Einstein, Kant & the Relativised A Priori

0:00 Thank you. I think I should. How about that? Yeah. Good example. Move it a bit closer. Okay. So my talk's going to be quite a lot from the previous. And by the absence of any of the technical people. But I would love an apology because it's basically going to be metaphysics, I know I shouldn't I think the good if you tell me that I've got it all completely wrong across the list. Well, well, I suppose I'll give you a question. Another caveat, I only have a very basic knowledge of basic economics, but I hope I'll give you a question. The reason I mention this meta-physics is that while meta-phositions often take notice of the philosophy of physics, if people are going to invoke quantum mechanics in the meta-physics effect, then we need to be kind of sensitive to the permitting meta-phositions' brain This is the last time we will all be together in the same room in this conference, because there is no closing session, there is a set of parallel sessions starting at 3, ending at five and there will be no final closing ceremony of this conference because this is

2:30 the first, we hope, of very many conferences like this. So I want to make a few announcements, take the opportunity that we're all here together to make a few final announcements. First of all, the reminder about lunch. Lunch will be served downstairs as usual, and those of you with a blue badge are all welcome there. Those of you with a black badge have to find your own food in the cafeteria, which is happily open today, usually. There will be a proceeding published of a selection of papers in this conference. The format, however, is still undecided, and decisions in this regard will probably not be made before the spring, end of April might be a likely date. In the meantime, we would like to invite all of you who are interested in publishing in the proceedings to submit your papers to the Pittsburgh Archive. We have a section in the Pittsburgh Archive that the Pittsburgh people kindly made available to us, and you can submit your papers electronically. I have a large number of thank yous to give, thanks to many people who have made this conference possible. Everybody, in particular everybody in the local organizing committee, it's been a long and difficult year for all of us. particularly difficult has been the lack of a model for this conference we've had to improvise constantly and I've been struck by the very good sense and the ability for creative last minute improvisation that the local people in the local committee have, people at Complutense and the Spanish people generally seem to be good at this so thank you all And more especially, I want to thank the people in my own research group who have devoted

5:00 the last couple of months almost full time to organizing the conference, and I'd like to name them Pedro Sánchez, Iñaki San Pedro, Isabel Guerra, and Albert Solé. Thank you very much. Also, I would like to announce for those of you who have enjoyed Madrid so much that you've decided to delay your flights back to your own countries, there is a workshop in honor of Michael that will take place here at Complutense on Monday morning, and you're all welcome to attend. If you want to change your flights and delay your departure, that would certainly may be a very nice thing to do, and we will welcome you here again on Monday. It's a pleasure and an honour, very special honour, to introduce Michael Friedman. Michael is a most appropriate closing plenary speaker for the first foundational conference Philosophy of Science Association. EPSA is an association that is born out of the desire of collegiality and inclusion and is open to people of all nationalities and backgrounds and it of course wants to maintain a particularly warm and friendly relationship with its sister association, the North American PSA, the Philosophy of Science Association. The EPSA, by the way, is not, as many people have remarked to me in the last few days, the electronic version of the PSA. But we certainly look towards and would like to emulate many of the things that we find much worthy about our sister associations. and to the extent that there has been a model for this conference there hasn't really been a model that I already said has been a constant problem throughout the year but to the extent that there has been a model for this conference it has been its CASSINS, the PSA conferences in North America

7:30 but also in a way the founding of the European Philosophy of Science Association return, a closing of the circle, we could say, because the origins of the American PSA, of course, are firmly rooted in European culture and European traditions, and most particularly in the intellectual diaspora of the logical empiricists to North America in the 1930s. The philosophy of science afflourish in North America and has been spread throughout the world in the last half of a century is undeniably European in origin and character, so it seems only right that it should come back to us. Nobody impersonates this closing of the circle, the returning to our origins and our own traditions, better than Michael Friedman. He's an American who has worked and was trained by some of the most prominent American philosophers, and he has worked at some of its leading academic institutions such as Princeton, Indiana and Stanford where he is now the Remus Professor of Humanities. However, his thought and his work has always been engaged with European ideas and philosophy and particularly with the work and the influence of the logical empiricists. In his first book, Foundations of Space and Theories, published by Princeton in 1983, a classic, if not maybe the classic, book of reference in the philosophy of space-time, Michael persuasively argued against, or perhaps around, the conventionalist theaters of Reichenbach and Poincaré. This is a detailed, supremely technically gifted analysis of the notions of space and time and their history from the perspective of modern four-dimensional mathematical formulations of general relativity theory. Kant and the Exact Sciences, published in 1992 by Harvard, inaugurates Friedman's interest in Kant's work and its influence upon the logical empiricists that continues to the present day. Another book of his, Reconsidering Logical Positivism,

10:00 published by Cambridge in 1999, collects Michael's papers for over a decade on the history and the impact of the ideas of logical empiricism upon present-day philosophy. Michael's new novel Reconstruction of the Ideas of the Logical Empiricists, and particularly his re-evaluation and re-institution of the future of Karnav has had a deep influence in the history of our discipline and pretty much has set up a new and strong revisionary agenda that very many of us work today in order to advance. Now this concerns to revise and re-evaluate the impact and origins of a European way of thinking, logical empiricism, continue in Michael's present work, and in particular his most ambitious, yet the thinnest, of his books to date, The Dynamics of Reason, is a defense of the pertinence of the logical empiricist's key notion of the a priori constitutive for present philosophy of science and physics. Michael's ideas are not just discussed and talked about, they are actually setting the present day philosophical agenda, and the agenda is a re-evaluation and re-appraisal of a characteristically European way of thinking. It's a pleasure to introduce him and his talk at this founding conference. The title of his talk is Einstein can be a priori. Thank you very much, Mauricio. Let me also take the opportunity, while we're thanking everyone who organized the conference, since I guess Mauricio couldn't thank himself. He thanks all those we could thank. Let us thank Mauricio for that. Thank you for that very, very nice introduction. I'm very excited that there is this new European Philosophy of Science Association. I'm very excited and proud to be here representing North America. And if you all consider me as an honorary European philosopher of science, I'll be even happy.

