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Entities Without Intrinsic Physical Identity

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Abstract

This paper critically discusses recent objections that have been raised against the contextual understanding of fundamental physical objects advocated by non-eliminative ontic structural realism. One of these recent objections claims that such a purely relational understanding of objects cannot account for there being a determinate number of them. A more general objection concerns a well-known circularity threat: relations presuppose the objects they relate and so cannot account for them. A similar circularity objection has also been raised within the framework of the weak discernibility claims made in the last few years about quantum particles. We argue that these objections rely either on mere metaphysical prejudice or on confusing the logico-mathematical formalism within which a physical theory is formulated with the physical theory itself. Furthermore, we defend the motivations for taking numerical diversity as a primitive fact in this context.

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Notes

  1. Bain (2013) recently suggests that category theory provides a formal framework for this radical version of OSR; see Lam and Wüthrich (2014) for a critical perspective.

  2. We can draw on Spinoza’s metaphysics in order to make this idea more precise. Following Spinoza’s Ethics, one can understand properties and relations as modes, that is, concrete, particular ways in which objects are. There is no ontological distinction between objects and their properties and relations in the sense of modes: the modes are the way in which the objects exist. Objects do not have any existence in distinction to their ways of existence, and their ways of existence do not have any existence in distinction to the objects. One can draw a conceptual distinction between objects and their ways of existence, but not an ontological one, applying to reality.

  3. This ‘existential dependence’ of the objects on the relations in which they stand (or more precisely on there being other objects) is nicely encoded in the understanding of relations in terms of ways (modes) in which objects exist. Within this framework, objects explicitly belong to the fundamental ontology (in contrast to eliminativist, radical OSR), and are therefore not reduced to mere ‘bundles of relations’ (a conception that might face the ‘relations without relata’ objection): if relations are the ways (modes) in which objects exist, there is a clear and meaningful sense in which there are fundamental physical objects in the world—namely, there are objects whose existence depends on there being other objects (and in this sense, this conception clearly constitutes a non-eliminativist version of OSR, see Esfeld and Lam 2011), thus avoiding the ‘relations without relata’ objection. We thank the referees for pressing us on this point.

  4. See e.g. French and Ladyman (2003), Lyre (2004), Rickles (2006), Stachel (2006), Ladyman et al. (2007, Chap. 3), Esfeld and Lam (2008), Kantorovich (2009), Muller (2011), Caulton and Butterfield (2012b), French (2012), Lam and Esfeld (2012), Lam (2013).

  5. Jantzen (2011) also considers alternative notions of cardinality, such as within the quasi-set theoretic approach, and argues that they too ultimately rely on identity facts. See Arenhart (2012) and Arenhart and Krause (2013) for a rebuttal of Jantzen’s objection in the quasi-set theoretic context. For the purpose of this article, we can restrict ourselves to standard set-theory and the standard (von Neumann), intuitive notion of cardinality described above—suffice is to note that quasi-set theory may well provide a favourable environment for OSR (Krause 2005).

  6. As already mentioned above (see footnote 5), the proponent of quasi-set theory argues that determinate cardinality does not necessarily presuppose self-identity (Arenhart 2012; Arenhart and Krause 2013).

  7. The point here is not that there is an obvious, clear-cut distinction between mathematical formalism and physical concepts. As noted above, physical concepts are described in mathematical terms and the link between the two is complex. The task of interpreting a physical theory (of articulating its ontology) precisely involves investigating this link; the point here is that not all aspects of the mathematical (e.g. set-theoretic) formalism is physically relevant. We thank one of the referees for helpful comments on this point.

  8. We are not suggesting here that the broad standard mathematical (logical, set-theoretic) framework within which physical theories are usually formulated is not metaphysically loaded at all—it is to some extent, but mainly once physically interpreted. In this sense, we don’t think for instance that standard set theory with identity is committed to an ontology of individuals that possess some primitive intrinsic thisness (represented by the formal primitive self-identity relation in this context). Therefore, as interesting as it might be on its own right, the motivation (especially from quantum physics) for quasi-set theory does not appear to us as strong as it is claimed to be. Of course, it might still be interesting to look for alternative formal frameworks, which could allow physical theories to develop in new directions.

  9. Completely indiscernible objects easily appear in the mathematical domain (see Leitgeb and Ladyman 2008, who on this basis argue for primitive numerical diversity within mathematical structuralism); whether there are such physical objects is an open (and controversial) question. In this context, primitive numerical diversity has been considered in Pooley (2006), Ladyman (2007), Esfeld and Lam (2008, 2011); see also the recent discussion in Caulton and Butterfield (2012a).

  10. “We have already argued that primitivists can agree wholeheartedly with reductionists that mysterious, real yet non-physical, entities should be avoided when providing an account of reality. [\(\ldots\)] But then it follows that, exactly in the same way as the relations of numerical difference emphasised by the contextualists, primitive intrinsic identities need not be taken to constitute ‘metaphysical additions’ to the qualities of things, and may simply coincide with fundamental, ungrounded facts about the existence of certain entities” (Dorato and Morganti 2013, 602).

  11. Dorato and Morganti (2013) restrict their ‘primitivist’ considerations to non-relativistic quantum mechanics, where the particle number is always well-defined. More generally, they advocate a form of ‘pluralism’ with respect to identity and individuality, possibly with different approaches at different levels.

  12. Arenhart and Krause (2013) have recently also highlighted the analogy between Dorato and Morganti (2013) and Jantzen (2011): both assume that a definite cardinality requires individuals with intrinsic identity. As mentioned above, using quasi-set-theoretical tools, Arenhart and Krause (2013) further aim to show that the very formal notion of self-identity is not required for a definite cardinality (see footnote 8 for a comment on this program in relation to this paper).

  13. Dorato and Morganti (2013, §6) claim that the suggested diversity of primitive intrinsic identities is compatible with the results about weak discernibility (since all particles are qualitatively identical—we thank one of the referees for highlighting this point to us); however, the former is assumed quite independently of the latter.

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Acknowledgments

We wish to thank the audience in the Department of Philosophy at the University of Auckland, and in particular Denis Robinson, as well as the referees of this journal. We are grateful to the Swiss National Science Foundation (Ambizione grant PZ00P1_142536/1) for financial support.

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  1. Department of Philosophy, University of Lausanne, 1015, Lausanne, Switzerland

    Vincent Lam

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Lam, V. Entities Without Intrinsic Physical Identity. Erkenn 79, 1157–1171 (2014). https://doi.org/10.1007/s10670-014-9601-5

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