Abstract
The basic principles of dispositional essentialism do not require that the fundamental spatiotemporal relations are dispositional in nature. Nevertheless, Bird (who defends dispositional monism) argues that they possess dispositional essences in virtue of the fact that the obtaining of these relations can be characterised by the satisfaction of a certain counterfactual. In this paper I argue that his suggestion fails, and so, despite his attempt, the case of the spatiotemporal relations remains the ‘big bad bug’ for the thesis of dispositional monism.
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Notes
Dispositional monism is the thesis that all fundamental natural properties have a dispositional essence. According to a possible extension of dispositional monism, non-fundamental natural properties are also essentially dispositional or supervene on natural properties that are essentially dispositional.
Substantivalists (in contrast to relationists) insist that spatiotemporal relations hold primarily between spacetime points and only derivatively between material objects or events.
Bird argues that dispositional monism should concentrate on the fundamental metrical relations and not on familiar geometrical (structural) properties such as shape. He thinks that even if structural properties fail to satisfy any criterion of dispositionality, they would not provide counterexamples to the monist’s claim which concerns only the fundamental properties and relations.
According to the orthodox view, entailment of subjunctive conditionals is a distinctive feature of dispositional properties.
Nevertheless, some arguments that appear in this paper (as, for instance, those related to the alleged causal behaviour of the spatiotemporal relations) may plausibly hit any dispositional essentialist account of spatiotemporal relations.
In the case of a fink, the disposition may be lost after the stimulus event but before the manifestation event. Antidotes leave the causal basis of the disposition intact but break the causal chain leading to the manifestation M of the disposition, so that M does not occur.
Bird thinks that the case for fundamental antidote-free dispositions is less clear than the case for fink-free ones. Nevertheless, as he notes, the development of physical science shows that the prospects for antidote-free fundamental properties are promising (2007, p. 63).
Einstein endorses the action–reaction principle as a scientific principle and insists that it is contrary to the mode of scientific thinking to conceive of a thing which acts itself, but which cannot be acted upon. Leibniz is one philosopher who thinks that conforming to this principle is a defining feature of substances.
Strictly speaking, the entailment holds between the propositions expressing the content of sentences in parentheses.
The problem arises for a dispositional monist who thinks that spatiotemporal relations are fundamental. In the opposite case, there is no problem, because the causal inefficiency of derivative relations does not (arguably) pose any threat to the monist.
Einstein’s equations are six independent differential equations having the form \( G_{\alpha \beta } = 8\pi \cdot {\rm T}_{\alpha \beta } \) where T αβ is the stress-energy tensor (related to the distribution of mass-energy of the universe) and G αβ is the Einstein’s tensor (related to the curvature of spacetime and constructed by the metric and its derivatives).
Perhaps, it does not even make sense considering the global matter distribution in spacetime as variable, since the very notion of change in a possible world involves variation from one time to another. I would like to thank an anonymous referee for this suggestion.
For a recent defence of the claim that the 4-dimensional ontological framework constitutes condition of possibility of the kinematic relativistic effects, see Petkov (2005).
A test body in GTR is a non-rotating freely falling point particle.
This is a necessary qualification, because, strictly speaking, only in certain special circumstances does the geodesic law of motion follow from the vanishing of the covariant divergence of the stress-energy tensor. No known model candidates for test particles which satisfy the condition of the vanishing divergence do also satisfy the Einstein equations. (Tavakol and Zalaletdinov 1998, p. 312).
Non-ideal force-free particles with internal degrees of freedom, such as intrinsic angular momentum, do not follow geodesics. Hence, it could be argued that this fact casts doubt on the geometrical character of the explanation of inertial motion. However, one can plausibly claim that what the attempted treatment of extended particles actually reveals is the need for a more general (than Riemannian geometry) geometrical framework in order to geometrise their force-free motion (Tavakol and Zalaletdinov 1998, p. 314).
Another philosopher who admits a kind of explanation related to spacetime structures, although a non-causal one, is Robert DiSalle (2006). According to his view, aspects of spacetime structure are explicitly co-ordinated with idealised physical processes defined by basic physical laws. This co-ordination provides physical definitions of the geometrical aspects of spacetime. For example, the physical process of inertial motion is co-ordinated with the concept of geodesic providing (through the claim that force-free particles follow geodesics) a physical definition of the latter. So, a kind of explanation of inertial motion is offered (obviously a non-causal one) by the recognition that this phenomenon conforms to the laws of metric structure, an aspect of which is the concept of geodesic.
Though I talk about the instantiation of properties I do not presuppose that they are universals. Perhaps, both the world-property and its constituents are particularised features. In any case nothing important to the purposes of this paper hinges on that. So the trope theorist may replace the verb “instantiates” with the more neutral term “having”. Furthermore, I do no take sides on whether the structural world-property is a first or a second order property of the actual world. For details about the ontology of structural universals, see Armstrong (1978), Lewis (1986) and Bigelow and Pargetter (1989).
According to Mumford’s view, each natural property has an essence and identity only in relation to the other properties.
More precisely, between space–time structure and mass–energy distribution of any (physically) possible world.
I would like to thank two anonymous referees for their comments and helpful suggestions.
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Livanios, V. Bird and the Dispositional Essentialist Account of Spatiotemporal Relations. J Gen Philos Sci 39, 383–394 (2008). https://doi.org/10.1007/s10838-009-9075-3
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DOI: https://doi.org/10.1007/s10838-009-9075-3