Einstein and Eindeutigkeit — Philosophical Background to General Relativity

0:00 The university of Kentucky is going to talk to us about Einstein and Eindeutigkeit, an objective theme in the philosophical background of general relativity. Thank you. The next session will be in Did everyone get a copy of this handout of the quotations that I would be relying on? Let me begin by explaining that the talk I want to give today is a part of a larger project. There's a part of a larger project that I've been engaged in for several years now to do a book on Einstein as a philosopher of science. And there are sort of two guiding principles that I have for this project. One is to put Einstein's philosophy of science in its proper historical context. My worry here being that much of what has been written about Einstein's philosophy of science is sort of, well, I'm not exactly sure how to describe the error that troubles me in this. Basically, the problem is that most people who have written Einstein's philosophy of science have tended to take what I would call mid-century concerns and problems and questions that concern us today in the philosophy of science and try to bring them to bear in the reading of Einstein's comments on philosophical issues. instance, people are always asking, was Einstein a realist or an instrumentalist? And the thing that strikes me about that question is that it's really an inappropriate question, that that controversy wasn't a controversy that was as important to Einstein as it is to us

2:30 today. And there were really rather different controversies that were important to him. So one point is to try to understand the philosophical world in which he lived and understand what issues and controversies were important for him. The second thing that has guided me in this is the desire to anchor discussion of Einstein's philosophy of science directly in his scientific work, because after all, Einstein is not a systematic philosopher of science. He is first and foremost a physicist who turns to philosophy when he is more or less compelled to do so in order to help with the solution of scientific problems. So the second point, again, is to try to root all of these investigations in actual problems that concern in physics. And I would rather like to think that today's paper conforms to both of these, at least desiderato. Specifically, today, I want to talk about what I call the Eindeutig-type principle in Einstein's philosophy of science, and specifically as it occurs in the context of his whole and point coincidence arguments. Now let me very briefly characterize the issue. I will give a somewhat more detailed characterization in a moment. Many people have spoken about the whole argument and the point coincidence argument already, so I don't want to bore you with this, but you will remember that what's key to the whole argument, first of all, is this as Einstein's believing that he has an argument in 1913 and 1914 to show that fully generally covariant equations, don't determine a unique solution for the gravitational field without a hole. And he thinks that that is a sufficient condition for repudiating generally covariant equations. Well, there seems to be a methodological principle that he's appealing to there. And that is, as I would describe it, and now my description here is somewhat deliberately anachronistic. The methodological principle he seems to be appealing to here is that a theory should uniquely determine its own models. That's the principle that I have in mind by the principle of Eindeutig, that the theory should determine its models Eindeutig, uniquely. Now, when you first encounter this principle in the context of the whole argument, you're immediately reminded of

5:00 the concept from formal semantics of categoricity, because a categorical theory is described in this literature on formal semantics as a theory that determines its models uniquely, or uniquely at least up to the point of isomorphism, that is, determining an isomorphic class of models. Is this the principle that Einstein is appealing to? Is he familiar with this concept from the literature on formal semantics? Well, I think not. Even though the concept of categoricity had already been introduced as early as 1904 in the work of Oswald Bedwin, and he is basically reinterpreting some remarks at Hilbert's on his Bluntlog in Deometria on one specific kind of completeness, even though that concept had been introduced as early as 1904, It really wasn't a prominent issue in the literature on the foundations of geometry. So I don't think Einstein was picking up this principle from that literature. I also don't think that this is simply a mathematical commonplace. That is, Einstein saying that a set of equations should determine a unique solution. It is at least a mathematical commonplace, but I think it is quite a bit more than that. Specifically, I think that there is a very interesting philosophical history to be told here, a history of a discussion of this principle of Eindeutigkeit, of the idea that theories should uniquely determine their own models, should uniquely determine what it is that they pretend to talk about. And what I want to focus on today is this philosophical history and this concept of Eindeutigkeit. one other footnote, and that is that in the discussions of the whole argument, one thing that has always puzzled me, and has puzzled a number of people, John Stachel referred to this yesterday in his talk on the Cauchy problem, is that Einstein describes this problem with generally covariant field equations also as a problem about causality. And frankly, I have never understood why he calls this a problem of causality. Well, one of the dividends that I think is paid by our learning about this history of the philosophical discussion of Eindoyakite is that maybe we can get a clue as to why he described this problem

7:30 as a problem of causality. Because as you will see, when this principle of Eindoyakite is first introduced in the philosophical literature, it is in the context of a discussion of causality. So there was a link between these two issues, causality and eindeutigkeit, from the very beginning of the discussion of this issue in philosophical literature. One last point. I've said that I don't think Einstein was familiar with what little was being said by mathematicians about the concept of categoricity at the time that he developed the whole and point coincidence arguments. In fact, quite the contrary, I even have the suspicion that one of the many consequences of the discussion of the whole and point coincidence argument by Einstein and others was that this was one of the many stimuli to the clarification of the concept of categoricity as a concept in formal semantics 1920s. That's just a conjecture at this point, and I won't talk about it in the paper today, but perhaps in the questions afterwards I can tell you why I conjecture that there might, that this discussion of the whole argument might have influenced the discussion of categoricity and literature on formal semantics in the 1920s. Okay, next item. Before we actually plunge into a discussion of the whole argument, the point coincidence argument, and the philosophical background to these, just a little bit of conceptual clarification. I will sometimes talk simply of the Eindeutigke principle, but I really want to distinguish three different kinds of Eindeutigke principles that I call the metaphysical Eindeutigke principle, the model-theoretic Eindeutigke principle, and the epistemological Eindeutigke principle. These are my terms for these different principles. You don't find these in the period and we can argue about whether or not they are the most helpful designations for these various principles. Briefly, what I mean by each is the following. By the metaphysical eindeutigkeit principle, I will mean the claim, you can put it in several different forms, but basically the claim that reality in and of itself is unique, that it is given eindeutigkeit, that there's an