12:30 So, Kant's original version of transcendental philosophy took both Euclidean geometry and the Newtonian laws of motion to be synthetic a priori constitutive principles, which, from Kant's point of view, function as necessary presuppositions for applying our fundamental concepts of space, time, matter, and motion to our sensible experience of the natural world. Although Kant had very good reasons to view the principles in question as having such a constitutively a priori role, we now know in the wake of Einstein's work that they are not in fact a priori in the stronger sense of being fixed necessary conditions for all human experience in general, eternally valid once and for all. And it is for precisely this reason that Kant's original version of transcendental philosophy must now be either rejected entirely, or at least radically reconceived. Most philosophy of science since Einstein has taken the former route, rejecting Kant completely. The dominant view in logical and heuricism, for example, was that the Kantian synthetic a priori had to be rejected once and for all, in the light of the general theory of relativity. Yet Hans Reichenbach, interestingly enough, took the latter revision rather than rejection in his first published book. In Relativität Thierry, Umer Chemies a Priore, published in 1920, Reichenbach proposed instead that Kantian constitutively a priori principles of geometry and mechanics should be relativized to a given time theoretical context. Such principles still function, according to Reichenbach, throughout the development from Newton to Einstein as necessary presuppositions for applying our changing conceptions of space, time, and motion to our sensible experience. But they are no longer eternally valid once and for all, precisely because of the changes. For example, while Euclidean geometry and Newtonian laws of motion are indeed necessary conditions for giving empirical meaning to the Newtonian theory of universal gravitation, the situation in

15:00 Einstein's general theory of relativity is quite different. The crucial mediating role between abstract mathematical theory and concrete sensible experience is now played in general relativity by the light principle and the principle of equivalence, which together ensure that Einstein's revolutionary new description of gravitation by a four-dimensional geometry of variable curvature in fact says something about concrete empirical phenomena, which is physics, not just mathematics, mainly to represent the picture of life and gravitation for its interoperative bodies. In my recent book, Dynamics of Reason, I have taken up and further developed Reichenbach's idea. You see here in part two, I begin with this notion of relativized a priori, which is the key notion in the book. But my interpretation of this idea of relativized constitutively a priori principles of geometry and mechanics essentially depends on a historical argument, a historical narrative, really, describing the developmental process by which the transition from Newton to Einstein actually took place, as mediated, in my view, by the parallel developments in scientific philosophy involving especially Hermann von Hemholtz, Ernst Mach, and Henri Poincaré. However, since this argument or narrative depends on the concrete details of the actual historical process in question, it would therefore appear to be an entirely contingent story. How then can it possibly be comprehended within a properly transcendental philosophy in the Kantian sense? Indeed, once we have given up on Kant's original ambition to delineate in advance the a priori structure of all possible scientific theories, it might easily seem that a properly transcendental argument is impossible. We have no way of anticipating a priori, the specific constitutive principles of future theories, and so all we can do, it appears, is wait for the historical process to show us what emerges a posteriori as a matter of fact. So how more generally can we develop a philosophical understanding of the evolution of modern science, or at least this part of it,

17:30 that is at once generally historical and properly transcendental? Let us begin by asking how Kant's original transcendental method is supposed to explain the sense in which certain fundamental principles of geometry and mechanics are, in fact, both a priori and necessary. This method, of course, appeals to Kant's conception of the two rational faculties of sensibility, receptivity, and understanding, reactive, conceptual faculty. The answer to the question, how is pure mathematics possible, appeals to the necessary structure of our pure sensibility, as articulated in the transcendental aesthetic of the critique of pure reason. Here I show the second, the 1787 edition, which as we'll go on, we'll see why I show that one is particularly important. Actually, these two questions, how is pure mathematics possible, how is pure natural science possible, only occur in the second edition, not in the first, following the intervening prolegomena of 1783. This is 1787. The answer to the question, how is pure natural science possible, appeals to the necessary structure of our pure understanding as articulated in the transcendental analytic, as opposed to aesthetic. Yet there is an obvious objection to this procedure, which has been made many times. How can such proposed transcendental explanations in terms of these faculties inherit the assumed a priori necessity of the sciences, and physics, whose possibility they purport to explain, unless we can also somehow establish that they are the unique such explanations of this possibility. From our present point of view, for example, it does not appear that Kant's explanation of the possibility of pure mathematics is uniquely singled out in any way. On the contrary, our greatly expanded conception of purely logical or analytical truth, starting of Frege, suggest that an appeal to the faculty of pure sensibility, receptivity, may, after all, be explanatorily superfluous. The intellect can do it all by itself. Indeed, from the point of view of the anti-psychological approach to such questions that dominated much of 20th century analytic philosophy, it appears that all considerations of our

20:00 subjective cognitive faculties is similarly explanatorily superfluous, say, from a Freudian point of view. In Kant's own intellectual context, however, explanations of scientific knowledge in terms of our cognitive faculties were the norm for empiricists, rationalists, and, of course, Aristotelians. Everyone had read, in addition, that the relevant faculties to consider were the senses and the intellect. What was then controversial was the precise nature and relative importance of these two faculties. Eberus' views, which deny or downplay the existence of the pure intellect or its importance for scientific knowledge, were, for Kant, simply out of the question, since they make a priori rational knowledge, in mathematics, say, incomprehensible. Moreover, the conception of the pure intellect that was most salient for Kant was that of Leibniz, of course, where the structure of this faculty, the intellect, was delineated, in effect, by the logical forms of traditional Aristotelian Symmogista. But this Lyrician conception of the pure intellect, Kant rightly saw, is entirely inadequate for representing, say, the assumed infinite extendability and divisibility of geometrical space, which had recently proven itself to be both indispensable and extremely fruitful in Newtonian mathematical physics. Nevertheless, Newton's own conception of space as the divine sensorium was also unacceptable on theological and metaphysical grounds for Kant and most everyone else, and so the only live alternative left to Kant was the one he actually came up with. Space is a pure form of our sensibility, as opposed to divine sensibility, wherein both infinitely iterable geometrical constructions, and the perception of spatial objects in nature, like the heavenly bodies, then becomes first possible. It is, of course, entirely contingent that Kant operated against the background of precisely these intellectual resources, a kind of normative faculty psychology, Leibniz, Newton, and so on. Given these resources, just as it is entirely contingent, that Kant was born in 1724 and died in 1804,

22:30 given these resources, that is, given his situation, and given the problems with which he was then faced, the solution he came up with is not contingent. On the contrary, the intellectual situation in which he found himself had a definite inner logic, as old-fashioned intellectual historians used to say, mathematical, logical, metaphysical, and even theological, which allowed Kant to triangulate, as it were, on a practically unique and, in this sense, necessary solution in its context. Beginning with this understanding of Kant's transcendental method and its associated rational necessity, we can then see a way forward for extending this method continuum developments in both the mathematical exact sciences and in transcendental or more generally scientific philosophy. We can trace out how the inner logic of the relevant intellectual situation evolves and changes after Kant in response to both new developments in the mathematical exact sciences themselves and the manifold and intricate ways in which post-continent scientific philosophers attempted to reconfigure Kant's original version of transcendental philosophy in light of those very developments. That each of these successive new intellectual situations has its own inner logic implies that the enterprise does not collapse into total contingency, despite the fact that the history is contingent. That, in addition they successively evolved out of and even liked of Kant's original system suggests that it may still count as transcendental philosophy of a kind and that's what I hope to illustrate. Hermann von Hemel's neocognian scientific epistemology, for example, had deep roots in Kant's original conception. In particular, Hemel developed a distinctive conception of space as what he, Hemmels, called a subjective and necessary form of our external intuition in the sense of kind. And while this conception was certainly developed within Hemmels' empirical program in sensory psychology and psychophysics, it nevertheless retained

