Our remaining tests, as we will now argue, are infected by a problem analogous to Hempel’s famous dilemma for materialism (Hempel 1969). Materialism (roughly) states that everything is (or is made of, or is grounded in) matter. Materialism’s dilemma is that ‘matter’ is either defined by present physics or by ideal future physics. If the former, materialism is (most likely) false since our present theories of matter are (most likely) false. If the latter then we don’t know what materialism says because we don’t know what ideal future physics says. This dilemma is relevant for Lonely and Perfect Duplication*. For when performing the relevant thought experiments we need to isolate the atomic constituents of the objects we are testing for the presence of intrinsic properties, before sending those objects (or their duplicates) into other possible worlds. The first step—isolating the atomic constituents—will require some understanding of those constituents. We either use our current limited understanding of the atomic constituents, or we use non-existent (ideal completed) physics. Either way, we have no reliable way of executing the tests for a given case, as we will now argue.
The second horn of the dilemma is clearly problematic. Our tests are intended to offer ways of determining whether a given property is intrinsic or not. However, if the tests require a physical theory we do not have (ideal future physics) then we simply cannot perform the tests.
The first horn of the dilemma states that if the tests require current physics, then we cannot trust our tests due to the fallibility of the physical theories. To illustrate the fallibility of physics compare the following two theories, one that resembles classical physics, and one that resembles modern physics. We now show that even for the most mundane properties, test results are radically different depending on the physical theory one adopts. Here are the two theories:
Theory 1: Billiardballism: the atomic constituents of the Queen (and every other object) are tiny billiard balls, that differ from normal billiard balls only in scale—both ultimately obey the laws of Newtonian physics.
Theory 2: Global Nonseparability: the atomic constituents of the Queen (and every other object) are described by textbook quantum mechanics and the physical states (including the positions) of any given atom in the universe are nonseparable from the physical states of all other atoms in the universe.Footnote 7
Billiardballism is self-explanatory. Let’s begin by considering how Lonely categorizes the Queen’s shape, and the Queen’s wearing a golden ring, given Billiardballism. We take all the atoms that compose the Queen, and remove every other atom, to see whether the Queen retains her shape and her ring. In the lonely universe the atomic billiard balls retain their configuration. Since the Queen’s shape presumably supervenes on the configuration of her atomic parts, the Queen presumably retains her shape. Her shape is therefore intrinsic.Footnote 8 Since we do not deem the atomic parts of the Queen’s ring to be parts of the Queen, the ring’s parts are removed, so the Queen does not retain the ring. Her wearing a golden ring is therefore extrinsic.
Perfect Duplication*, given Billiardballism, will effectively give the same results: since the configuration of the Queen’s parts are duplicated, her shape is duplicated (necessarily), so her shape is intrinsic; since the ring’s parts are not duplicated, her ring is not duplicated (necessarily), so her wearing the ring is extrinsic.
Before we consider how Global Nonseparability affects our tests, a gentle introduction to the idea of nonseparability will be useful. To simplify, consider an atom that is a part of the Queen (particle 1) and another that is not part of the Queen (particle 2). In quantum mechanics, particle states (e.g. particle positions) are designated by vectors. So if particle 1 is located at Xa (i.e. point a on the X axis) then we represent its position with the term |Xa > 1, where ‘|>’ indicates a vector. However, particles are not typically in definite positions (the same goes for other physical properties like momentum and spin). Instead, particles are in so-called superpositions of different positions. Metaphysically, superpositions are notoriously difficult. But mathematically they are well understood, and can be represented by weighted sums of vectors. For example, particle 1’s being in a superposition of Xa and Xc is represented as #|Xa > 1 + #|Xc > 1.Footnote 9 Crucially, if particle 1 has (in almost any way) interacted with particle 2, then their positions will be non-separable such that their joint position-state will be represented by something like:
$$\# \left( {\left| {Xa >_{1} } \right|Xb >_{2} } \right) + \# \left( {\left| {Xc >_{1} } \right|Xd >_{2} } \right)$$
According to this quantum state, particle 1 is not (strictly speaking) in a superposition of being located at Xa and being located at Xc: it is in a nonseparable superposition with particle 2. This entails that particle 1 has no position of its own: the nonseparable state is (as the name suggests) not decomposable into individual component position states. Global nonseparability is the thesis that no particle has a position of its own: every particle is in a nonseparable superposition with every other particle.