10:00 eindeutigkeit characterizing reality itself. By the model-theoretic eindeutigkeit principle, I name the idea that a theory should determine its own models eindeutig, that there should be an eindeutigkeit in the uniqueness in the theory's determination of its models. One can easily imagine that you might appeal to a metaphysical eindeutigkeit principle as a justification for a model-theoretic Eindeutigke principle, that is to say, a theory should determine its models uniquely because the reality it aims to describe is given uniquely. I happen to think that's not a good argument for justifying a model-theoretic Eindeutigke principle, but whether or not it's a good argument is not the issue for the moment. By the epistemological Eindeutigke principle, and I should add that this is something I will not speak about at any great length today, that is really rather different from these two, but occurs in the same literature, the principle that could be formulated perhaps is following. A set of observations, a body of empirical evidence, determines uniquely a single theory that correctly predicts or correctly explains all of that empirical evidence. It's the idea that empirical evidence all by itself provides a selection criterion among theories. This would be denied, of course, by someone like a Duhemian, under-determinationist conventionalist, would deny this epistemological Eindroide-type principle. But again, I don't want to talk about that very much today. I want to talk about metaphysical and model-theoretic Eindroide-type. One final conceptual clarification before we begin. When we find Einstein invoking what I call the model-theoretic Einweig-type principle. He says, in effect, and again, this is my paraphrase, he says that a theory should uniquely determine its own models. He fails to make this distinction that does become important later on in literature on formal semantics, the distinction between a theory determining an absolutely unique model and a theory determining a class of models that are isomorphic to one another. I just want to alert you to the fact that there is that, well, if you want a bit of that confusion in Einstein's discussion of this, I don't think that's necessarily a failing on Einstein's part, because, again, in the literature on the foundations of mathematics,

12:30 that distinction had not yet been clarified by the time Einstein was writing. But you might find yourself being a little bit confused by this not being clear on that point. let's take a somewhat more detailed but still brief look at the whole and point coincidence arguments first of all the whole argument Einstein first introduced this whole argument as best we can determine in the fall of 1913 and again without going into great detail in the reconstruction of the argument the basic point is this he believed that he had convinced himself that fully generally covariant equations field, do not uniquely determine a solution for the field. They do not uniquely determine a G field within a hole, a hole being what he calls a region of the manifold devoid of, quote, material processes, no matter no energy in the field. T is equal to zero in the field. He characterized this aspect of the argument on a number of different occasions, and on the vocabulary that he used was quite similar. And I've pulled together three of these remarks in the handout here. They're the first three quotations on the handout. And I just asked you to take a look at them and pay careful attention to the vocabulary that he uses here. For instance, in his last published statement of the argument, this in his 1914 paper, Die Formale Grundlage der Allgemeinen Relativitätstheorie, he said, events, the jargon is in the gravitational field, cannot be determined uniquely, by means of generally covariant differential equations in the gravitational field. If we demand, therefore, that the course of events in the gravitational field be completely determined, by means of the laws that are to be established, then we are obliged to restrict the choice of the coordinate system. generally covariance equations. Similarly, in a letter to Paul Ehrenfest from what is probably the late fall of 1913, he says, the questions regarding the theory of gravitation that were still undecided in the summer have clarified themselves in the meantime. A unique determination,

15:00 an Eindötegebistimmel, of the g mu nu out of the t mu nu is possible only with the choice of special coordinate systems. And this, he says, is a rigorously prudible result. And then lastly, in a letter to Ludwig Hopp of 2 November 1913, he says, I am now quite satisfied with the theory of gravitation. The fact that the equations of gravitation are not generally covariant, which troubled me inordinately a little while ago, has turned out to be unavoidable. It can easily be proven that a theory with generally covariant equations cannot exist in case it is demanded the field be mathematically completely determined, fullständig bestimmt by the matter. That for the whole argument, then. When, in late 1915, he finally returned to fully generally covariant field equations, he was faced with the problem of getting rid of the embarrassment of the whole argument, which had seemed to provide a conclusive argument against generally covariant equations, this purpose, he developed the point coincidence argument, or the so-called point coincidence argument. And again, without going into great detail in the reconstruction of the argument, the basic move that he makes here is to try to find a way to... I don't want to go into great tale. Let me just say this. He makes the point that all that is observable are point coincidences, intersections of world lines. And why is this important? Because, he says, these intersections of world lines are preserved under arbitrary continuous coordinate transformations. That is to say, again, to use his own vocabulary here, that they are uniquely determined. They are and that this Eindeutigkeit is not disturbed by any coordinate transformation, it seems to me that he is appealing in this point-coincidence argument to the very same methodological principle that he was appealing to in the whole argument, that is, this model-theoretic Eindeutigkeit principle, again, insisting that an adequate theory must determine uniquely its own models.