25:00 important transcendental elements, and he uses that word too. More specifically, space's insofar as the principle of premobility, which allows arbitrary continuous motions of rigid bodies, is a necessary condition in this space for the possibility of spatial measurement using measured rise. And indeed, it's a necessary condition for the very existence of space and spatial objects, as opposed to mirror sensations. Moreover, the condition of premobility generalization of Kant's original Euclidean conception of geometrical construction. In the sense that Euclidean constructions with straight edge and compass carried out within Kant's form of spatial intuition, which is of course Euclidean, the only one that exists for him, these constructions are generated by the group of specifically Euclidean rigid motion, that is translation and rotation. The essential point, however, is that free mobility also works, and there's a corresponding group of rigid motions, for all, for the classical non-lipidium geometries of constant curvature, that is, hyperbolic and elliptic geometry, and so it is no longer, that is, free mobility, a transcendental and necessary condition of our spatial intuition for handholds, that perceptions of bodily motion obeys the specific laws of Euclidean geometry. So it does necessarily involve free mobility, but since free mobility holds in all three cases of constant curvature, it's not necessary that space with Euclidean. Nevertheless, Hamels' generalization of the Kantian conception of spatial intuition to all constant curvature spaces is in an important sense the minimal, and in this sense such generalization, consistent with the 19th century discovery of the non-equivalent geometries of constant curvature. The great French mathematician Henri Poincaré then transformed Helmholtz's conception in turn. In particular, Poincaré's use of the principle of free

27:30 mobility, where he follows Helmholtz, which plays a central role in the philosophy of geometry, that is, is explicitly framed by a hierarchical conception of the mathematical sciences, beginning with arithmetic and proceeding through analysis, geometry, mechanics, and empirical physics, where, in particular, each lower level in the hierarchy, after arithmetic, presupposes that all earlier levels are already in place. This, of course, is in Mastillon's set where he pretends. So, arithmetic is at the top, the next level analysis presupposes arithmetic, builds on it, geometry presupposes what came before, mechanics, which is still partly in priori, that is conventional, presupposes all the others, and finally, popular empirical physics presupposes this stratified sequence of a priori-conventional structures above it. This hierarchical conception of the mathematical sciences underlies Poincaré's fundamental disagreement with Hemmels. For Hemmels, as we have seen, the principle of free mobility expresses the necessary structure of our form of external intuition. And following Kant, Hemmels views all empirical investigation as necessarily taking place within this already given form, have geometrical measurements, and therefore geometry. Hamilton's conception is continent, that is, insofar as space has a necessary form, his words, expressed in the condition of free mobility, but it is also empiricist, insofar as which of the three possible geometries of constant curvature obtained is then determined by experience, by actual measurements. For Poincaré, by contrast, although the principle of free mobility is still fundamental and in that sense necessary for geometry, our actual perceptual experience of bodily displacements, Poincaré's word, arising in accordance with free mobility is far too imprecise, Poincaré argues, to yield the empirical determination of the specific mathematical geometry. Our experience, for example, is not exactly a group, let alone a continuous lead group. We have to idealize it to come up with those notions.

30:00 In particular, experience, so our own, sorry, let me just say that again, our experience, our actual experience is too imprecise to yield the empirical determination of a specific mathematical geometry. So our only option, Poincaré thinks, is to stipulate Euclidean geometry by convention as the simplest and most convenient idealization of our actual perceptual experience that is the simplest lead group that actually idealizes what our experience is like. In particular, experiments with putatively rigid bodies for Poincaré involve essentially physical processes at the level of mechanics and experimental physics, so below geometry in the hierarchy. And these sciences, in turn, therefore presuppose that the science of geometry is already firmly in place. So how can you measure forces unless you have space, unless you can already measure space, for example. In the context of Poincare's hierarchy, therefore, the principle of free mobility expresses to choose by a convention or definition in disguise, as Poincare says, which of the three classical geometries of constant curvature is the most suitable idealization of physical space, and of course, for him, it must be convenient. One of the most important applications of Poincare's hierarchical conception involves his characteristic perspective on the problem of absolute space and the the relativity of motion, explained in his discussion of the next lower level after geometry, mainly mechanics, and mechanics for him means classical Newtonian mechanics. Poirier's key idea is that what he calls the physical law of relativity, which is what we would call Galilean and Barrios, rests squarely on the relativity and passivity of space, a purely spatial principle. And therefore it reflects, that is, physical relativity, the circumstance essential to free mobility, that the space constructed from our experience of bodily displacements is both homogeneous and isotropic. but that's what constant curvature and the distance of this lead group says. So it reflects the fact that the space

32:30 that we actually construct from bodily displacements is homogeneous, same at every point, and isotropic, all directions, equivalent. Thus, Parqueray's conception of the relativity of motion depends on the philosophy of geometry. And this is especially significant from our present point of view, because Poincaré's ideas on the relativity of motion were also inextricably entangled with the deep problems then afflicting the electrodynamics of moving bodies that were eventually solved, according to our current understanding, by Einstein's special theory of relativity. Poincaré, of course, being one of the pioneers and some argue co-inventor of this theory. I shall return to Einstein below, but I first want to emphasize that the connection Carré makes, between his philosophy of geometry and the relativity of motion, represents a continuation of a problematic that was originally present in Kant. Hamels, as we have seen, transformed Kant's philosophy of space and geometry. He was the first to do that. And Ernst Mach, among others, I'll talk about that in a moment, participated in a parallel transformation of Kant's approach to the relativity of motion, which finally in the modern concept of an inertial frame of reference in the late 19th century. Neither Hemmholtz nor Mott, however, established any kind of conceptual connection between the foundations of geometry on the one side and the relativity of motion on the other, which at the time appeared to be entirely independent of one another. On Kant's original approach to transcendental philosophy by contrast, these two problems, geometry and motion, very closely connected. While Kant's answer to the question, how is pure mathematics possible, essentially involved his distinctive perspective on completed and constructive operations, his answer to the question, how is pure natural science possible, involved an analogous constructive procedure by which Newton, from Kant's point of view, arrived at successive approximations to absolute space by means of a definite sequence of rule-governed operations, starting with our parropial perspective here on Earth, proceeding to the center of mass of the solar system, then to the center of mass of the Milky Way galaxy,