Now consider what happens when we try to make the Queen’s constituents lonely, given Global Nonseparability. Since the positions of 1 and 2 are nonseparable, if we remove particle 2 we inevitably remove particle 1. The idea is that removing particle 2 entails that particle 2 no longer has a position. But removing 2’s position inevitably removes particle 1’s position, thereby removing particle 1 itself. Given global nonseparability, particle 2’s position is nonseparable with all the particles that compose the Queen. So removing particle 2 removes the Queen.Footnote 10 Similarly for the Queen’s property of wearing a golden ring: since the positions of the ring’s constituents and the positions of the Queen’s constituents are nonseparable, removing the ring (i.e. literally removing it from the world in the process of making the Queen lonely) removes the Queen. This would appear to destroy the test entirely: given Global Nonseparability, it is simply not possible to make the Queen lonely.
Assuming Global Nonseparabilty, is there any way to recast Lonely in such a way that it can yield determinate results? We’ve been working with a conception of Lonely under which one removes all particles except for those that constitute the property bearer of interest. But we could try to make the property bearer lonely in another way, viz. by transporting it to an empty possible world. But even that wouldn’t help: how could particle 1 be transported to another world by itself, given its nonseparability with particle 2? Perhaps, however, we can fix Lonely with an additional ad hoc stipulation: if particles to be made lonely happen to be nonseparable from particles that are not to be made lonely, then “separate” them first. However, since separating nonseparable particles requires changing their physical states entirely, the question arises: what states do we change them to before making them lonely? The states that guarantee that Lonely yields intuitive results? But this would make Lonely circular. Furthermore, even if we fixed on some way of separating nonseparable particles, we have no reliable way of knowing what effect that will have on a complex object like the Queen, so we would not know what properties she would retain, so Lonely still gives no results.
Finally, one might think that if it really is the case that removing particle 2 removes the Queen, then this is evidence that particle 2 is actually a part of the Queen after all. But then given global nonseparability, the Queen is composed of every particle in the universe. Removing every particle that does not compose the Queen then means removing nothing. Alternatively, transporting the Queen to an empty world means duplicating the actual world. Consequently, every property of the Queen would turn out to be intrinsic. This is the bullet that we think defenders of Lonely must ultimately bite. Before explaining the problem with this consequence, we will show that the same problem arises for Perfect Duplication*.
As with Lonely there are two ways we can understand the duplication test: either the duplication machine puts the duplicate in the actual world (Perfect Duplication) or it puts the duplicate in any possible world (Perfect Duplication*). Either way, the problem is that we cannot literally isolate the Queen’s parts to put them (and only them) in the machine, given their nonseparability with all other particles. Duplicating the Queen in the actual world (in accordance with Perfect Duplication) requires that the Queen-duplicate is constructed so that her parts are nonseparable from every other particle in the universe in the same way as the Queen-original. We cannot see any way of making sense of this situation. Alternatively, if the machine puts the Queen in an alternative possible world, then to be a duplicate her nonseparable state must remain, and so the machine does not duplicate only the Queen, but duplicates the entire actual world in the alternative possible world. Here we at least get meaningful results, but ones which deem all of the Queen’s properties intrinsic. This is the bullet that we think defenders of Perfect Duplication* must ultimately bite.
We now have our illustration of (horn one of) our Hempel-like dilemma: Lonely and Perfect Duplication* give radically different results depending on whether we appeal to a theory resembling classical physics (Billiardballism) or a theory resembling modern physics (Global Nonseparability). For example, on the former theory, only a small portion of the Queen’s properties are intrinsic, while on the latter, all of them are.
Now, a defender of these tests might simply bite these bullets and respond that although the tests do not give us the information we were hoping for, they still give us some information—enough to render them acceptable tests for intrinsicality. In particular, although the tests do not yield information of the form:
-
properties X, Y, and Z, are intrinsic;
-
properties U, V, and W are non-intrinsic;
they at least yield information of the form:
-
if GNS then properties X, Y, and Z, are intrinsic;
-
if Billiardballism then properties X, Y, and Z are non-intrinsic.
However, we do not think these conditionals are enough to render them acceptable tests. To explain why we use an analogy. Suppose a physician knows the following two conditionals:
-
if my patient S suffers from disease D, then cure C will cure S;
-
if S suffers from disease D*, then C will kill S;
but the medical tests available to him don’t enable him to conclude whether S suffers from D or D*. Then these conditionals, true as they may be, are not epistemic helps for deciding whether or not to apply cure C. Analogously, the intrinsicality conditionals, true as they may be, are not epistemic helps for deciding whether or not to apply the predicate ‘is intrinsic’.