17:30 Only now, he says, I now understand that a theory with fully generally covariate equations does determine uniquely its own model, and therefore it is acceptable. It's interesting, again, to look at the way he describes this conclusion in some of his correspondence. In particular, I draw your attention to the letter to Ehrenfest from late December of 1913, which is the quotation starting at the bottom of page 1 where he says the following in section 12 of my work of last year everything is correct in the first three paragraphs up to that which is printed with emphasis at the end of the third paragraph from the fact that the two systems gx and g prime x two solutions of the field equation referred to the same reference system satisfy the conditions of the gravitational field, no contradiction follows with the uniqueness of events. His term is eindeutigkeit des geschehens. That which was apparently well let me spare you the rest of the quotations at this point, you can read it at your leisure. It's that remark that I'm most interested in here where he says that we now understand that there is no contradiction with this eindeutigkeit des geschehens. You keep saying that the theory should determine what Einstein says is the theory plus the matter distribution should determine it. Well, the field... No, no, no, you're quite right. The field equations plus some boundary conditions have to do that. I don't mean to deny that. Not just some boundary conditions, very restrictive boundary conditions. Right, the conditions on the boundary as a whole. You can make this whole very small. That's the idea. You have lots and lots of matter all the way outside. to deny that. I mean, this actually is a question of, when I speak here of a theory determining its model uniquely, I'm using the vocabulary as it's used in the formal semantics literature, and we need to do a little interpretation to adapt that to Einstein's way of speaking about this when he speaks about a set of equations determining a unique solution. It's of course equations plus boundary conditions that determine the solution, but I want to make the point that the relationship between a set of equations plus boundary conditions and the solutions determined thereby is formally

20:00 analogous to the relationship between a set of axioms and the models that are determined by those axioms if you do a formal reconstruction of the theory. So that's the point that I need to make here. Well, in any case, it's interesting to keep in mind, it's important to keep in mind this vocabulary that Einstein uses here, and especially that phrase I find to be a really quite remarkable expression, because we will hear echoes of that vocabulary in this philosophical literature that I want to tell you about. So let's turn to that literature. What I think I have found is that there is a very rich and a very interesting tradition of discussion of this very question, whether or not nature is eindogic and whether or not a theory should determine uniquely which it talks about. Most of this literature seems to go back to a paper by Josef Petzl in 1895. A paper whose title of which is quite revealing, Das Gesetz der Einweiterkeit. just a word about Petzl Petzl was a minor positivist quite well known in his own day but not all that well known to us today he was a close follower of Mach and Abenarius never really very well established professionally but a quite prolific writer he wrote a lot on relativity among other things to interpret relativity in a way flattering to his own particular brand of positivism. We'll come back to that in a moment. The idea that he presents in his 1895 paper, Das Gesetzt der Eindeutigkeit, was first anticipated five years earlier in his inaugural dissertation that bears the title Maxima Minima Economia, 1890, in which he criticized what I call the biological-economical doctrines of Mach

22:30 and Avenarius, arguing that instead of the principle of biological economy, we should appeal to what he called the principles of Eindeutigkeit and Stabilität, stability. his this 1890 inaugural dissertation concludes with the words i quoted them here on the top of page three of the handout not maxima minima and economy but rather uniqueness and stability highlight the aspects of reality that must be the focus of our interest well he picked up this theme in this 1895 paper. The specific context in this paper is his attempt to reinterpret the conception of causality that one finds developed in the early editions of Marx's Mechanic, to reinterpret this sort of Humean conception of causality that you find there, and simultaneously to defend this doctrine of causality against some criticisms that had been advanced against it by Wilhelm Wund. The basic proposal that he makes is that we should replace the traditional concept of causality with the more or less mathematical concept of an eindeutige functional connection between events. That's the basic idea. To quote his own words on this point, this is the second quotation on page three, he says To the question raised at the outset, what should take the place of the concepts, cause, and effect, we may answer. The concepts of uniquely, I'm going to be, determining and determine elements or element complexes. And to the second question, about the meaning or essence of processes in nature, they are of such a kind that we can reduce them to the continuous and anisotropic, his word is ein Zinnige, I have trouble figuring out how to translate that, change of a small number of ever-recurring elements, that is, determining elements or means of determination that mutually determine one another uniquely. This is his proposal for a reinterpretation of the Mafia and conception of causality. Now, he has a very interesting argument to defend this doctrine.

25:00 it in what I like to call either a methodological or a metaphysical anthropic principle almost. He wants to argue, in effect, that both nature and our theories, or our way of knowing about the natural world, have to conform to this principle of Eindoydikai because of our very biological nature. You know, if we are the kinds of beings we are, then the world must be such a way in on to be such beings, and number two, for us to know about it in the way we know about There's one quotation on this score. It's the third quotation on page three of this handout. He says, all inorganic and organic systems that undergo development maintain themselves for a certain time as closed holes, and they change in the direction of certain stationary states. In particular, the human central nervous system has the capacity to persist for a relatively long time as a particular organism, and all of the processes that occur within the human being, and specifically those that run parallel to psychical life, can most easily be understood by considering that tendency to stability. We must conceive of this conservation and development in connection with a certain general character of natural processes, without which they would not be possible. We must at the same time bring to bear on nature a certain general presupposition without whose confirmation we ourselves could not live either mentally or bodily. Such a presupposition lies more or less consciously at the basis of all scientific research, and we may be of the firm conviction that it will hold up everywhere since we could not conceive of ourselves with our particular constitution, and that postulate, excuse me, with our particular constitution, excuse me, particular mental nature, if we once imagined it being given up. Both our individual constitution and that postulate, as we may designate the relevant presupposition, belong inseparably together. The latter consists in nothing other than the assumption of the thoroughgoing, complete determination, or, as we want to say, in order side of the matter in the assumption of the uniqueness of all processes, the Eindeutigkeit aller Vorgehen. And he reinforces this point a little bit later on in the same paper, saying

