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Spatial Relations Are External


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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  1. 1.

    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.

  2. 2.

    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.

  3. 3.

    See Paolini Paoletti (2016) for more details.

  4. 4.

    On relations, see also MacBride (2020).

  5. 5.

    See Newton’s unfinished manuscript De gravitatione and his 1687 Philosophiae naturalis principia mathematica, Definitiones – Scholium, and Leibniz’s 1715–1716 correspondence with Samuel Clarke. See also Dainton (2010), Pooley (2013), Huggett and Hoefer (2015) and Koons and Pickavance (2017).

  6. 6.

    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.

  7. 7.

    On the distinction between relational and extrinsic properties, see Humberstone (1996). On the distinction between intrinsic and extrinsic properties, see, for example, Hoffmann-Kolss (2010) and Marshall and Weatherson (2018).

  8. 8.

    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.

  9. 9.

    See Schaffer (2009), Lehmkuhl (2018).

  10. 10.

    On haecceities, see for example Rosenkrantz (1993) and Cowling (2016).

  11. 11.

    See Le Bihan (2016).

  12. 12.

    The locus classicus for counterpart theory is Lewis (1986), where some objections are discussed.

  13. 13.

    See for example Mulligan (1998) and Simons (2016).

  14. 14.

    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.

  15. 15.

    For a philosophical discussion of this phenomenon, see for example Dainton (2010), Maudlin (2012) and Huggett and Hoefer (2015).


  1. Black, M. (1952). The identity of indiscernibles. Mind, 61(242), 153–164.

    Article  Google Scholar 

  2. Cleland, C. (1984). Space: an abstract system of non-supervenient relations. Philosophical Studies, 46(1), 19–40.

    Article  Google Scholar 

  3. Cowling, S. (2016). “Haecceitism”. In: Zalta, E. N. (ed.), Stanford Encyclopedia of Philosophy Online ( - last visited on April, 9th, 2020).

  4. Dainton, B. (2010). Time and space (2nd ed.). Durham: Acumen.

    Google Scholar 

  5. Dorato, M. (2000). Substantivalism, relationism, and structural spacetime realism. Foundations of Physics, 30(10), 1605–1628.

    Article  Google Scholar 

  6. Heil, J. (2012). The universe as we find it. Oxford: Oxford University Press.

    Book  Google Scholar 

  7. Hoffmann-Kolss, V. (2010). The metaphysics of extrinsic properties. Frankfurt: Ontos.

    Book  Google Scholar 

  8. Huggett, N., Hoefer, C. (2015). “Absolute and relational theories of space and motion”. In: Zalta, E. N. (ed.), Stanford Encyclopedia of Philosophy Online ( - last visited on April, 9th, 2020).

  9. Humberstone, I. L. (1996). Intrinsic/extrinsic. Synthese, 108(2), 205–267.

    Article  Google Scholar 

  10. Koons, R., & Pickavance, T. (2017). The atlas of reality. London: Wiley-Blackwell.

    Google Scholar 

  11. Le Bihan, B. (2016). Super-relationism: combining eliminativism about objects and relationism about spacetime. Philosophical Studies, 173(8), 2151–2172.

    Article  Google Scholar 

  12. Lehmkuhl, D. (2018). The metaphysics of super-substantivalism. Noûs, 52, 24–46.

    Article  Google Scholar 

  13. Lewis, D. K. (1986). On the plurality of worlds. Oxford: Oxford University Press.

    Google Scholar 

  14. Lowe, E. J. (2016). There are (probably) no relations. In A. Marmodoro & D. Yates (Eds.), The metaphysics of relations (pp. 100–112). Oxford: Oxford University Press.

    Chapter  Google Scholar 

  15. MacBride, F. (2020). “Relations”. In: Zalta, E. N. (ed.), Stanford Encyclopedia of Philosophy Online ( - last visited on November, 17th, 2020).

  16. Marshall, D., Weatherson, B. (2018). “Intrinsic vs. extrinsic properties”. In: Zalta, E. N. (ed.), Stanford encyclopedia of philosophy Online ( - last visited on April, 9th, 2020).

  17. Maudlin, T. (2012). Philosophy of physics - space and time. Princeton (NJ): Princeton University Press.

    Book  Google Scholar 

  18. Mulligan, K. (1998). Relations: Through thick and thin. Erkenntnis, 48(2–3), 325–353.

    Article  Google Scholar 

  19. Paolini Paoletti, M. (2016). Non-symmetrical relations, O-roles and modes. Acta Analytica, 31(4), 373–395.

    Article  Google Scholar 

  20. Pooley, O. (2013). Substantivalist and relationalist approaches to spacetime. In R. Batterman (Ed.), The Oxford handbook of philosophy of physics. Oxford: Oxford University Press.

    Google Scholar 

  21. Rosenkrantz, G. (1993). Haecceity. Dordrecht: Kluwer.

    Book  Google Scholar 

  22. Schaffer, J. (2009). Spacetime the one substance. Philosophical Studies, 145(1), 131–148.

    Article  Google Scholar 

  23. Simons, P. (2016). External relations, causal coincidence, and contingency. In A. Marmodoro & D. Yates (Eds.), The metaphysics of relations (pp. 113–126). Oxford: Oxford University Press.

    Chapter  Google Scholar 

  24. Slowik, E. (2016). The deep metaphysics of space. Dordrecht: Springer.

    Book  Google Scholar 

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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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Correspondence to Michele Paolini Paoletti.

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Paolini Paoletti, M. Spatial Relations Are External. Acta Anal 36, 341–355 (2021).

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