Abstract
The modern debate around scientific structuralism has revealed the need to reassess the standing and role of both structure and objects in the metaphysics of physics. Ontic structural realism recommends that metaphysics be purged of objects. Nonetheless, its proponents have failed to specify what it means for properties to be relational and structural, and, consequently, to show how the elementary objects postulated by our best theories can be re-conceptualized in structural terms or altogether eliminated. In this chapter, I draw from modern physics in order to untangle various types of relational properties and propose conditions that should be fulfilled for properties to be characterized as structural properties.
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Notes
- 1.
French (2009, 15) too admits: “the structuralist still has some work to do in supplementing the [group theoretic] ‘object structure’ with the relevant dynamical structure”.
- 2.
To be complete, Ladyman’s list should be supplemented with yet another type of OSR proposed by [1], which takes both properties and relations to be ontological primitives but objects to supervene on properties and relations. The proposal, however, is still in embryonic stages and lacks explication as to how exactly one may think of properties as ontological primitives. In my view, there are two options open, none of which seems compelling: either properties attach to some-thing, in which case properties and relations are not the only ontological primitives; or they are free floating, in which case one would opt for one of the already existing metaphysical accounts, like categoricalism or dispositional essentialism , and inherit their problems. For these reasons I chose to leave this account out of the present discussion.
- 3.
In this context, the terms ‘identity’ and ‘individuality’ appear to be inseparable, if only because attributing identity to an object presupposes that the object in question can be individuated. Later on, I will use the term ‘identity’ in reference to kinds of objects, in which case individuation will be irrelevant.
- 4.
The argument from metaphysical underdetermination has been the subject of various renditions and criticisms. For example, Muller and others, [18–20] disagree with OSRs that QM involves the kind of metaphysical underdetermination posited by OSRs. Ainsworth [1] too argues that the OSR assertion that QM and general relativity underdetermine their object-ontology is problematic, but also that a structural ontology does not necessarily solve the alleged problem. In what follows, we follow the discussion of the argument in Chapter 5, not only because it is more nuanced than the rest but also because it tackles the issue of the relation between individuation and objecthood explicitly.
- 5.
Note, however, that the issue of discernibility is not rendered irrelevant [8].
- 6.
Note that in this case it is not only properties but also their specific values that should be ontologically dependent on structure, because it is the specific values that account for the diversity of objects or kinds thereof—but more on this in what follows.
- 7.
To be exhaustive, we should mention that #2 does not constitute a variety of OSR as it only states a fact of QM, which hardly suffices for concluding that structure is all there really is. On the contrary, Morganti [17] argues that we can still talk about individual objects with relational properties meaningfully. As for #3, it mentions natures and I’d rather steer clear off such talk. Moreover, even Ladyman and Ross [15] duly replace talk of natures by talk of properties. Thus, if we replace ‘natures’ with ‘properties’ in #3 then we obtain #4, i.e. r-OSR.
- 8.
The total number of objects is not conserved in QFT processes. This fact, however, does not endanger my claim because the number and diversity of objects in the initial and final states of interacting systems are granted; and so are the number and diversity of objects involved in interactions—‘virtual particles’ aside. Another possible objection might be that there is no unique vacuum state in QFTs in curved space-time, and that countability fails therein because accelerating observers detect objects that inertial observers don’t. A more careful reading of the relevant literature [21], though, reveals that (i) objects manifest in such a vacuum through interactions only; hence the theory talks sensibly only about objects that are being detected, and (ii) if a non-inertial observer detects a number of objects, the inertial observer reports the non-inertial observer as having detected the same number of objects. Therefore, numerical distinctness and countability of QFT objects remain intact even in curved space-times.
- 9.
- 10.
From now on I put aside e-OSR and c-OSR and focus on r-OSR and od-OSR only. For one, e-OSR has been criticized severely from many, mostly on the basis that relational structure without relata makes no sense. I believe that the only way to make sense of e-OSR is to reduce it to some version of r-OSR or od-OSR if either of the two proves to be viable. It is for this reason that I will ignore it in what follows. As for c-OSR, I really don’t know how to translate the term ‘being a construct’ unless talking about reduction again. Hence in what follows, I stop worrying about c-OSR also.
- 11.
Recall that ‘concrete models’ differ from ‘generic models’ as follows. Concrete models are used in representing physical systems, and they are distinct from the specific but generic models of (or compatible with) a theory, which typically represent physically possible systems or physically possible worlds.
- 12.
Strictly speaking, QM does not describe individual objects and but rather systems of objects belonging to kinds 1 and 2 respectively (leaving open the possibility that 1 and 2 may be of the same kind also). My rather loose use of the jargon, however, does not affect the point I discuss here.
- 13.
Note in passing that the properties spin, helicity, etc. referred to above are not projections, specific values, but the generic properties that characterize the objects of QM and QFTs. For a discussion of failure of Humean supervenience involving projections, I refer the interested reader to [12].
- 14.
Strictly speaking ‘mean lifetime’ is a statistical property. Hence the actual lifetime of particular muons is not equal to \(2.2 \times 10^{-6}\). The claim above, however, is accurate enough for the purposes of the current discussion.
- 15.
Such worlds are physically possible because the masses of the elementary kinds of objects described by the Standard Model are free parameters. Therefore, if muons truly were the only or the lightest leptons in a world, no physical law would necessitate or even permit their decay. Masses and charges are not determined by any tentative extensions of the SM either.
- 16.
Indeed, had a QFT or some other theory existed that would deliver the masses of the existing leptons and quarks theoretically/structurally, the masses of the SM and hence the masses of the kinds of objects populating our world would have been determined theoretically/structurally. But adhering to what Ladyman and Ross [15] have called ‘principle of scientific closure’ and the associated stipulations (pp. 37–38), we are compelled to include to our discussion bona fide ‘specific scientific hypotheses’ that either have been investigated or might be investigated in the future. This excludes hypotheses like ‘the ultimate theory of fundamental objects is within reach’ that that fall with science fiction rather than science proper. Hence, given the present state of scientific knowledge I press on.
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Acknowledgments
The work that resulted in this paper begun in preparation for the Banff Workshop on ‘Structure, Objects, and Causality’. Earlier versions of this paper were presented at the 5th Meeting of Pittsburgh Fellows, at the Notre Dame workshop ‘Structuralism in Physics’ and at the colloquium of the department of History and Philosophy of Science at the University of Athens. I would like to thank the organizers and participants of all these events for extremely beneficial (to me at least) comments and discussions. Special thanks go to Aris Arageorgis, Katherine Brading, Elena Castellani, Ron Giere, Steven French, Elaine Landry, Matteo Morganti, F. A. Muller, Stathis Psillos and Vassilis Sakelariou for helpful comments and constructive criticisms. I would also like to acknowledge my substantial intellectual debt to Serge Rudaz. This work owes a lot to his unparalleled grasp of physics and to his eagerness to share this knowledge with me. At its latest stages, the research leading to this paper was funded by the European Union’s Seventh Framework Programme [FP7/2007-2013] under grant agreement n°229825.
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Nounou, A.M. (2012). Kinds of Objects and Varieties of Properties. In: Landry, E., Rickles, D. (eds) Structural Realism. The Western Ontario Series in Philosophy of Science, vol 77. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2579-9_6
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