27:30 our highest mental existence, the most highly developed parts of the central nervous system, are not at all conceivable without the uniqueness of all being and events. Now, in this paper, he goes on to identify a large number of other manifestations of Eindeutichkeit. And I won't go through all of these with you, but let me just list a few of them that he mentions. He thinks that the principle of continuity of physical processes is a manifestation of Eindeutichkeit. He thinks that variational principles in physics are a manifestation of this. He thinks that the law of inertia is a manifestation of the principle of Eindeutichkeit. He thinks that the laws of identity and non-contradiction and logic are instances of this principle of ayendoidekeit, and so on and so forth. There's a real litany of manifestations that he presents in this paper. Okay, so much for what he has to say in this 1895 paper. Shortly after the publication of this paper, Petzl found a very sympathetic reception for his ideas. importantly, on the part of Mach, because in every edition of The Mechanic, starting after 1895, that is to say, beginning with the third edition of The Mechanic in 1897, and in all subsequent editions, Mach refers in a number of places to this paper, and also to the earlier paper of Petzold, basically commending what Petzold has had to say about this principle of andoidigkeit. Just to take one of these remarks of Mach's from the third edition of The Mechanic, he says, and this is the quotation at the top of page five on this handout, he says, but in reference to the dynamical cases, the meaning of unique determination, Eindotica Fischimtheit, has been portrayed better and more perspicuously by J. Petzel than I succeeded in doing. In a number of his other works, Mach also referred in a flattering way to Petzold on this issue of Eindeutigkeit. For instance, in the Vermelera, where he was actually at pains to defend his own what I call biological economism against Petzold's criticism, he still says in a very flattering way, and this is the second quote on page five,

30:00 of justice with Petzl, I am convinced that in nature only that and only that much happens as can happen, and that this can happen in only one way. And then lastly, in Erkenntnis and Eartorn, published first in 1905, he says again, this is the next quotation on page five, only a theory which represents the facts of observation always complicated and influenced by manifold accompanying circumstances more simply and than these can actually be established by means of observation, only such a theory measures up to the ideal of unique determination. Certainly, Mach's frequent citations of Petzl won for him a much larger audience than he probably would have found on his own. And it's important, of course, in our thinking of this as part of the background to Einstein's employment of this Eindeutigke principle and the whole argument and the point coincidence argument, it's important to remind ourselves of Einstein's reading of Mach already as a student. We know in particular of his reading of both the mechanic and the Wermel era. Now, all of this would just be an interesting historical footnote if it weren't also for the many things relativity theory, starting in 1912. And it's really a very long list of publications on relativity theory. His first paper in 1912 bore the title Die Relativitätstheorie in der Erkenntnistheoretischer Zusammenhang des Relativistischen Positivismus. In 1914 he wrote another paper called Die Relativitätstheorie der Physik, This series of publications on relativity and philosophy continued well into the 1920s, including, very importantly, the appendix that he wrote for the 8th edition of Mach's Mechanic in 1921, an appendix which bore the title Das Gehäfnis dem Aktion Gedankenhev zur Relativitätstheorie. In virtually every one of the papers that he wrote on relativity theory, self-emphasized the connection between his principle of Eindeutigkeit and the theory of

32:30 relativity. Let me just share with you the most interesting of these remarks, this from the very first paper he published on relativity theory, the 1912 paper, and you'll find this quotation at the bottom of page five on the handout. He says, the task of physics becomes thereby the eindeutige, general representation of events from different standpoints. The fact that he uses the word standpoint there as opposed to frame of reference or some other locution is itself an interesting matter, but I don't have time to go into it today. Representation of events from different standpoints moving relative to one another with constant velocities. And the eindeutige setting into relationship, the German is inbeziehungsetzung, of these representations. Every such representation of whatever totality of events must be eindeutig mappable, abbildbar, onto every other one of these representations of the same events. The theory of relativity is one such mapping theory, abbildungstheorie. What is essential is that eindeutige connection. Physical concepts must be bent to fit for its sake. We have theoretical and technical command only of that which is represented, eindeutig, by concepts. I find his footnote here especially interesting because I see in it an anticipation of one of the central moves in the point coincidence argument, especially as it is reconstructed by John Norton. In the footnote he says, and remember this comes off of the remark where he says that every such representation of whatever totality of events must be mappable onto every other one of these representations of the same event. Putnam comes off the word same. He says, better representations of events in arbitrarily many of those systems of reference that are mappable onto one another are representations of the same event. And then the remark that I really love here is that identity must be defined since it is not given from the outset. So, as I say, this kind of an argument about the linkage between relativity theory and an Eindoldi, the determination of that of which relativity theory is pretending to describe, is repeated in virtually every one of the papers

35:00 that Petzold wrote on relativity theory. Now, the question is, did Einstein know anything about Petzold's work on relativity theory and philosophy? And the answer is, well, we can't be entirely certain, but there's strong evidence suggesting that he did know this work. For one thing, Petzl was one of the founders in 1912 of the Gesellschaft für Positivistische Philosophia, and in the summer of 1912, Einstein allowed his name to be used as one of the founding members of the society. And in fact, the next paper that Petzl wrote on relativity theory. In his 1914 paper, Die Relativität, Thierry und der Physik, was one of the first papers published in the new journal founded in association with the Gesellschaft, this being the Zeitstrick für positivistische Philosophia. But again, Einstein is listed as one of the founding members of this Gesellschaft für positivistische Philosophia. But there is other evidence also linking Einstein and Petzl at this early stage. For one thing, there is some evidence reported by Jochen Thiele, who first published the letters of Einstein to Petzl. I won't have more to say about these letters in just a moment. Thiele reports that there is some evidence that Petzl was attending Einstein's lectures on relativity in Berlin in 1914 and 1915. So there's good reason to suspect a personal relationship by this time. There is next the fact that in the appendix to the eighth edition of Mach's mechanic, Petzl refers to his own 1914 paper, and he remarks in a footnote there that Einstein read this paper and agreed fully with its content. Unfortunately, he doesn't tell us read the 1914 paper, but he does say definitely in his book note that Einstein read the paper. Most interestingly, however, is one of the items in the correspondence between Einstein and Petzl. This is a postcard that is undated. It has been dated by Helen Dukas, Einstein's secretary, to the summer of 1919,