35:00 then to the center of mass of a system of such galaxies, and so on ad infinitum to an infinite number of nested systems of galaxies. And this solution to the problem of absolute space Kant's Metaphysical Foundations of Natural Science, 1786, published between, therefore, the first and second editions of the critique, and I think had an important influence on the third edition. Indeed, the way in which Kant thereby established a connection between the problems, so for Kant, there is no absolute space before we experience matter and motion. It's an ideal, a limiting endpoint that we construct through this sequence of centers of gravity. So the way in which Kant did this, made this connection, connecting space as a certain kind of constructive procedure and absolute space, that is geometry and then absolute space as another but related type of constructive procedure, was intimately connected in turn with both the overarching conception of the relationship between sensibility and understanding that frames Kant's transcendental method, and Kant's characteristic perspective more generally on the relationship between constitutive and regulative transcendental principles. Absolute space, in particular, is a forever unreachable regulative idea of reason that you will always approximate but never get to, while geometry is a constitutive principle because the nuclear geometry of space is constructed as it were once and for all. Okay, now it was Ernst Mach, as I have suggested, who first forged a connection between Kant's original solution to the problem of absolute space, returning absolute space, and the late 19th century solution based on the concept of an inertial frame of reference. Both involve that we're looking for the center of mass of some cosmic frame. Kant, from a modern point of view, in looking for such a center of mass frame, is constructing a sequence of better and better approximations to what we now call an inertial frame of reference, although he does not have yellow-laying relativity. and it is clear moreover that Poincaré was familiar with this late 19th century solution

37:30 and which is very clear of that. It is also clear however that Poincaré's attempt to base his discussion of the relativity of motion on his philosophy of geometry runs into serious difficulties at precisely this point for Poincaré is here forced to distinguish his physical relativity which is about motion from what he calls the principle of relative motion sorry that was confusing the physical law of relativity which is based on the geometry of space from what he calls the principle of relative motion the latter principle relative motion applies only to inertial frames of reference it's Galilean relativity moving uniformly and rectilinear, three, with respect to one another. While the former applies, that is, relativity of space, to non-inertial frames of reference in a state of uniform rotation. It follows from the relativity and passivity of space, for Poincare, that uniform rotation around a point, that's the isothermia, should be just as irrelevant to the motions of the physical system which is the homogeneous part. So the spatial group, the purely spatial group, doesn't distinguish between locations and translations, and if relativity of motion is based on that, it looks like there should be relativity of locations in exactly the same sense in which there's relativity of initial motion, which of course there isn't. So, therefore, the full law of relativity, as Poincaré says, which puts rotations and translations on a par, ought to impose itself, Poincaré says, upon us with the same force as does the more restrictive principle of relative motion, that is Galilean relativity. So, a priori the two are on a par, because they're both based on geometry. He must also admit, however, that the more extended law of relativity, which puts rotation and inertial motion on the arm, does not seem to be in accordance with our experiments. We can say this rotating book on experiments and so on. He has something to say about that, but he has to go through some contortions to deal with this question.

40:00 So it is for this reason I suggest, among others, that Einstein's appeal to what Einstein calls the principle of relativity 1905 paper, I'm special to remember the paper, is independent of Poincaré's Law of Relativity. And it is also independent accordingly of Poincaré's conventionalist philosophy of geometry. We know, by the way, that Einstein had been reading La Sionse de la Hypothesa intensively in the years 1902-1904 in his Olympia Academy. So he's quite familiar with Poincaré's treatment of these issues. But Einstein's of relativity is limited from the beginning to inertial frames of reference. That's where he starts. Moving relative to one another with constant velocity and no rotation. There's no temptation at all about Einstein to put rotation on a plot. And Einstein's concern is to apply this limited principle of relativity, that is Galilean relativity, that it used to be dealing with relativity, to both electromagnetic and mechanical phenomena at the same time. Thus, in particular, whereas Poincaré's law of relativity involves very strong a priori motivations deriving from Poincaré's philosophy of geometry, based on relativity and sensitivity of space, and therefore rotation should be on a par with translations, Einstein's principle of relativity has no such a pluralization, at least none coming from Moncleray's celestial geometry. Instead rests on the emerging experimental evidence suggesting that electro-magnetic and optical phenomena do not in fact distinguish one inertial plane from another. So here's the well-known second paragraph of Einstein's 1905 paper. In this book, he talks about these examples of trying to determine the motion, the absolute motion of the ether, using the electrodynamic and optical phenomenon. He says, interestingly here, he only mentions that we establish it after the first order of small quantities. And then he goes on to say, he conjectures, Einstein says, that this experimental law, which he limits to first order, interestingly enough, at this time, although it was known at that time that second order, too, would hold.

42:30 But he says, I conjecture that it holds for all orders. And then he says, he proposes to elevate the principle, or hate them, this conjecture, and that would be the principle of relativity, to the status of apostate or presupposition for our system. And he also introduces the other postulate than this life principle. Hence, Einstein's understanding of the principle of relativity here is quite independent of Poincare's carefully, Poincare's conventional philosophy of geometry, which would put, again, translations and notations on the top, and therefore it's also explicitly independent of Poincare's carefully constructed hierarchy according to which you first have to have space symmetry group, as it were, before you could say anything about what we would call the symmetry group of space-time. So, Einstein has to reject that to move to special relativity. And it's for precisely this reason, I think, that Poincare himself, although he's very close to Einstein's version of it, and very close to what we call Minkowski's space-time, he could never accept that. And in his 1912 paper on space and geometry, I think you can see quite clearly why he wanted to mix up the four-dimensional picture. Nevertheless, it appears overwhelmingly that although Einstein did not embrace Poincaré's conventional philosophy of geometry, Einstein's use of the principle of relativity was still explicitly inspired by Poincaré's more general methodology described in Monsignor and Sede de Contesa, according to which the fundamental principles of mechanics in particular are conventions or definitions in disguise, so here's Poincaré in 1922, they are drawn from experimental laws, so to speak, and they have been elevated, into principles which our mind attributes an absolute value so i'm saying einstein's corresponds to this uh give you a little bit more evidence of that in the second in Einstein's case the experimental law in question that is going to be elevated comprises the recent results of electrodynamics and optics the first order

45:00 of Lorentz invariance, as we would put it. Einstein now proposes to elevate that, to make it rigorously true for all our orders, but also to make it what he calls a postulate, a presupposition. And he now proposes to elevate both the principle of relativity and the light principle, which together imply that the velocity is hard to be invariant in all initial frames to the status of pre-sufficiency or constant. Right here, that's the Einstein message. And to make my argument, or my idea, that this notion of elevation really is Poincare's, if you look at what Einstein says in 1921, this is in Lippon-Vegas, in Geometry and Experience, here he's describing Poincare's philosophy of geometry, which is here rejected. that same word, elevation, and that they're holding on to capture Conqueret's notion of elevation. So I think that gives me reason to think anyway that when he deserves even here, we know he's been reading the power of his promises. He had this in mind already in 1905. Just let me ask, for the best of my knowledge, this striking language, this language of elevation, In Einstein's 1905 paper, together with its reappearance in 1921, has not been previously noted in the literature on Poincaré's possible influence on Einstein. I think it could be significant. So, back to Einstein's 1905, these two oscillates, which he's now elevated, together then allow him to stipulate, as he puts it, to stipulate by convention, best result, a new definition of time with the name, based on the assumed burden of the velocity of light, which implies as a radical position in the classical kinematics of space, time, and motion. In particular, whereas the fundamental kinematical structure of an inertial frame of reference in classical mechanics is defined by the internally inverse of motion, a revised version of the same structure, in Einstein's theory, that is inertial frame, is rather defined by the scheme of space. Now, a central contention of Kant's original version of transcendental philosophy, as we

