The thesis I wish to argue for in this article is that spatial relations such as occupying (a certain place) and being 1 km distant from (something) are external. In the “Section 1” section, I shall introduce the distinction between external and internal relations and some other basic concepts in the ontology of relations. Afterwards, in the subsequent sections, I shall deal with different theories of space: substantivalism and relationism (the “Section 2” section); the spatial property theory (the “Section 3” section); super-substantivalism and super-relationism (the “Section 4” section); and spatial essentialism (the “Section 5” section). I shall demonstrate that, in all such theories, spatial relations need to be considered external. Otherwise, unacceptable consequences or spatial properties that are non-relational by mere façon de parler are in order. Finally, in the “Section 6” section, I shall briefly tackle length contraction in special relativity theory.
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The entities on which something entirely depends are the ones that are jointly necessary and sufficient to explain why that thing exists and why it is what it is (i.e., its essence). “Entire dependence” may be taken as expressing a primitive relation between entities or as a placeholder for one’s favourite relation of dependence.
However, if simultaneity is relative to reference frames and if it is essential to the identity of times, apparently simultaneous events may actually turn out to happen at different times. For their essential times may turn out to be different with respect to different frames. To solve this problem, either we may try to define the identity of times without invoking simultaneity, or we may hold that time t1 is identical with time t2 whenever they are simultaneous with respect to all and the same rest frames, or we may introduce more complex identity conditions for times, or we may bite the bullet and accept the latter consequence.
See Paolini Paoletti (2016) for more details.
On relations, see also MacBride (2020).
With a different argument, Carol Cleland (1984) shows that distance relations are external on both substantivalism and relationism. Dorato (2000) defends a middle position between substantivalism and relationism that he labels “structural spacetime realism”. On such a position, point-events owe their identity to the chronogeometrical structure of spacetime. Such a structure is a web of spacetime relations flowing from gravitational fields. There are two reasons why, on such a position, we may take spacetime relations as external. First, spacetime relations fix the identity of their relata (i.e., point-events), but they does not depend on the essences, nor on the existence, nor on the intrinsic properties of their relata. At best, spacetime relations are part of the essences of point-events. Therefore, they count as external relations with respect to their relata. Secondly, spacetime relations flow from gravitational fields. Yet, they flow from gravitational fields via the “geometrical, causally active relational properties” of the latter. Indeed, spacetime relations do not flow from the mere causal powers of gravitational fields—which gravitational fields may possess even independently of other entities in the universe. Spacetime relations flow from the exercise of these powers by gravitational fields with respect to groups of entities (so to say)—and not just with respect to single entities. Therefore, the exercise of one of such powers consists in an external relation between, on the one hand, a certain gravitational field and, on the other hand, a certain group of entities to be structured in a certain way. The resulting structure is a proper fragment of the web of spacetime relations. Moreover, to obtain the whole web of spacetime relations, one must not consider gravitational fields in isolation. One must consider gravitational fields put together in specific configurations, that may turn out to differ from possible case to possible case. This is another reason why spacetime relations should not be deemed internal.
Therefore, a successful way of referring to occupying P cannot be through the description “the property of being where x is”—where x is the bearer of occupying P. For that description can pick out properties different from occupying P at times/possible worlds when/where x has a different spatial location.
See Le Bihan (2016).
The locus classicus for counterpart theory is Lewis (1986), where some objections are discussed.
One may suggest that, while Tom generically depends on Tom’s (actual) life, Tom’s (actual) life rigidly depends on Tom for its being the very life it is. Thus, Tom’s having Tom’s (actual) life is an internal relational fact. This seems to introduce some form of symmetric dependence between Tom and Tom’s (actual) life. At any rate, the dependence relation going from Tom’s (actual) life to Tom now looks stronger than that going from Tom to Tom’s (actual) life. This plausibly entails that Tom is more fundamental than Tom’s (actual) life—or that they are at least equally fundamental. If this is the case, it is not clear why a certain fact about Tom (i.e., his occupying a certain spacetime location) must be grounded on a fact involving a less fundamental or an equally fundamental entity (i.e., Tom’s (actual) life), rather than the other way round.
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This study received financial support from the Italian “Ministero dell’Istruzione, dell’Università e della Ricerca”, as part of the PRIN-2017 Project “The Manifest Image and the Scientific Image” (prot. n. 2017ZNWW7F).
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Paolini Paoletti, M. Spatial Relations Are External. Acta Anal 36, 341–355 (2021). https://doi.org/10.1007/s12136-020-00455-9