37:30 and I think that the argument for that dating is not very good at all. In fact, it's a rather silly argument that she gives. Tila, who first published this correspondence, dates it to 1918. I think his argument is also weak, and I'll tell you what it is in just a moment. Let me ask you to read the crucial passage from this letter. This is a remark I quote at the top of page 6 on the handout. Einstein says in his postcard, Today I have with great interest read your book in its entirety, and I happily infer from it that I have for a long time been your companion in your way of thinking. I have told a gentleman who is ill, a friend of mine, about your paper on relativity theory. He has shown a great interest in it. You would give him great pleasure if you wanted to send him a reprint of it. And then in a footnote, Einstein says, I'm sending you my new paper on the covariance of the gravitational equations. Now, Thiele dates this letter to 1918 on the basis of that PS, but I think he has misidentified the paper that Einstein is referring to. He thinks that it's this 1918 paper of Einstein's. It's a very brief little reply to a paper of Schrödinger's, a paper entitled I think for many reasons why that's probably not the paper mentioned here, but most importantly, it's simply the title. Because in 1914, the second of the so-called Einstein and Grossmann papers bears the title, let me quote it to you exactly, The title that he gives in the postcard to Petzl is almost a straightforward quote of the title of this 1914 paper. So on the strength of that identification, and since Einstein says here, I'm sending you my new paper on the covariance to gravitational equations, I conjecture that this card really dates from late 1914 or at the latest, probably early 1915. Now, what is the paper of Petzold's and what is the book that he refers to here? Well, there's little doubt about the book that he has in mind. It is virtually, certainly, the second edition of Petzold's,

40:00 Let's see, Petzold's book first appeared in 1906 called Das Weltproblem von positivistischem Standpunkte aus. The second edition of this was published in 1912 with a slightly different title, and it's a quite revealing change in the title in the second edition. It is titled, Das Weltproblem vom Standpunkte des relativistischen Positivismus aus historisch kritisch dargestellt. He's introduced the term relativistischen Positivismus in the title. I'm virtually certain that's the book that is referred to there. As far as the paper is concerned, Petzl had published only two papers by this time on relativity theory. it either has to be the 1912 paper, from which I previously quoted, or the 1914 paper, Die Relativitätstheorie der Physik. Whichever of these papers it was, Einstein would have found there this argument linking relativity theory and Einbrotigkeit. Okay, that's the first chapter in my story, is Petzl on the Einbrotigkeit principle. What's interesting to me is how many other thinkers with rather different philosophical orientations also discuss this principle of Eindeutigkeit in one way or another. And the next person I want to speak about in this connection is the Marburg-Neo-Kantian, Paul Nothorp. And in particular, I want to talk about Nothorp's very influential 1910 book, die logischen Grundlagen der exacten Wissenschaften. One of the many things that is distinctive about Nahor's book is that it is really the first treatment of the philosophical implications of relativity theory by what I would call a respectable philosopher. In particular, in the last chapter, one finds a lengthy discussion of the theory of relativity. And in this last chapter on relativity theory, you find, again, a discussion only now from a radically different philosophical perspective.

42:30 You find a discussion of the principle of Eindeutigke in connection with the relativity theory. Petzl plunges into this theme of Eindeutigkeit and relativity theory first in a discussion of Mach, and in particular in a discussion of Mach's repudiation of absolute space and time. Let me back up and just say one more thing by way of background. Noddorp was of the opinion that relativity theory, far from being a threat to his own neo-Kantian decision, really, in an ironic way, a confirmation of his neo-Kandian position. He argued, and this is, of course, a grotesque non-sequitur, but he argued that relativity theory is a confirmation of the typically Kantian thesis of the ideality of space and time, the argument being that since empirical space and time, as revealed by relativity theory, are not absolute, therefore, if there is to be an absolute space and time, must be space and time conceived as ideal entities. It's a terrible argument, but that's the argument that you find in this last section. Well, in any case, he's concerned, among other things, in this part of the book, to criticize Mach's repudiation of absolute space and time. And I want to just read to you a number of his remarks on the score. And if you don't mind, I'd like to actually read from my manuscript at this point. what is important for our story is Nathorp's frequent and crucial employment in these sections of the metaphysical Eindeutigkeit principles, it appears for example in his criticism of Mach's denial of absolute space and time according to Nathorp, Mach is willing to conceive the existence of at best an Eindeutige functional connection a one to one mapping Petzl's old reinterpretation of Mach's conception of causality willing to conceive the existence of, at best, an eindeutige functional connection, a one-to-one mapping between the times or spaces of different observers, while denying the existence of a single absolute time or space behind these relative times and spaces. But this functional connection may be enough to satisfy Nathorp, who writes, and this is the first quotation under of Nautilus' name on page 6 of the handout,

45:00 he writes, Really, therefore, the question can meaningfully be put only so. Is there a single uniquely determined ordering, ein Gott in bestimmte Stellenordnung, of that which exists, namely those series of changes that we conceive of as being functionally connected with one another, the totality of which we call nature. But this question reduces without remainder to this other one. call nature really exist? Does this single functional connection of events exist? Or more concisely, does existence exist? According to Nothorp, such existence would mean to the empiricist, and this is the next quotation, quote, nothing less than a functional connection of the events nothing less than that a functional connection of the events merely would be or at least could be given in a uniquely determined fashion in a single way for existence means nothing else to him and nothing else in general than complete in no respect uncompleted determination of being And indeed, since it is a question here of spatiotemporal being, completed determination in regard to space and time. Continuing then, Nader says that even if we deny that an absolute time is given in experience, and then here comes the next bit quoted on page 6, even if we deny that an absolute time is given in experience, quote, it does not follow from that that the requirement of a unique determination of the ordering is to be repudiated as meaningless. That would mean giving up the content. And Nauter concludes that he and Kant are really in agreement, since there is this underlying eindeutige, functional abbezion, functional connection, except that Mach neglects the fact that even as a mere idea, absolute time and space are necessary, as that to which all relative temporal and spatial determinations are reduced, as that which secures the possibility of a unique functional connection of events.

