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Space, Time, and Space-Time

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Abstract

Animals experience both space and time. But there is a long way from that evolutionary fact to the development of modern space-time theories and sophisticated discussions about relationism and substantivalism. It is well known that Kant believed that space and time belong to the human intuition that structured our sense impressions. The evolutionary naturalist is in agreement with Kant and cannot accept relationism or substantivalism. Both positions are expressions of the tendency among human beings to reify abstract concepts such like space-time. The evolutionary naturalist sees ordinary space and time as conceptual abstractions that at the same time reflect our experience of things’ locations and changes, as well as their duration and distances, and help us out in constructing the experiential unity and continuity of our perception.

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Notes

  1. 1.

    See Brown (2006). In a series of experiments with rats using a 5 × 5 pole box, Brown was able to demonstrate that their choices can be controlled by a spatial pattern among goal locations that does not correspond to any perceptual cues. The evidence for spatial pattern learning is reviewed, and some possible mechanisms are discussed. He concludes: “In order to abstract the spatial relations among goal locations, given that the goal locations change unpredictably in allocentric space, rats must somehow be perceiving the spatial relations among the baited poles found during individual trials. Two possible mechanisms for doing so can be distinguished. First, a working memory system could be used to code the allocentric location of poles previously discovered during a trial. The spatial relations among those locations could then be determined on the basis of working memories for their locations. The abstracted spatial relations among baited locations would then be coded in a more permanent memory system. According to this view, the process of spatial pattern learning is analogous to concept learning in that the spatial relations are abstracted from particular exemplars of baited pole locations experienced over trials.

    Alternatively, a dead reckoning system could be used that integrates the distance and direction from each baited pole discovered to the next. According to this view, rats need not code the locations of particular baited poles during the trial. Instead, their spatial relationship is coded directly in terms of the vector provided by dead reckoning as the rat moves in the pole box and chooses poles. A new vector is initiated each time the rat discovers a baited pole. The resulting set of vectors specifying the relations among each pair of poles forming the pattern constitutes the learned spatial pattern.”

  2. 2.

    See, for instance, Church (2002) and (2003).

  3. 3.

    Earman (1989), p. 199.

  4. 4.

    In an earlier paper (Faye 2006b), I argued that time is an abstract entity but kept a door open for the concreteness of space. Also I counted Leibniz as a proponent of space and time as concretes because I took him for being a reductionist by heart. Now, having reconsidered, I must admit that this remark may be too hasty.

  5. 5.

    Indeed, ‘ideal’ have several meanings. By using ‘ideal’ in contrast to ‘real,’ Leibniz seems to think of space and time as something whose existence (partly) depends on the mind.

  6. 6.

    See Gassendi (1971), p. 383 ff.

  7. 7.

    Newton (1962), p. 138.

  8. 8.

    Alexander (1956), p. 71.

  9. 9.

    Newton (1962), p. 136.

  10. 10.

    Physics, 219b2.

  11. 11.

    Physics 239b30–3.

  12. 12.

    Faye (1989), pp. 153–160.

  13. 13.

    Earman & Norton (1987), p 516.

  14. 14.

    Ibid., pp. 518–519.

  15. 15.

    See also Maudlin (1989), p. 86.

  16. 16.

    Norton (2004).

  17. 17.

    Sklar (1974), p. 75.

  18. 18.

    Ibid., p 75.

  19. 19.

    Earman and Norton (1987)

  20. 20.

    See Earman (1989), Ch. 9.

  21. 21.

    See Norton (1988).

  22. 22.

    See Maudlin (1989) and (1990).

  23. 23.

    Butterfield (1989).

  24. 24.

    Earman (1989), pp. 207–208.

  25. 25.

    Maudlin (1990), p. 545.

  26. 26.

    Ibid., p. 547.

  27. 27.

    For a discussion of this argument, see Hoefer (2000).

  28. 28.

    In his introduction to the Leibniz-Clare Correspondence, Alexander (1956), p. liv states two quotations of Einstein without any references, one in which Einstein says that the gravitational field “influences or even determines the metric laws of the space-time continuum,” the other in which he maintains that the gravitational fields “define the metrical properties of the space measured.” The first is from Einstein (1955), p. 62, whereas the second has not been possible to locate.

  29. 29.

    However, Einstein saw GTR as a theory unifying inertia and gravity, not as a theory of geometrization of the gravitational field. Lehmkuhl (2014) strongly argues that Einstein, contrary to the folklore, emphatically believed that GRT “should not be interpreted as a ‘geometrization’ of gravity, especially if ‘geometrization’ was seen as a reduction of gravity/inertia to space-time geometry.” (p.317)

  30. 30.

    When Maudlin (1990) argues that “The substantivalist can regard the field equation as contingent truths, so that it is metaphysically possible for a particularly curved space-time to exist even if all of the matter in it were annihilated” (p. 551), he is talking about something else. Even if all matter is annihilated there still exists a so-called source free gravitational field that constitutes the metric field (see Norton 1985, pp. 243–244).

  31. 31.

    Dorato (2000). In a paper written together with Massimo Pauli, Dorato and Pauli (2007) argue for a theory named point structuralism which according to them is a combination of features from both substantivalism and relationism: “including elements common to the tradition of both substantivalism (spacetime has an autonomous existence independently of other bodies or matter fields) and relationism (the physical meaning of spacetime depends upon the relations between bodies or, in modern language, the specific reality of spacetime depends (also) upon the (matter) fields it contains).” (p. 147) They explain that their theory embodies entity realism as the metric field exists physically “as an extended entity together with its point-events.” It is not just reducible to a mathematical structure. Furthermore, they claim that the space-time points exist, but their nature is relational. The effect is, if this is correct, that the metric field individuates the points of the manifold. See also Lusanna and Pauri (2006). Their view may be characterized as a form of non-reductive relationism; see note 32 and the discussion below.

  32. 32.

    Carlo Rovelli (1997), pp. 193–194, argues that Einstein’s identification between gravitational field and geometry can be understood in opposite ways: (1) “the gravitational field is nothing but a local distortion of spacetime geometry” or (2) “spacetime geometry is nothing but a manifestation of a particular physical field, the gravitational field.” He himself defends the second option, which I take to be an example of reductive relationism. The metric field is the manifestation of the gravitational field and as such “The metric/gravitational field has acquired most, if not all, the attributes that have characterized matter (as opposed to spacetime) from Descartes to Feynman.” In contrast, the non-reductive relationist would say the actual geometry is an exemplification of infinitely many possible geometries and that physical space-time seems to gain individuality by being instantiated by the gravitational field.

  33. 33.

    Friedman (1983), p. 223.

  34. 34.

    See for instance Earman (1989), p. 155.

  35. 35.

    Oliver Pooley (2006).

  36. 36.

    Belot and Earman (2001), p. 228. See also Belot and Earman (1999).

  37. 37.

    Rickles (2008), p. vi.

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Faye, J. (2016). Space, Time, and Space-Time. In: Experience and Beyond. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-31077-0_8

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