can actually benefit from following Newton’s conceptions more closely.
- 14.
For example: “place is the part of space that a body occupies” (N 65); and “we define all places on the basis of the positions and distances of things from some body that we regard as immovable, and then we reckon all motions with respect to these places” (66). He adds that “absolute motions can be determined only by means of unmoving places,…and relative motions to movable places” (67). As for absolute place/space: “the only places that are unmoving are those that all keep given positions in relation to one another from infinity to infinity” (67).
- 15.
In what follows, similar conclusions can be reached for quantum gravity hypotheses, although that discussion will be the topic of Chap. 10. Hence our analysis in this chapter will remain confined to GR.
- 16.
As noted in Chap. 5, all references to GR’s metric incorporate its unique relationship with the gravitational field, via the Christoffel symbols of the metric. As Cao explains, “although the spatio-temporal relations are constituted by the chrono-geometrical structure (the metric), the latter itself is constituted, or ontologically supported, by the inertio-gravitational field (the connection)” (Cao 2006, 45).
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Slowik, E. (2016). Newton’s Immobility Arguments and the Holism of Spatial Ontology. In: The Deep Metaphysics of Space. European Studies in Philosophy of Science. Springer, Cham. https://doi.org/10.1007/978-3-319-44868-8_6
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