47:30 Now, Knothorp's argument with Mach here is deeply rooted in his own reading of Kant, and I want to share with you just a few of his remarks on this score. Knothorp's employment of the metaphysical Eindoy-Hikai principle rooted in his reading of Kant, this Eindeutigkeit, or Einzigkeit, as he also calls it, being the chief characteristic whereby what is real, an object, in our experience, or in intuition, I should really say, is distinguished from mere concepts. And he also adds that, according to Kant, the Eindeutigkeit, or Einzigkeit, of time and space, are therefore necessary grounds for the possibility of experience. Now, quoting Petzl, again, starting at the bottom of page six on the handout, or excuse me, an author, he says, reality means a determination, such that nothing remains undetermined. Indeterminacy is just mere possibility. In other words, possibility is multifaceted. It always permits a choice. Reality is absolutely singular. it is conceived as being determined in a singular fashion, excluding all choice. This singularity plays a great role in Kant's theory of experience. Upon its being required rests in particular his distinction of the intuition from the concept. Intuition means to him, quote, the representation that can only be given through a singular object. Time and space are in this sense essentially singular representations, and therefore intuitions. time, only one space, just as there is only one experience, quote, in Kant again, in which all perceptions are represented as being in thoroughgoing and law-governed connection. Clearly, the singularity of time and space counts necessarily for him as the condition for the singularity of experience. How can the connection of experience be a singular one without the singular time and the singular space being its foundation? Continually, he sees here the foundation for the argument for the existence of an absolute space and time, because empirical time, space and time being relative, don't have the requisite Eingoldigkeit or Einzigkeit. He says, and I quote again, this being the large quotation that begins at the top of page 7, it is certain from the outset that no really achievable foundation for temporal or spatial determination based upon empirical means of determination may claim any absolute security.

50:00 Nevertheless, indeed precisely thereby, one makes the fundamental presupposition that there is an absolute time, an absolute space for events in themselves, des geschéens ans sich, by means of which, if they were determinable, events themselves would be absolutely determined. By comparison with these, every empirically possible determination only the significance of a useful approximation. Upon what basis do we make this presupposition? It lies originally in the demand, in the final fundamental supposition, that experience is directed toward knowledge of that which is or proceeds real. Existence can be conceived only in a single way, because it really means nothing other than determination in a single way. It is thus an analytic proposition that, insofar as existence should be spatio-temporally determined, this determination itself is required to be simply unique, simply eindeutig, although it is never given as such. Only a simply unique eindeutig, and that means absolute temporal and spatial determination, would be the determination of existence itself, that the empirically possible determination can never be simply unique. Eindoidy in no way changes this conditional maxim. Well, we could go on and talk a little bit more specifically about other remarks of Natork's on relativity theory, and I think there's some interesting remarks he makes about how the kind of Eindoidy type prized by the Kantian is preserved in Minkowski's formulation of special relativity, but let's pass over that. Let me ask with respect to Knopfler, the same question I asked with respect to Petzold, and that is, did Einstein know about this work of Knopfler's? Here it's harder to come to some definite determination. I have no definite evidence pointing to Einstein's reading of the Emotion, Buntlog, and Der Exopter, and Misenchopper. It is, of course, important in this connection that this was the first major discussion of relativity theory by a prominent philosopher. For that reason alone, I think it's likely that it would have come to Einstein's attention. But again, I have no definite One other suggested piece of evidence, though, concerns Einstein's relationship with one of Nahtorff's best students, a man by the name of Otto Bück, who was active in Berlin

52:30 at the time Einstein moved to Berlin. We have evidence of Bück's having attended Einstein's lectures on relativity also. But most importantly, Böck was one of the four people who, along with Einstein and this classicist Nikolai, signed the so-called Manifesto to the Europeans that Einstein and Nikolai and Forster and Böck composed in reply to this notorious Manifesto to the Civilized World where a cluster of prominent German intellectuals had tried to justify the German invasion of Belgium at the beginning of World War I. And again, this is evidence of how close the relationship was between Böck and Einstein at this time. We know besides that they were socializing together regularly at this time. And given that Böck was a prominent student of Dantrop's, Böck had written a dissertation in 1904 on Faraday's concept of matter. given that I think it's at least plausible that if Einstein hadn't read Knopf he would have learned about Knopf through discussion with Duke I'm running out of time I wanted to talk at some length about one other thinker who has an important role to play in this story let me just summarize very quickly this last part of my story the last person I wanted to talk about as we know there was a very close relationship with Schlick and Einstein starting in whether or not there was a prior relationship I don't know I have some evidence that again points to the possibility of a prior relationship but it's very weak evidence what I'm most interested in speaking about here though is an interesting paper of Schlick's that he wrote in 1910 devaheit nach demodemn logit. This was an extraordinarily influential paper in its day, and the conception of truth that he developed here is repeated in its essentials in a number of Schlicht's later publications,