47:30 know, is that the Newtonian laws of notion are not merely theoretical laws, but atrialized constitutive principles on the basis of which alone the Newtonian concept of space, time, and notion can then have a theoretical application and meaning. What we object to do is that and Einstein's two fundamental presuppositions, or populists, play a precisely parallel role in the context of special relativity. They define the privilege frame. But we have also seen significantly more. Francaret's conception of how a near-empirical law can be elevated to the status of a convention or definition in the sky from 1902 is a continuation, in turn, of Kant's original conception of the conspicuous entry world. Whereas Hamilton's principle of free mobility, generalized and extending Kant's original theory of geometrical construction, within our subjective and necessary realm of extramural intuition, Hamilton's words, Harkeray's idea that specifically Euclidean geometry is then imposed on this thing, that mobility, by its invention or definition of each side, represents an extension or continuation or generalization of Hamilton's architecture. In particular, specifically Euclidean geometry is applied to our experience by precisely such a process of elevation, in which the merely This geometry governs, very roughly and approximately, our actual perceptual experience of bodily displacements, gives rise to something else, an idealized, precise mathematical framework within which alone our properly physical theories can then be subsequently formulated. This same process of elevation, for the last time, in Einstein's hands, then makes it of how an extension or continuation of Kant's original conception can also accommodate new and surprising empirical facts. In this case, the very surprising empirical discovery to one or another degree of approximation, that light has the same constant velocity in general electromagnetic processes, propagating the same constant velocity in every inertial

50:00 It now turns out, in particular, that we can not only impose already familiar and accepted mathematical frameworks, including in geometry and Poincaré's case, on our rough and approximate perceptual experience, but in appropriate circumstances, we can also impose entirely unfamiliar such frameworks, which is my friend's break with Poincaré, namely the kinematical framework of special relativity, what we now call the geometry of Minkowski's desktop. Einstein's creation of special relativity from this point of view then represents the very first instantiation of a relativized and dynamical conception of the a priori, which in virtue of precisely its historical origin, Kant, Hemel, von Karel, Einstein, then has a legitimate claim, my saying, to be considered as genuinely constitutive in a consulent transcendental sense. So that's how I try to make the historical narrative have a philosophical punch. Okay, I'll go on a little bit. Yet Einstein's creation of the general theory of relativity in 1915, again Einstein around 1915, involved an even more striking engagement with Poincare's conventionalist methodology, can make the transcendentally constitual role of these theories, general relativity's fundamental postulates, the life principle and the principle of equivalence, even more evident. The first, and this may be a surprising thing to hear, the first point to make in this connection is that the principle of equivalence, together with the life principle, plays the same role in the context of the general theory of relativity that Einstein's two fundamental presuppositions, or apostolates, played in the context of the special theory. Namely, they define a new inertial kinematical structure, defining a privileged state of motion, force-free motion, that is, free-falling gravitational motion, a privileged inertial kinematical structure for describing space-time and motion. Because Newtonian gravitation theory involved the instantaneous action of the distance, and therefore necessarily absolute form of humanity, it was necessary after special relativity to develop a new theory of gravitation

52:30 where the interactions in question, gravitational, propagate with the velocity of light. And Einstein solved this problem by means of the principle of equivalence by defining the new inertial kinematic structure wherein the three-to-follow trajectories in a gravitational field replace the inertial trajectory described by three particles affected by no forces at all, including gravitation. The principle of equivalence in this sense replaces the classical law of inertia, holding in both the fermion mechanics and special noticeability. But the principle of equivalence itself rests on a well-known empirical fact, known since Galileo, that gravitational and inertial mass, of course you didn't have no context for it, meaning that all bodies fall the same in a gravitational field, or at least in the earth's gravitational field, namely that all bodies, regardless of their mass, fall with exactly the same acceleration in a gravitational field. In using the principle of equivalence to define a new inertial kinematical structure therefore, Einstein has elevated this merely empirical fact to the status of a conventional definition in disguise, again, in Parker-Rey's sense. Jen has, as he had earlier undertaken, a parallel elevation in the case of the new concept of simultaneity introduced by the special people. Nevertheless, Einstein did not reach this understanding of the principle of equivalence all at once, our model of four-dimensional understanding. He first operated instead within an essentially three-dimensional understanding of special relativity. He rejected Nkoski's work when he first heard about it as a mere mathematical subtlety. I think he used a less nice word than subtlety at the time. And he proceeded in the years 1907 to 1912 to develop relativistically acceptable models of the gravitational field by considering the inertial forces, like centrifugal and Coriolis forces, arising in non-inertial frames of reference, accelerating and rotating frames, within the framework of special relativity. It was in precisely this context in particular that Einstein finally, in 1912, came upon the example of the uniformly rotating frame, the rotating disk.

55:00 And it is at this point, and only at this point, that he then arrived at the conclusion that the gravitational field may be represented by a non-Euclidean geometry. Okay, so this is a rotating reference frame in special relativity, uniformly rotated. And the idea is if we consider these tiny little measuring rods that are tangent to the rotation, say on these two different circles, and you consider their velocities, they're going to experience a Lorentz contraction because this is special relativity. And so the circumference of these circles are going to be Lorentz-contracted, and differentially as you move out from the distance from the center of the circle. However, if you consider a rod that's perpendicular to the motion, that is a radius, a radial line, it's of course not contracted because it's perpendicular to the motion. So the circumference is contracted, the radius is not contracted, the ratio of the circumference to the diameter is different from pi, on the size of the circle, and so this must be Einstein recalls from his study of non-Euclidean geometry. A non-Euclidean geometry is arising here. So the principle of equivalence says a non-inertial plane, an ips-inertial plane, in which they're from physical places, can model the radical shape here. And now we notice that in such a plane we also have the non-Euclidean geometry arising arising for exactly the same reason, and Einstein said, well, that means that the gravitational field could be itself modeled by a non-equilibrium geometry. Here it's all in a three-dimensional context, but something similar happens to time, and so he realizes it's four-dimensional. At that point, he says, hey, Minkowski had a great idea, after all, I really need a four-dimensional non-equilibrium space, and that's how he finally got to our current, something like our current understanding. It was in precisely the context of this line of thought, the rotating gist funders, that Einstein found that he now has explicitly to oppose Poincare's conventional philosophy of geometry. Yet Einstein's argument, as described in his celebrated paper, that's where the earlier quote came from, in his quote, 1921,