Is there any way other to salvage our tests? One common reaction we have faced by defenders of intrinsicness consists in the following suspicion: our argument somehow depends on the assumption that worlds containing lonely individuals (or worlds that host the duplicates) are governed by the same laws of nature as the actual world. The upshot is then meant to be that the interpretation of quantum mechanics is irrelevant to what happens in such worlds.Footnote 11 However, this reaction is based on a fundamental misunderstanding of the nature of quantum nonseparabilty.
The reaction appears to suppose that by placing the Queen in a world with different laws (or no laws at all), the nonseparabilty of the Queen’s components somehow vanishes. But this is wrong. Imagine that we aim to make the Queen lonely. Will removing the laws of quantum mechanics remove the nonseparabilty of the Queen’s components? No it will not. The reason is that nonseparabilty refers not to features of the laws of quantum mechanics, but to physical states that are brought on by the laws of quantum mechanics. If you remove the laws of nature you do not thereby remove the physical states that those laws previously gave rise to. This reaction therefore appears to treat nonseparability as a feature of physical laws when in reality it is a feature of physical states.
Perhaps what the defender of intrinsicality wants is this: when the Queen is duplicated to a possible world with different (or no) laws, or when she is made lonely (in a way that removes quantum laws) then any physical states that can only be brought on by actual-world-laws must be removed. But this is no help either: how do we go about removing the relevant physical states of the Queen (or her duplicate)? As mentioned above, doing so will inevitably change the Queen. But there is no fact of the matter as to how this will change her! The defender of intrinsicality may want to change the Queen so that she is gauranteed to retain only those properties that are intuitively intrinsic. But then the test itself becomes superfluous, and we are left with no reliable way of testing for intrinsicness.
Are there any other ways out for the defender of intrinsicality? Perhaps one could reject Global Nonseparability in some way. Let’s consider two responses along these lines. The first denies modern quantum mechanics in general, the second denies Global Nonseparability more specifically.
One might respond with skepticism about modern physics, and therefore skepticism about any theory that resembles it, such as Global Nonseparabilty. Indeed, a response in this spirit was advocated by David Lewis when he realized that an aspect of his metaphysics made the same problematic assumption that is apparently made by Lonely and Perfect Duplication. The assumption often comes under the label locality. To the nonlocalityFootnote 12 inherent in quantum mechanics Lewis famously replied:
I am not ready to take lessons in ontology from quantum physics as it is now. First I must see how it looks when it is purified of instrumentalist frivolity, and dares to say something not just about pointer readings but about the constitution of the world; and when it is purified of double thinking deviant logic; and—most of all—when it is purified of supernatural tales about the observant mind to make things jump. If, after all that, it still teaches nonlocality, I shall submit willingly to the best of authority. (Lewis 1986: xi)
Could a similar defense be given on behalf of our tests? That is, could we ignore the results from above by asserting that quantum mechanics itself is in bad shape (e.g. due to the suspicious causal role it apparently attributes to the observant mind)? Not likely, since modern realist materialist reconstructions of quantum mechanics still postulate nonlocality.Footnote 13 Furthermore Global Nonseparability itself is hardly an outlandish possibility. As Schaffer (2010 Sect. 2.2) has pointed out, many physicists suspect that the big bang made the positions of all particles nonseparable. Thus, if anything, Global Nonseparability should be a serious candidate physical theory that guides our tests.
This brings us to the second response: instead of denying quantum mechanics, just deny Global Nonseparabilty, and advocate an alternative understanding of quantum mechanics. There is some precedent for this. After all, quantum mechanics faces difficult problems, which have given rise to a number of so-called “interpretations” of quantum mechanics, which are essentially different physical theories attempting to deal with those problems. And in particular, some interpretations introduce additional fundamental ontology over and above what is described by Global Nonseparability (e.g. Bohm 1952). Perhaps it could be argued that such additions (and their composites) have some intrinsic properties that our tests classify in an intuitively satisfying way. However, this simply brings out how sharp the first horn of the dilemma is: there is no consensus at all as to which (if any) is the correct interpretation of quantum mechanics. Thus, for even the most mundane properties (such as the Queen’s wearing a golden ring), our tests only have a chance of giving intuitive results under very specific, highly controversial, interpretations of quantum mechanics. The fact that intuitive results may only obtain under theories resembling classical physics suggests that intrinsicality may just be a notion that belongs to a metaphysics that builds on a now outdated physics. At any rate, we conclude that the tests for intrinsicness considered here cannot be relied upon.