55:00 most importantly in the things he wrote on the theory of relativity, his 1915 paper, The Philosophical of the Deutung des Relativités Principes, and also in his 1917, Rauhman's Side of the Gegen-Vetican Physique. It's repeated also in the first sections of his Algemeine, a Kenton's letter, and so on. What is this conception of truth? Very quickly, what he says is the following. He says that judgments are to be understood merely as symbols, standing for facts. What is truth? between these judgments, symbols, and facts. What kind of relationship is it? It's an eindeutige Beziehung between propositions conceived of as symbols and facts. Now, again, we don't have time to go into great detail unpacking his appropriation of the mathematical concept of an eindeutige functional relationship of a one-to-one or possibly many-to-one functional relationship between judgments thought of as symbols and facts. But I think I see here again in Schlick's conception of truth yet another manifestation of this idea of Eindeutigkeit. And most importantly, I read Schlick's conception of truth as an expression of this model-theoretic conception of Eindeutigkeit. but in view of the time perhaps I should stop here at this point and perhaps we can discuss more of this in question if you would like let me just summarize with one final comment what point am I trying to make here I don't mean to be claiming that Einstein that Einstein's development of the whole argument or his solution or his development of the point coincidence argument I don't want to be claiming that these are in any way directly influenced that we've discussed here. I mean, it's possible that some of this stuff Petzl wrote may have played an important role, but I can't be sure of that, and I don't want to claim that. All I want to claim is that when you find Einstein invoking this principle of Eindeutigype in the whole and point coincidence arguments, you have to realize that he is speaking in the context of an old and rich philosophical tradition on this very point. That's the claim that I want to make. Thank you very much for this splendid portrayal of the philosophical sea in which Einstein was swimming.

57:30 The rules of politeness require that the chairman ask his question last, but I'm not polite, and I'm going to ask my question first. Because it is a rather fundamental question. and it seems to me that there was an awful lot of discussion of this particular problem in mathematical logic at this period with, you mentioned Hilbert's, but this in fact of course comes after a long discussion by people, everyone whose name seems to begin with P, like Betzoff, there's Pash, and Peano, and Padua, and so on, but it's a particular Padua. I wondered whether this is a kind of second order reference, does Petzold, for instance, referred to this matter-of-the-logic discussion. That's the interesting thing. Not at all. There is no mention of that work in Petzold's papers, in Marx's papers, in Nauberg's discussion of this, or in Schlicht's discussion of this. There seems to have been, from what I can tell, a wholly autonomous philosophical tradition on this store, running through Petzold and Nauberg's papers. And they all cite one another, of course, on this store, with no citations of the literature and the foundations And Frege does, as of interest, as you know, bring into a polemic about the whole question of postulation or this definition at about the same time as Einstein is writing. Does Einstein ever refer to Frege on this point? No, I've never seen any reference to Frege on this point either. In Einstein, or again, in any of his other literature. Actually, one of the very interesting puzzles here is the title of Schlicht's paper, Nacht der Moderne Logie. I cannot satisfy myself as to what he has in mind here. He seemed not to have read Russell or Whitehead. Well, he couldn't have read it in 1910. One of my immediate thoughts was maybe he's familiar with this piano of Padua Schroeder tradition. But again, I find no discussion of that in any of Flick's early writings, no evidence of his having looked at that material. I frankly don't know what he means. And he doesn't ever say himself what he means by the term He must have been at the 1901 Congress. I don't know that either. He took his degree in 1906 under Planck. He took a degree in physics.

1:00:00 And as far as I know, and here I defer to Anna Cox, who knows the history of Schlicht a lot better than I do, his interest in philosophy really developed only after his degree in physics. So I'm not sure that it would have been likely that he would have attended any philosophical conferences before the end of the first decade. I also admire very much your lecture and I think you have done a very solid job but I would like to so if I'm going to express some criticism it's not so much a criticism of this particular lecture but it is a remark on a general problem which you face in treating this kind of problem and this problem as sort of a problem of eindeutigkeit in the history of science because the problem in evaluating the influence or the possible influence and you made a very cautious remark at the end of your lecture is really the question what do you explain in Einstein's development by this kind of by pointing to this kind of philosophical background and you have made a strategic move to be a rhetorical move in precisely the second line of your scheme by calling what Einstein did with respect to Eindeutigkeit a model theoretic Eindeutigkeit, in principle. And what I mean by rhetorical move is that by this very designation you lifted Einstein's occasional remark to a philosophical statuess argue that what Einstein has in mind when he speaks about Eindeutigat is first of all something that is immediately related to the scientific work context in which he was working I mean Eindeutigat first of all for a working physicist has a meaning that it's determined by the mathematics he is operating and this is precisely the general problem to which I was trying to draw attention problem of your lecture, that is, which relationship, in an epistemological problem of the history of science, which relationship is there between external influences which you have nailed

1:02:30 down in a very precise way, as good as you quote, by pointing the attention to letters, to books, by paying attention to the precise dating, and which respect is there between this line of external influences and the internal development determined by the research problems Einstein was facing, determined by the scientific tradition in which he was working. Well, let's see, what to say in response to that. I am myself really very unclear about the connection between, I'm not sure I want to make the distinction between external and internal, I don't think that's the happiest way to characterize the difference. Let's just talk about the difference between the broader philosophical context and the narrower scientific line of investigation that's going on here. I am myself unclear about that exact relationship with respect to this principle of Eindoidigkeit. I frankly don't know where the real origin of this vocabulary is in Einstein's employment of the vocabulary. As a point of fact, and I didn't talk about this in the paper today, you even see this vocabulary a little bit in earlier work on special relativity and talking about the fact that that the metric interval is determined aindoide, whereas the measured length or the measured duration of the process is not determined aindoide. It's dependent upon a frame of reference. Even in Einstein's own work, there is a history of this vocabulary. But where it first enters his work, whether he gets it from the mathematical literature, whether he gets it from the philosophical literature, I don't think we're ever going to get a definitive answer to that question. he's responding to influences of both times. I mean, this vocabulary occurs, of course, in the mathematics literature. My guess is that he probably picks it up from there, but most importantly, he's reinforced in this employment of the vocabulary, especially as it regards the methodological issues that are posed by, and the philosophical issues that are connected with it. He's reinforced in this connection by his acquaintance with that philosophical tradition, starting, I imagine, when he read Mach's Mechanic, the third edition of Mach's, or fourth edition of Mach's Mechanic. So probably the philosophical tradition reinforces a way of thinking that he may first have encountered just as a commonplace in the mathematics. May I remind us that we mustn't nibble too much