57:30 was far from a simple rejection of Poincare's methodology in favor of a straightforward impuracy, or Helmholtzian view. For Einstein also famously says, in the same work, that such specie in turn, Parcomet is actually correct. So that in particular, Einstein's reliance on a Helmholtzian conception of practically rigid bodies that Lorenz contracted, is here merely provisional. I have suggested therefore that we can best understand Einstein's procedure as one of delicately situating himself in between Hamilton and Poincaré. Whereas Einstein had earlier followed Poincaré's general conventionalist methodology, maybe we should call it an elevationist methodology, in elevating the principle of relativity to the status of a presupposition or postulate, he here, in general relativity, follows Hamilton's impuricism in rejecting Poincaré's more specific philosophy of geometry in favor of practically rigid bodies. We just read off the geometry from there. It does not follow, however, that Einstein is radically rejecting his earlier embrace of Poincare's general conventionalist, or as I say, perhaps we should say, elevationist methodology. Indeed, Einstein had already sidestepped Poincare's specific philosophy of geometry in the case of special relativity, and for essentially the same reason he explicitly opposes it here in 1921. Poincare's rigid hierarchy of the sciences in both cases stands in the way of the radical new innovations himself introduced first in 1905 where we replace space by space-time and then in 1915 where euclidean geometric space is also but why was it necessary after all for einstein to engage in this delicate dance between himald's and planqueray because we don't of course do that That's not the way we get with the principle of equivalent, and to four-dimensional non-equity in geometry. The crucial point is that Einstein thereby arrived for the first time at a radically new conception of the relationship between the foundations of physical geometry on the one side and the relativity of space and emotion on the other.

1:00:00 Here's where they're put together. Geometry and experience on the one hand and the rotating disk, the relativity of motion, On the other, as I say, the rotating disk is a crucial part of the 1921 paper. I point that people haven't emphasized sufficiently. So these two problems, geometry and its foundations, relativity of space and of motion, as we have seen, were closely connected in Kant, but they then split apart and were pursued independently in Hamels and Maas. In Poincaré, as we have also seen, the two were perceptively reconnected once again, insofar as Poincaré's hierarchical conception of the mathematical sciences incorporated both a modification of Hamlet's philosophy of geometry, which eventually goes back to Kant, and both a Hamlet's philosophy of geometry and a serious engagement with the late 19th century concept of initial frame in Poincaré. Indeed, it is for precisely this reason, as we now see, that Poincaré's scientific epistemology was so important for Einstein. Einstein could not simply rest content with Himmels' empiricist conception of geometry, because the most important problem with which he, Einstein, was now faced was to connect the foundations of geometry with the relativity of Einstein, which the company of Dumbled's doesn't do. But Einstein could not rest with Poincaré's conception either, even though Poincaré connects the two, because Einstein's new models of gravitation have suggested that geometry has genuine physical or empirical content versus Poincaré's conventionalism. Einstein's radically new way of reconfiguring the relationship between the foundations of geometry and the relativity of motion, therefore represents a natural, but again entirely unexpected and surprising, extension or continuation of the same conception of dynamical and relativized constitutive a priori principles he had first instantiated in the creation of special relativity. Just as he had earlier shown how an extension or continuation of Kant's original conception and surprising empirical facts, the discovery of the invariance in the velocity of life, Einstein here shows how a further extension of this same tradition

1:02:30 can do something very similar in facilitating for the first time the application of a non-Euclidean geometry to nature. In this case, however, it is not the relevant empirical fact, the well-known equality of gravitational inertia and mass, that is surprising, but the entirely unforeseen connection between this fact and the new geometry, and in general the foundations of geometry. And what makes this connection itself possible for Einstein is precisely the principle of equivalence, which thereby constitutively frames the resulting physical space-time geometry of general relativity in just the same sense that Einstein's two fundamental presuppositions or posthumates figuratively framed his mathematical description of the electrodynamics of moving bodies in structural relativity. Wherein the particular geometry in a given general relativistic space-time is now determined empirically by the distribution of mass and energy according to Dunstrand's field equations, the principle of equivalence itself is not empirical in this sense. this principle is instead presupposed as a transcendental constituent condition for any such geometrical description of space-time to have genuine empirical meaning in the first place. This historicized version of transcendental philosophy I am attempting to exemplify therefore sheds striking new light, I believe, on the truly remarkable depth and fruitfulness of Kant's original version. Kant's particular way of establishing a connection between the foundations of geometry and the relativity of motion, which, as we have seen, lies at the heart of his transcendental method, has not only led, through the intervening philosophical-scientific work of Hemmholtz, Mach and Poincaré, to a new conception of the relativized a priori, first instantiated in Einstein's theories, both special and then general relativity, it has also led, through this same tradition, to a radically new configuration of the connection between geometry and physics in the general theory of relativity itself. There can be no question, of course, of Kant's having anticipated this theory, general relativity,

1:05:00 in any way. Of course not. The point, rather, is that Kant's own conception of the relationship between geometry and physics, which was limited of necessity in his context to Euclidean geometry and Newtonian physics, then set in motion a remarkable series of successive reconceptualizations of this relationship between geometry and physics, in light of profound discoveries in both pure mathematics and the empirical basis of mathematical physics, and this series of reconfigurations finally eventuated in Einstein's general theory of religion. Thank you. We have some time for a few questions, so please raise your hands. Jim Brown. This was wonderfully interesting, but this is just a... I knew you were going to write it. No, it's actually an invitation to fill in one thing. Einstein's own take on this, when he sort of commented on what he was doing, was to formulate this principle constructive distinction. and principal theories here are I can't remember all of the characterizations but it included obviousness certainty or surety foundation does that fit nicely into into your story or is there a bit of tension he of course would be wrong I guess it seems to me that the principle of constructive distinction fits very well because, I mean, of course here, special relativity is the first very important instantiation of that distinction. and the idea is, let's forget about the detailed physical structure of matter lying behind massive electrodynamics, and let's forget about the electromagnetic worldview, and let's

1:07:30 forget about the dynamics of the electron in Poincaré's sense, and all of that. Let's not worry about what the constituents of matter are, and what are the forces binding together electrons in matter? Could they be causing the contraption? Let's abstract from all of those details of physical matter theory and think about general presuppositions or postulates, principles, for us, which give the kinematics of space and time independently of the empirical details of So that seems to me to fit very well with this idea. The same kind of thing happens in general relativity in this 1921 argument, because there the argument is, well of course, eventually I cannot take the practically rigid body as a primitive in physics. Poincare is right, because it's a physical structure, it will depend on the theory of matter. Einstein is then worrying about his program in unified field theories versus quantum mechanics. And the point, though, is we still don't know what to think about that. We actually don't know the right way to think about matter. He's going to prefer his field theory program over quantum mechanics. That's clear. But general relativity has got to set itself up as a generalization of special relativity before we worry about this. independent of that. And it defines as it were a kinematical, geometrical structure by the principle of equivalence and the life principle without yet having to worry about those physical details. That's why he says it's merely provisional. Of course, later we have a promissory note. We have to have such an account of that. Yeah, the problem is sort of it's merely provisional versus those other remarks where he says it's certain. That's the part I was sort of figuring on. It's as if he was making a trivial observation. Oh yeah, I said it. This is a green fashion for me, I can't deny it. Sometimes he describes it almost in those terms. Well, I mean, do you mean, for example, when he talks about the thought experiment of following a light ring? I know you're such a principle, both the relativity and the algorithm is that they are obvious, they are certain. It's not a conjecture, the way...

