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Humean Supervenience, Composition as Identity and Quantum Wholes

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Abstract

In this paper, we focus on two related reductive theses in metaphysics—Humean Supervenience and Composition as Identity—and on their status in light of the indications coming from science, in particular quantum mechanics. While defenders of these reductive theses (at least those who do not simply deny the metaphysical import of empirical data and their proposed interpretation) claim that they can be updated so as to resist the quantum evidence, we provide arguments against this contention. We claim that physics gives us reason for thinking that both Humean Supervenience and Composition as Identity are at least contingently false, as the very process of composition determines, at least in some cases, the nature of composed systems. The argument has essentially to do with the fact that denying the reductive theses in question allows one to provide better explanations for the quantum evidence.

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Notes

  1. Here’s a significant quote: “[HS] says that all else supervenes on the spatiotemporal arrangement of local qualities throughout all history” (Lewis 1994: 474).

  2. We use lower-case letters for singular names and variables whereas we use capitals for plural terms (both names and variables). The standard notion of mereological fusion is this: x is a fusion of the Xs iff (1) each X is part of x and (2) each part of x shares a part with at least one X. If we abbreviate “x is the fusion of the Xs” with \( xFuX, \) the thesis that is relevant for our discussion is that: \( xFuX \to x = X. \) It is important to point out that we are only interested here in the idea that composition is identity, not in the weaker (but much more imprecise and vague) view that composition is ‘analogous’ to identity. The broader label ‘composition as identity' is often used to refer to either thesis (and we use it in this sense in the present paper). For details, see Cotnoir (2014).

  3. Note that no commitment is made with respect to the truth of the converse implication. If the latter were in fact true, one would have so-called ‘strong composition as identity', which we need not take into account in the present discussion.

  4. We will return to this issue later, see Sect. 4.

  5. Notice that we are glossing over differences that depend on whether properties and relations are parts (as suggested, for instance, by Paul (2002, forthcoming) with her ‘mereological bundle theory') or just features of parts. Either way, CII follows.

  6. Upon measurement but, it is also plausible to say, even independently of whether a measurement is actually carried out.

  7. This is an example of Miller’s type-c differences, namely differences in the wave-function or quantum states of physical systems that are due neither to phase factors, nor can be washed away by symmetry transformations such as velocity boosts (Miller 2013: 572). Other paradigmatic cases are the singlet and triplet states discussed in Maudlin (2007: 59–60).

  8. Lewis (2009: 205) addresses whether there are “all-or-nothing n-adic relations, at least for smallish n”. He envisages possible worlds in which the relation of having opposite electric charge is fundamental and non-reducible.

  9. The idea that entangled systems exhibit ‘inherent’ relations that are irreducible to fundamental, intrinsic properties of the relata comes from Teller (1986). Teller argues that the existence of such relations is one of the most crucial ontological lessons to be drawn from quantum mechanics. Although the view can be questioned (e.g., by contending that entanglement corresponds to monadic properties of certain wholes, or that it does in fact supervene on the properties of the parts, albeit via a functional relation weaker than multiplication (Winsberg and Fine 2003), we will keep talking of (seemingly non-supervening) ‘entanglement relations’ here.

  10. McDaniel (2008:132) explicitly considers such an option, but finds it unconvincing.

  11. For simplicity’s sake, we refer to operators here (and elsewhere), while of course it is the corresponding physical properties that are relevant.

  12. Essentially, Darby complains that it is always the case for entangled states that nothing short of the entire set of n component states and the corresponding n-ary fundamental relations can make sense of the properties of the whole. Thus, HS* holds only at the expense of adding very ‘global' facts to the point-like, i.e., local, facts that were originally presented as fundamental. We will say something more on HS and globality in a later section.

  13. We should point out that Sider (2007), while explicitly acknowledging the possibility of adding non-supervenient relations to the supervenience basis, ends up rejecting CII anyway, on the grounds that it would distort plural logic. He then goes on to endorse the weaker thesis, mentioned earlier, that composition is analogous to identity.

  14. \( x \prec y \) abbreviates “x is part of y”, whereas Xx abbreviates “x is one of the/among the X”. Informally, the principle says that if y is part of x, then it is among some W whose fusion is x.

  15. Obviously enough, on the same basis Sider rejects McDaniel's argument from duplication.

  16. Thus we are not claiming that the reductionist position is internally inconsistent, but rather that it should be considered implausible and uncalled for.

  17. In Sect. 6 we will discuss interpretations of quantum mechanics that might challenge such a picture.

  18. Reductionist friendly-literature, such as Esfeld (2014), recognizes that this was the preferred reductionist strategy at first (see e.g., Darby 2012). Different ways to save reductionism in the quantum realm have been recently explored in the literature. We will return to those in Sect. 6.