1:05:00 into the next speaker's time. We have about five or six hands up. I think, join me on the next. Can we keep these questions, these exchanges fairly? I'll try and be brief, I actually had three questions I'll still ask them very quickly I wanted to really say much the same sort of thing as the organ and try and press you a little more on exactly what the connection is between this philosophical tradition and Einstein's work and offer you perhaps some kind of continuum you could locate a point in at one end you've got Einstein simply taking a vocabulary from what's there at the other end you've got Einstein saying what he says by virtue of the fact that it's there trouble to have this lack of uniqueness except he now knows from reading the philosophical literature that this is a problem. Now I don't think you want that final extreme. Exactly where do you want to be in that continuum? That was the first question. The other two are quite a difficult one. The dating of the letter to Petzold on a basis of length of variance paper. That paper was written with Grossman before Einstein And I think the move was in April. So why don't you date the letter a lot earlier? I mean, I know you have to wait a bit of time before he has offence. But remember, by November, he's written a very major review article in the Linn, which completely supersedes what he's working on. Well, that's right. Before not a grunt log, it's published, actually, by that time, isn't it? I'm not sure. He might have offence to it at that point. But I don't think he's ugly. to flush around the earlier paper, which has been completely superseded. And then the third question was the following. I think what's truly significant about the terminology that I've started using is the connection to the causality principle and uniqueness. And here, I think you have read Mark more recently than I, but I seem to remember that kind of juxtaposition coming in Mark's book on the conservation of energy. Yeah, in fact, that's a very good point. When Mark discusses Petzl in the Mechanic, he himself sort of petulantly insists on priority on this very point, and he cites his own Die Halldung der Arbeit already in 1872 as the origin for the idea. But Petzl did not cite it, Die Halldung der Arbeit. So what I'm wondering now is, if we are going to just talk about where Einstein's getting his terminology from,

1:07:30 might it not possibly just be marked on the strength of those particular passages? Well, it may well be, but the vocabulary of the adjective Eindoidy and the now Eindoidy, that doesn't occur in the mechanic, at least, until the third edition, post-Petzel's painting. In the first and second edition, that vocabulary is simply not there. It becomes commonly employed in the third edition. That's why I'm conjecture when I first learned it there. Now, just very quickly in response to your other two questions, on your spectrum, I want Einstein to be very close to the end of the spectrum you were shying away from, but I'm not sure I can make that claim. I want him, because I'd like to think of him as a methodologically very sophisticated thinker, so I want him to be very close to that end of the spectrum. On the dating of the latter, I'm just being cautious on that. I don't know exactly, I haven't been able to check yet to see exactly what publication date of the Einstein Grossman paper was, so I'm just trying to be cautious. And, of course, I'd like to push the dating of that as far back to the beginning of 1914 as I could. I think you'd be able to... May I make a suggestion with you for Coupé? But can I make a suggestion with a couple of, perhaps even three, short observations rather than questions? If anyone has a... John Stachel, I think he has a... You said you were puzzled by us, I think it's the word causality. an explanation, which also does allocate both of the type. Remember, Einstein was always looking for a unifying way of seeing the world. And we have the one that quickly had the field is the fundamental thing, part of the matter, epi-phenomenal point of view we could point you that part of the matter is the fundamental thing and fields is epi-phenomenal point of view. And in his early years, Einstein leans towards the latter point of view is that the field is an anti-phenomenon. Positive matter is fundamental. Therefore, when he says that the demand that the field be mathematically to be determined by the matter fails, I think that's really what's the crux of the matter. No pun intended. If you give the matter distribution and the field is not completely determined by that in the sense of, in a causal sense, that the matter is primary and the field should be the cause, I mean, the matter, the possible matter should be caused the field to be effect. If that relationship fails, distribution does not uniquely determine the field in the sense of this

1:10:00 causality sense as well, so this sideways type, causality and determination going together, then there's something fundamentally wrong with the field. I think that is what is in the back of it. Well, I would disagree with you on one point there, and that is the reading of the point, for instance, argument, I think, is important. I'm talking about what I was thinking in 1913, 1914, not what motivated you to hold on. H-O-L-E. may we have I think we are down to our last is it a question or a remark I have a question I think we simply haven't got the time if anyone has a suggestion Heinrich Herz was very influential in his treatment of physical theory and people like Schmitt and Wittgenstein accepted the idea that theory is built and maybe in Herz I've looked at Hertz with just this question in mind, and what you find in Hertz is actually, it's very interesting, what you find in Hertz is the denial of this principle. And I think that Schlick probably, and if I had time to talk about Schlick, you'll see that Schlick denies this principle, actually. And I think that Schlick picked that up from Hertz. I found nothing in Hertz with respect to what I call the metaphysical model theoretic I'm doing about principles. I had thought I would find it there, but I didn't, surprisingly. I very much regret having to cut things short, but we must do so, and go on to our next speaker, Arthur Miller, who is, as everyone here knows, the author of a monumental work on Einstein's special theory of relativity. He's going to extend his attention to the 1907 revolution, and the first step from the special theory of the general initiative. Thank you. Thank you, sir. Yes, thank you. What I'd like to do today... Thank you.

1:12:30 Thank you.