1:10:00 Of course, here he says it's based on a conjecture, and it's elevating. So, this I take to be the... I like this way of putting it. Richard Hidd is next, but Alexey Greenbaum, you would have a follow-up? Michael, it seems that Einstein's own unhappiness with the notion of principle theory refuse your argument that he kept this idea of elevating principle as a dominant idea of how to do business. Because, you know, if he himself historically, I mean, if this is a state of excellence, he insisted that constructive theory should be our ultimate goal, then your argument that elevation is the way you proceeded... No, because we still have to remember the Kantian distinction between constitutive and regulative principles. So the idea of the Maya is that we still have that distinction. The big break we make with Kant is that there are constitutive principles but they are vocal and relativized and they occur at a historical moment. So I think Einstein would stick to the idea that when he introduced general relativity, what he said in 1921, if I didn't reject Poincare, and if I didn't side with Hamels about practically rigid bodies, he says, I never would have discovered the theory of relativity in the first place. And what he means is this argument with the rotating disk. And I think he sticks to that. But of course, as a regulative ideal, there has to be a unified theory of matter and space. There has to be a unified field theory. That doesn't mean there isn't an important constitutive role. Again, that's why it's so important that this is historicized and dynamical. It doesn't stay a priori, because there is no timeless constitutive of a priori, and this I think is one kind of illustration of that.

1:12:30 Eventually we have to have a constitutive theory, we have to show the quantum theoreticians that following the special relativity, general relativity route, rather than the quantum probability route, we can arrive at a satisfactory matter theory, and a better data theory. But that doesn't negate that at the time in which we put Lorentz in variance and then general covariance as crucial framework principles for any possible physics, that at those moments it was a constitutive a priori moment where when we did it then, we had to do it before we knew what the matter theory was, which we're only going to know in the future. return. If you read what Eidsen wrote much later in response to Hans Reichenbach's contribution to the Schilt volume, he refers, I think, to himself, but certainly to the scientist in general, as an unscrupulous epistemological opportunist, which rather suggests that he didn't have such a sort of a grand aim in reconciling one guy's philosophical system with another, and that he would just take bits from wherever they seemed to be handy at the time, and change his mind later if some other alternative epistemologies seem more fruitful in the new context. But I'm wondering whether seeing him as sort of following in this tradition of philosophers starting with Kant isn't sort of overemphasizing the influence of the epistemological considerations. Good, good. Very good question. I'm not saying that Einstein is a scientific philosopher in the tradition of Kant, Hamilton, Bunker. Certainly not. He never writes his version of his films today. This is my philosophy of science. This is what it has to do with Kant. Of course, he'll say various things about Kant at various times. Interestingly, around the time of special relativity and general relativity, he basically said, ooh, I don't like Kant and I don't like the near-continence either. This is the point that Don Howard was always making. Now, Vader, interestingly, when he's in the Reichenbach, in the Schilt volume, where he's saying,

1:15:00 no, no, Reichenbach is wrong, why is he wrong? Because the rigid rod is not primitive. We have to have a unified field theory. Although interestingly, he still says, my respect for Poincare at this point is so great that I have to stop using Reichenbach's name in his debate. So his position is always opportunistic, like he said. He borrows anything he can at any moment. His point is to develop ongoing physical theories, and he uses what is useful to him. So I'm not saying in any way, shape, or form that he sees himself self-consciously in his philosophical... He's not even as much of a philosopher as Hamilton Poincaré. Certainly not. But I am arguing that if you look in this period, 1905, 1915, 1921, you see him engaging with the problems that they were engaging in. And I focus on this elevation concept. And he also talks about Hamilton and Poincaré. Not in Geometry Experience in 1921, but in 1925, in a paper that I think was in a little room shower somewhere, he actually said, well, no, the practically rigid body standpoint, that's Hamilton's standpoint. So he puts himself into this Poincaré-Hemmholtz debate about the foundations of geometry, explicitly. And he says, if I didn't do it that way, I never would have arrived at the principle of religion, at the general theory of religion. So all I'm saying is his engagement with this philosophical tradition, an opportunistic engagement to be sure, allows us, as philosophers who worry about these things in a way that he didn't, who worry systematically about these things, to say, therefore what he's doing here, when he's elevating things to the status of the pastoral, is he's instantiating a relativized a priori notion which has this Kantian lineage. is a, is constitutively a priority, that's my opinion.

1:17:30 Furthermore, it helped him opportunistically, you know, incredibly, brilliantly, and also luckily, to create these new theories by engaging with these philosophical debates opportunistically, as it were, at just the right time when it could pale off. It's tempting to view the interaction between geometry and physics in a Juhamian way, so only both together have empirical consequences and we can actually change geometry or change maybe the mechanical parts of the entire physical theory. Bonn-Groë wanted to keep Augurian geometry, Einstein, Kepferd, McIverland, so we have different theories which are empirically equivalent. My question would be what is the sense of your notion of relativized a priori? In this setting, is it just that we had a certain preference for certain parts of the theory system and we say that we need that in order to develop the theory dynamically, or would you say a relative value factor is more than such a preference for Nuhemian? Good, thank you. Well, as you know, this Duhemnian way of looking at it is just the way that Einstein formulates Poincaré's philosophy here in 1921. So here we have the classical Duhemnian kind of argument, right? And this, so a lot of people, the logical empiricists, therefore commonly interpreted Poincaré's argument as merely a Duhamelian argument following Einstein. That Poincare's conventionalism was simply, yes, why is geometry conventional? Well, because it's only geometry plus physics, say in the temperature field example that Poincare gives. You have to have forces and you have to have geometry. Only the sum has empirical content.

