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  A Peek behind the Veil of Maya: The Historical Background of theConception of Space as a Ground for the Individuationof Physical Systems Don HowardDepartment of PhilosophyUniversity of KentuckyWe find among their many efforts to bring to light theanalogy between all the phenomena of nature, manyattempts, although unfortunate ones, to derive laws of nature from the mere laws of space and time. How-ever, we cannot know how far the mind of a geniuswill one day realize both endeavors. —Arthur Schopenhauer,  Die Welt als Wille und Vorstellung  1 1.  Introduction: Einstein’s Berlin Portrait Gallery. According to Einstein’s son-in-law and biographer, Rudolf Kayser, portraits of three figureshung on the wall of Einstein’s Berlin study during the 1920s: Michael Faraday, James Clerk Maxwell, and Arthur Schopenhauer (Reiser-Kayser 1930, p. 194). One can easily guess why 2 Faraday and Maxwell, the inventors of field theory, were there. But why Schopenhauer? What ishe doing in this august company? This has long puzzled me.And something else has long puzzled me. From what source or sources, if any, did Einsteindraw the idea of “spatio-temporal separability,” the idea that a non-null spatio-temporal separationis a sufficient condition for the individuation of physical systems and their states, an ideafundamental both to his conception of field theory and to his famous reservations about the quantumtheory? This idea makes its first appearance in Einstein’s 1905 paper on the photon hypothesis(Einstein 1905) and gradually finds ever-clearer expression, until, by the late 1940s, Einstein hasdisentangled it from other, related conceptions of independence, such as the concept of “locality,”or “local action,” and has come to regard it as also the most essential aspect of his understanding of the very concept of physical reality. But, search as one will, this idea is not to be found anywherein the scientific and philosophical literature that we normally regard as having influenced Einstein’sworld view in his early years. It will not be found in Mach, Maxwell, Lorentz, Boltzmann, Hume,  - 2 - Poincaré, or Hertz. It is not to be found in the textbooks of the day, either elementary texts, such 3 Violle (1892-1893), or more advanced texts, such as Föppl (1894). It is not to be found in systematictreatments of phoronomy, as in Aurel Voss’s article in the  Encyclopädie der mathematischenWissenschaften  (Voss 1901). And it is not to be found in the popular-science literature of the day,such as the works by Aaron Bernstein (1853-1857) or Ludwig Büchner (1855) that Einstein read asa youth. I do not mean to deny the very real possibility that the idea was Einstein’s own. But still,I cannot help asking whether there may have been a source for this idea elsewhere in Einstein’sreadings.What I want to suggest in this paper is that the solutions to these two puzzles may well berelated to one another, that, surprising as it may seem, Schopenhauer may well have been the sourcefor the idea of spatio-temporal separability, and that, given how fundamental that idea was toEinstein’s conception of a field theory, Schopenhauer’s being the source may well explain his rather exalted place alongside Faraday and Maxwell in Einstein’s little Berlin gallery.The argument for this conjecture will, at many crucial places, be circumstantial; I have foundno smoking gun. All the more reason why one is likely to be skeptical, as I was at first (and still am,to some small extent) about the possibility that a thinker like Schopenhauer, famous as “the philosopher of pessimism,” could have had an important influence on Einstein’s thinking aboutfundamental questions of the ontology of space-time and field theories. Schopenhauer was certainlywidely-read in the late-nineteenth and early-twentieth centuries. His aesthetics is said to have beena crucial influence on Wagner’s notion of the Gesammtkunstwerk  . He was an important source for  Nietzsche’s concept of the will. And he influenced several generations of literary figures, ThomasMann being only the most famous of many. But such influences are so very different in kind from 4 that which I am suggesting he had on the young physicist, Einstein. Could Schopenhauer really  havehad an influence on Einstein’s thinking about fundamental questions of the ontology of spacetime?If I am to get this argument off of the ground, I must ask for some patience, for someforbearance. One must put on hold one’s initially strong disinclination to believe such a claim. For   - 3 -  part of that initial skepticism is a result of the fact that we have all grown to philosophical maturityin an anti-metaphysical age (at least the philosophers of science among us), an experience that leavesus ill-prepared for, if not positively ill-disposed to finding a Schopenhauer having this kind of influence on an Einstein. Indeed, I suspect that one reason why better documentation for thisinfluence is lacking is that, whereas many ardent young positivists were eager to ask Einstein abouthis reading of Mach and Hume, almost no one bothered to ask him about Schopenhauer.But, thankfully, a few people did ask, and, on at least a few occasions, Einstein himself wroteabout what he learned from Schopenhauer. And so there are some things we can say with reasonablecertainty about his reading of Schopenhauer, about his estimation of Schopenhauer as a writer, andabout the way in which Schopenhauer influenced his world view.What I will argue, more specifically, is that several crucial features of Einstein’s world view,not just the idea of spatio-temporal separability, could easily have been derived from his reading of Schopenhauer, or, at the very least, that they would have found important confirmation inSchopenhauer. In particular, we will find in Schopenhauer a unique view, a critical reaction to Kant,about the equally fundamental importance of, on the one hand, space and time as the “  principiumindividuationis ,” the “ground of being,” and, on the other hand, causality, the “ground of becoming,”for the constitution of representations of empirical objects in the understanding, both causality andspace and time being seen by Schopenhauer as forms of the principle of sufficient reason.There is a context for Schopenhauer’s development of these themes. It goes back at least to Newton, if not still earlier, to ancient and medieval discussions of the problem of individuation. Thespecific issue of space and time as principles of individuation comes to the fore in the disputes between Leibniz and the Newtonians over absolute versus relational conceptions of space and time,as we see from the Leibniz-Clarke correspondence. And an important chapter in the story concernsKant’s turn away from Leibniz and back to Newton, with his invention of the “incongruentcounterparts” argument around the time of his  Inaugural Dissertation . But it is Schopenhauer, more  - 4 - than anyone else—more even than the Marburg neo-Kantians—who brings the theme of space andtime as principles of individuation into nineteenth-century discussions of space and time.That Schopenhauer’s philosophy could have been read in this way by philosophers of scienceand philosophically-sophisticated physicists of Einstein’s generation will be shown by looking atwhat thinkers as diverse as Mach, Schrödinger, Weyl, Pauli, and Cassirer did, in fact, say aboutSchopenhauer. As one begins to appreciate who  it was who read Schopenhauer in this way, andexactly how  they read him, a picture begins to emerge in which Schopenhauer’s distinctive viewson the importance of space and time as the  principium individuationis  arguably form the backgroundand provide the vocabulary for the early-twentieth century discussion of the way in which the spatio-temporal manner of individuating physical objects is thrown into doubt by the development of thequantum theory. Thus, Einstein’s ardent defense of spatio-temporal separability as somethingfundamental to general relativity or any field theory, and the equally forceful critiques of separabilityin the work of Schrödinger and Pauli (and perhaps also Bohr), as something explicitly denied in thequantum-mechanical theory of interactions, must all be seen against this background informed bySchopenhauer.Finally, when Einstein’s defense of spatio-temporal separability is seen against thisSchopenhauerian background, its place in his understanding of the ontology of general relativityassumes a new significance, inasmuch as helps us to locate Einstein squarely within a traditionregarding the nature of space or space-time going all the way back to Newton. What defines thistradition is not one’s position in the dispute over absolute versus relative conceptions of space andtime, or one’s position in that more recent debate between substantival and relational conceptionsof space-time, both of which debates miss something essential in the Newtonian conception of space.What defines this tradition is, rather, one’s commitment to the idea that spatio-temporal separationis an objective feature of space-time, sufficient to serve as a ground for the individuation of systemsand their states. It was this characteristically Newtonian idea to which Leibniz really objected,arguing that systems are individuated not by extrinsic spatio-temporal determinations, but by
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