  19. Recall that they enter in different physically relevant relations with other parts of those wholes.

  20. This position resembles that recently defended in Cameron (2014), and which he traces back to Fine (1999). Cameron writes: “Fine agrees that the mereological sum of my parts is not me because those parts must be appropriately arranged: so the relevant relation gets in on the action with the parts for me to come about” (italics added). That relation is composition, which is, according to Cameron, a superinternal relation: that is, a relation R such that, if R holds between x and y, then necessarily the existence of x (or y) depends on the existence of y (or x) and R itself holds in virtue of the existence of y (or x). The crucial thing to notice for present purposes is that this establishes a clear dependence of wholes on their parts, but leaves it completely open whether—the existence of certain things being fixed—composition of those things occurs, and what the result is.

  21. Roughly, a maximally entangled state is one given which no proper subsystem of it has a complete set of properties of its own, and thus cannot be written as a tensor product of states of any of its components parts.

  22. The reductionist can react by taking the temporal dimension explicitly into account, and consequently conceiving of the Humean mosaic as 4-dimensional. We will discuss this option in Sect. 6, and argue that antireductionism remains preferable. But thanks to an anonymous referee for pointing out the need to make all this explicit already at this stage.

  23. As we will see in a later section, nihilism entails composition as identity. However, the converse doesn’t hold.

  24. For a discussion of ontological/existence and priority monism (the view that the universe is the only fundamental object) see Schaffer (2010).

  25. This is because if only simples exist it is trivially true that composites are identical to their parts—either because the antecedent of ‘if composites exist, then they are identical to their parts’ is false and the conditional consequently vacuously true; or because one includes in one’s consideration the limiting case of composites with only one (improper) part.

  26. For example, in Lewis (1994).

  27. See footnote 34 on the question of “minimal realism”.

  28. In so doing we conform to the extant literature. Indeed, a restriction to the Copenhagen interpretation or, for that matter, to any particular view on the collapse of the wave-function would be made superfluous by the fact that the issues being dealt here are simply independent of the measurement problem. For, the issue has to do—roughly—with the way in which certain properties relate to other properties at specific times, not with the way in which properties evolve diachronically.

  29. See Allori et al. (2008).

  30. See Bell (1987, chapter 7).

  31. As we will see later on, a better term would be “describes”.

  32. This is a move already made by Dürr et al. (2013) and recently endorsed by Callender (2014). The idea is, in particular, that the Best System Analysis of laws should be adopted, so that, e.g., “what makes it the case that there is a pilot wave is that the best system description of the physical world speaks in terms of it, and this description speaks in terms of it because it is part of an efficient and effective summary of what is fundamental” (Miller 2013: 580).

  33. We will return to this in a moment.

  34. We intend realism here in the very general sense that the theory describes objective features of reality, and the latter is not dependent on the minds of knowing subjects in any way. Two other realist interpretations are worth mentioning: the Everettian many-world interpretation and Rovelli’s relational interpretation (Rovelli 1996). The latter holds that every quantum state has an irreducible relational character, so that it only makes sense to attribute a state to a particular system from the perspective of another particular system. Although it is claimed (see Rovelli and Smerlak 2007) that this neutralizes EPR-type worries by rendering the consideration of space-like separated properties and events meaningless, hence seemingly lending support to the reductionist picture, this interpretation too might be regarded as too high a price to pay for saving reductionism. Something similar seems to apply for Everettians, since friends of reductionism would have to spell out clearly what their reductionist stance amount to in that setting. Should we take HS to apply to a single world or to the totality of Everettian worlds? In the latter case, is it worth to multiply worlds, as it were, in order to have a form of reductionism that only applies to their entirety, and not to any single one of them?

  35. For other critiques, see Monton (2006, 2013).

  36. See Ney (2013: 175).

  37. The notion traces back to Dennett (1991). Wallace (2004) discusses the possibility of reducing composite objects to Dennett-patterns in the corresponding wave-function.

  38. One may object that this is not the case for Bohmian conditional wave-functions for proper subsystems of the universe, which can seemingly be made as local as one wishes—for instance, one can effectively obtain the wave-function of a sharply localised particle a by evaluating the universal wavefunction ψ at the position of a at a given time t. This is, we think, an interesting avenue of inquiry, but it has to deal with the problem that the local conditional wave-function appears to still depend (especially for its temporal evolution) both on the a and on the global ψ. Thanks to an anonymous referee for drawing our attention to this particular Bohmian scenario.

  39. Of course, this is not a problem in itself, and might even be regarded as a welcome result in view of the intimations of relativity theory. Our argument in the main text still applies, though.

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Acknowledgments

We want to thank two anonymous referees for this journal for their detailed, careful and insightful comments which led to substantive revision and improvement. C.C acknowledges financial support from the Swiss National Science Foundation, Project No. BSCGI0_157792. M.M acknowledges funding from FIRB 2012, Project No. F81J12000430001.

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Calosi, C., Morganti, M. Humean Supervenience, Composition as Identity and Quantum Wholes. Erkenn 81, 1173–1194 (2016). https://doi.org/10.1007/s10670-015-9789-z

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