1:20:00 We then have the freedom to revise one or the other depending on our preferences. Poincaré prefers to take the simplest geometry, and what the logical empiricist always says, well, why not take the simplest overall theory? And then we can revise the theory. Now, I disagree completely with that way of understanding Poincaré's argument. I don't think that's what Poincaré is saying at all. So I think Einstein is misreading Poincaré here for his own purposes. Poincare has a much stronger idea, which I think is part of which involves this hierarchical conception, that is, look, you have to choose a geometry before it makes sense to talk about physics at all. You can't talk about forces unless you're in a position to talk about spatial dependence of fields. And you can't talk about spatial dependence unless you have geometry of space what is what is the d what is the what is the d that measures the uh the spatial distance from the from the center of the force field right well that's some kind of method it's got to be there already so it's not a holistic uh uh duhemian view that's pancarean it's more of this hierarchical view certain things we we need first arithmetic there's no possibility of changing that at all. There's only one possible arithmetic. After that, there are different possibilities due to various mathematical tests. So the reason there are different possibilities for geometry is not so much because of this kind of, I would say, a trivial Newhemian point. It's rather because the principle of premobility, which is not seen after Hemel's as our fundamental coordinating principle in Leichenbach's terms, that we used to relate geometry as being ruined through actual physical phenomena, say the behavior of rigid bodies, that that principle has three possible metrical realizations to be any space that comes into literature. So that principle doesn't determine what the geometry is, and so there's freedom to choose at that point. That's a very specific fact about geometry from his point of view. And so when you're in general relativity then, where you don't have constant curvature,

1:22:30 you don't have that argument, and I don't think you can say, using a Poincaré argument, that geometry is conventional in general relativity, even though Schlick and the logical empiricists thought you could extend it using the Duhemian version of Poincare. So would you really ask us, is my version of Constituent of a priori simply Duhemian? And I want to strenuously resist that because that would just be Aquinian's holistic view, and then all you would mean by Constituent of a priori is more entrenched or I like it better or I'm reluctant to revise it. That's not the point at all because these things can be revised. That's the beauty of it. The relativized constituent a priori, what's exciting about it is that it actually is revised all the time, or at least it's revised at various crucially important moments. So it's not that it's unrevisable, or you don't want to revise it. It's rather that those principles in a certain theoretical context play a special quasi-definitional role. That is, they're necessary conditions for the concept of our theory and having a well-defined empirical meaning. The simplest example, I think, is just the Newtonian case, where Newton's law of gravitation talks about the absolute acceleration between gravitationally interacting models. Those are not merely relative accelerations. Those are absolute accelerations defined relative to a privileged frame. Well, relative to what are those? What are the frames in which those hold? Well, we would say the inertial frames. And what are the inertial frames? They're the frames in which the three balls of motion hold. So the modern point of view would be, that is the inertial, late 19th century point of view would be, we define the concept of inertial frame to replace Newtonian absolute space. The three laws of motion are an inclusive definition, therefore, of what we mean by true acceleration. So they're not mere empirical statements. They're a necessary condition for the notion of true acceleration an empirical meaning. Otherwise we are just set with absolute space and that doesn't have by itself an empirical meaning.

1:25:00 So it has nothing to do with how reluctant we are to revise from our novels. It's that they are necessary conditions for a certain kind of empirical meaning. There's a large number of hands, but there's only time for one more question. That goes to Oliver Pulley. Okay, so I'm still struggling to understand how the principles you're thinking out in contexts of special relativity in general play exactly the kind of constitutive role where you just so nicely summarized Newton's order to play in the context of Newtonian mechanics. Now, in the context of Newtonian mechanics, when you go on to develop some kind of detailed pattern theory or some specific theory that isn't in the Newtonian framework, those rules remain absolutely true. And it's in that sense that you can guard the factors, Well, at least that's consistent with, you're regarding them as constitutive of the very project of Newtonian mechanics in the first place. But in the case of the light postulate, and the something like equivalence, principle mainly that what is not subject to non-grapassational interactions move on the GD space-time or something like that neither of these things remains true in theories which are within the framework of either special relativity or general relativity or they need not so for example if and it's conceivable in specially relativistic quantum field theory that light doesn't propagate long the GD system analogy it's you know it's automatically rotating bodies in general don't propagate on Jesus and when you can trust another reason for being unhappy about characterizing these constitutive principles is going back to the constructive principle theory distinction which Jim Brown mentioned. You said that fitting with what you say but of course Einstein's great example of that distinction

1:27:30 was thermodynamics versus the connected theory of gases so one question is would you say that the principles of thermodynamics may be that they can't exist certain kinds of perpetual motion machines, would you say that they're constituted principles or some kind of slice of mass consistent with thermostats? Okay, these are really good questions. Let me just start with a footnote that makes things easier for myself while I think about your question. Actually, the distinction between principle theories and constructive theories really goes back to Poincaré. between what he called principal theories, or theories of principle, and again he gave conservation of energy in both systems and dynamics, that's a principle theory, versus theories of specific atomic theories and essential forces. So, in effect, that vector of atomic theories is also a function of that. Now I think, with the special theories, what this shows is that, In Newtonian mechanics, of course, we say that the loss of motion we made absolutely true. Well, of course, they don't really make absolutely true if we have to put a magnitude into Newtonian physics either, because eventually we have to put electrodynamics into Newtonian framework. I mean, there isn't just gravity, after all, there is electromagnetism as well. And when we put the electromagnetic field into the Newtonian framework, because of the experimental indication that it too is going to be invariant in initial frames, the laws of Newtonian mechanism can't stay true. So when you have to take these general mechanical kinematical theories that define what I say is space, time, and motion. Sometimes I say matter, but actually what your question shows is that matter raises all kinds of other questions. Because as we develop matter theories, we have to keep bringing in other theories. to where we started. So we have Newton, we have to bring Maxwell in, but this is not a completely different theory with a different framework.

1:30:00 It turns out when we try to unify those two theories, Newton plus emotion can't be known exactly truth. They're only approximation. And that eventually means that gravity in general velocity also has to be changed because we don't have absolute simultaneity and so we now have to have a field theory of gravity where it propagates with the velocity of light and so on, so that changes. Quantum mechanics, of course, brings in other, and a lot of this, of course, has to do with the relation between mass and radiation. That's already happening with Maxwell's equations. This is, of course, at the heart of why quantum mechanics gets us into difficulties. How do we put those two together in a consistent picture? not just quantum field theory, but just ordinary elements of quantum mechanics and Bohr's atom and all of that. And so, as we further develop our matter theory that's, as it were, filling out the content of these general space-time motion frameworks, it keeps happening that those frameworks have got to be revised as we do that. That's a very important and deep, it's both deep physically and deep philosophically in terms of my picture, I think you're helping me see this right now. I don't think it's incompatible though with my picture, because again Newton's laws of course are not absolutely true for all interactions, they're only, they're not true for electromagnetic. Okay, so we thank you very much, Mark. Quite a tour de force. Yeah, yeah, yeah. I feel the benign ghost of Harvey Brown kind of hovering somewhere in the back of the room. Yes, yes. Well, I wanted to let out rather a loud dissenting note.

1:32:30 But Michael is well prepared. Oh, yes. Well, he always is. Very well prepared. I think it's an absolutely superb interpretation. I'm not sure it's what Einstein... I mean, I think it's a magnificent and very fruitful reconstruction. of Einstein. I do think Einstein was much more of an opportunist than this account suggests. And I think it's quite true. He certainly had a number of positions on how one should think of the first principles of mathematics and physics as meshing together There was a package which certainly shifted at various points in his career.