[I am reading Tim Maudlin’s The Metaphysics Within Physics with Fred Muller, Victor Gijsbers, and Lieven Decock. The following post was inspired by our recent discussion.—ES]
In the context of a critical discussion (that I admire) of what he calls a "Separability" doctrine that he attributes to David Lewis, Tim Maudlin quotes a letter from Einstein to Born:
"The following idea characterises the relative independence
of objects far apart in space (A and B): external influence on A
has no direct influence on B; this is known as the 'principle
of contiguity', which is used consistently only in the field
theory. If this axiom were to be completely abolished, the idea
of the existence of (quasi-) enclosed systems, and thereby the
postulation of laws which can be checked empirically in the
By ‘Separability,” Maudlin means “The complete physical state of the world is determined by (supervenes on) the intrinsic physical state of each spacetime point (or each pointlike object) and the spatio-temporal relations between those points.” (51) Maudlin takes Einstein’s letter as evidence that in the face of evidence from quantum mechanics, Einstein also endorses Separability (and, thus, Lewis’ position is not just “a philosopher’s fancy.”) In response, Maudlin writes, “Quantum theory has both been formulated and rigorously tested despite the centrality of non-Separable elements in its ontology. Whatever Einstein had in mind, he had to be wrong.” (64)
Now, I am no scholar of Einstein, but I suspect Maudlin is seriously misreading Einstein here.
Einstein’s methodological dictum is deeply entrenched in mathematical physics since Galileo’s and Descartes’ time and is not, especially, "a truly Kantian theme" (as Maudlin seems to imply on p. 63.) For example, even though we all know that Descartes denied the existence of a vacuum (and infamously defined motion in terms of a body’s relation to surrounding bodies), when it comes to formulating his (counterfactually true, but unempirical) rules of collision in the Principia, Descartes treats two simple, moving bodies in isolation from all other bodies. As later mathematical natural philosophers would emphasize, studying bodies in motion as if they are part of a closed system makes piecemeal progress possible.
In fact, Spinoza may have been the last great philosopher to be critical of this approach. In a famous letter (on the Infinite) to Meyer, Spinoza writes:
“from the fact that we can limit duration and quantity at our pleasure, when we conceive the latter abstractedly as apart from substance, and separate the former from the manner whereby it flows from things eternal, there arise time and measure; time for the purpose of limiting duration, measure for the purpose of limiting quantity, so that we may, as far as is possible, the more readily imagine them. Further, inasmuch as we separate the modifications of substance from substance itself, and reduce them to classes, so that we may, as far as is possible, the more readily imagine them, there arises number, whereby we limit them. Whence it is clearly to be seen, that measure, time, and number, are merely modes of thinking, or, rather, of imagining. It is not to be wondered at, therefore, that all, who have endeavoured to understand the course of nature by means of such notions, and without fully understanding even them, have entangled themselves so wondrously, that they have at last only been able to extricate themselves by breaking through every rule and admitting absurdities even of the grossest kind. (Rhijnsburg, 20 April, 1663)
First, the passage presupposes a distinction between i) knowing things as imagining—confusingly to modern readers, in Spinoza’s vocabulary this can be a form of abstraction--and ii) knowing things by way of the understanding, or rationally. Second, in Spinoza’s complicated epistemology, knowing things by abstraction has less adequacy than knowing them by the understanding (E1p15s). For Spinoza to imagine something does not always mean it is false. But it can never yield adequate knowledge (see E2p49s).
Third, it follows from the text and these two points that Spinoza thinks that the use of measure and number do not reveal to us how substance and eternity are. Because measure and number are crucial in applying mathematics to nature one can say without hesitation that Spinoza thinks mathematics does not help us get at how reality really is but only at how we imagine it. (See Savan “Spinoza: Scientist,”). This does not mean that Spinoza thinks mathematics is fundamentally unreliable; there is evidence that he thinks that geometry provides a reliable form of topic-neutral inference. He has, rather, reservations about the applicability of mathematics as a privileged way of grasping nature (as was not uncommonly thought during the seventeenth century). Number and measure do not reveal ultimate reality (the nature of substance, eternity, etc.; Spinoza also seems to have thought that nature has more conceivable parts than numbers we can assign to it (see Ep. 83)).
Fourth, we should note how broad Spinoza’s condemnation is. He is ruling out the science of motion as a privileged form of knowledge. For, without “time and measure,” assigning velocities, places, and trajectories (etc.) is impossible. Fifth, from this letter to Meyer we can infer that according to Spinoza when things are ‘determined’ mathematically, we focus on things that have infinite number of relations with (infinite) other things; by applying measure we create what we may call a limitation of some part of the whole that is (without complete knowledge of the whole) arbitrary. That is, when we use measure to ‘carve out’ a part of nature (that is, a mode) for close study we somehow are in no position to have adequate knowledge of the whole and, thus, of it (the mode). For Spinoza to know anything we must know everything (see also his famous letter on the Worm in the Blood). (I suspect Leibniz also embraces a doctrine like this which can probably be traced back to Protagoras.) Spinoza seems to connect that principle with the limitations on the application of mathematics. To be clear, this does not imply that Spinoza thinks applying mathematics to nature is without use.
As I have recounted elsewhere, Spinoza’s arguments on the applicability of mathematics had an important afterlife in the eighteenth century (we find variants of it in Mandeville, Hume, Diderot, Buffon, and maybe Adam Smith) and were targeted explicitly by Newtonians who embraced piecemeal methodology as epistemically suited to our cognitive limitations and morally appropriate to responsible scientists (see here and here).
So, Einstein’s methodological claim has deep roots in the experimental practice and self-conception of mathematical physics. Even today when we think of some of the great paradigmatic experiments in quantum mechanics (e.g., the double slit experiment, the Bell test experiment), we treat the experimental set-up including the measuring device as part of a closed system. (This is not to deny that one can understand the whole universe as, perhaps, an entangled system.)
Now, Maudlin comes close to recognizing that his interpretation of Einstein may have gone off-rails because he adds the following paranthetical paragraph:
“(If by ‘completely denied’ Einstein merely means that any empirically testable theory must postulate some local instrinsic physical states, but not that the total physical state of all systems is Separable, then he would be anticipating John Bell’s call that one carefully consider what the ‘local beables’ of a theory are, i.e., the objectively existing quantities which ‘(unlike the total energy, for example) can be assigned to some bounded space-time region.’ (Bell, 1987, p. 53). One could try to make an argument that a physical theory with no local beables cannot be brought into correspondence with our experience of the world, but even this weaker claim may face serious obstacles.)” (Maudlin, 64)
I am not sure if Bell coined the term “beable” (“be-able as against observ-able,) but he certainly made it important in physics (see here). I am certainly willing to trust Maudlin’s authority in his claim that a physical theory with no local beables cannot be brought into correspondence with our experience of the world may face serious obstacles. But while Maudlin’s parenthetical interpretation is certainly closer to Einstein’s view, it remains misleading because in the letter to Born all Einstein claims is that the objects that correspond to the field theory have “an existence independent of one another.” But in context Einstein is making no claims about the status (intrinsic or extrinsic) of the properties of these objects. So, it is no evidence of his rejection of Separability.
To be sure: none of these remarks suggests that there is anything wrong with Maudlin's main argument against Lewis on Separability. But about Maudlin's substantive views soon more.