Philosophy and Spacetime Physics: Introduction
Sklar (Lawrence)
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  1. Three major themes dominate the issues treated in the essays collected in this volume:
    • First, given the plausibility of the allegation that our geometric theories of the world outrun in their content the possibility of unique specification by all possible empirical data, how can we possibly avoid the skeptic's assertion that we ought not to claim to have genuine knowledge of the geometry of the world at all? Further, doesn't the skeptical threat present in the geometric case generalize to a threat of skepticism against alleged theoretical knowledge in general?
    • Second, ought we to view the apparent ontology of geometric theories, space and time (or, rather in the relativistic context, spacetime), as genuine constituents of the world, or ought we to, instead, interpret the apparent theoretical ontology of geometry in some instrumentalistic fashion, taking the reference only of the observational terms of the theory (light rays, particles, measuring rods and clocks, etc.) straightforwardly? Once again the ontological question asked here generalizes from the geometric to the general theoretical context.
    • Third, and finally, how ought we to evaluate those philosophical doctrines which claim a reducibility, in some important sense, of the concepts of geometric theory to concepts not prima facie geometrical at all? In particular how plausible are the claims that metric or topological aspects of spacetime are reducible to causal relations among events, and how plausible are the claims that the temporal asymmetry of the world is reducible to the asymmetry in time of features of the world captured by the application of the concept of entropy?
  2. Naturally these questions are not totally isolable from one another, for any answer to one of the questions posed above is replete with consequences for one's position regarding answers to questions in the other categories. For this reason many of the essays included here treat of problems in all three categories, although it might be plausible to claim that the emphasis in the first five chapters is on epistemic matters, of the next three, on questions of ontology, and of the last four, on issues of causal or entropic reducibility of spacetime concepts.
  3. The essays in this volume have all appeared subsequent to my earlier book1 on the philosophy of space and time, Space, Time, and Spacetime. While the reader of the present volume who is unfamiliar with the background of contemporary philosophical discussion of issues concerning space and time would find that book helpful in setting the stage for the discussions contained in these essays, the present introduction, along with the prefaces to the chapters in this volume, should make the context of argument sufficiently clear so that the reader can grasp the motivation for the arguments contained here without an extensive earlier background in the philosophy of space and time. For those familiar with the earlier work, however, it might be helpful to note several ways in which these essays hope to go beyond it.
  4. In some cases, recent developments in the foundational study of spacetime theories in physics has opened up new areas for philosophical inquiry and allowed for a more profound treatment of older issues. For example, the intensive study of the extent to which variously construed causal structures do or do not uniquely determine spacetime structures in models for general relativity has greatly expanded our opportunity to clarify aspects of causal theories of spacetime in philosophy. In other cases the rediscovery of earlier but neglected parts of foundational physics has been of importance. This is the case, again of importance when one is dealing with causal theories of spacetime, with the recent attention paid to Robb's early but frequently overlooked formulation of special relativity. Finally, there were some important aspects of the scientific framework which I felt simply had not received the attention they deserved, given their philosophical relevance, in the earlier work. Trautman's curved spacetime rendition of Newtonian gravitational theory, for example, failed to receive the attention it merited in Space, Time, and Spacetime.
  5. From the philosophical side, recent years have seen a diverse, yet related, number of attempts to reconcile a realist attitude toward theories with an antiskeptical epistemology, while at the same time acknowledging the force of the empiricist’s allegation of underdetermination of theory by the totality of possible empirical data. Such approaches offer an account of theoretical equivalence more stringent than that of the positivist, who dubs all observationally equivalent theories fully equivalent; accounts of confirmation which attempt to show us that even if they are fully observationally equivalent, two nonequivalent theories may be differentiated in their worthiness for our belief; and accounts of meaning, of reference, and of explanation which, again differing from those of the positivist, attempt to show us why we ought to take the putative ontologies of theories at realistic face value and not construe them away in some eliminationist or instrumentalistic manner.
  6. Many of the essays in this volume are directed at such realist accounts of theory, not primarily to decide whether or not they are correct, but, rather, to differentiate alternative realist approaches from one another in important ways, to lay out in as full a way as possible the necessary presuppositions which must be made to make the various approaches plausible, and, finally, to make it as clear as I can just what the more traditional empiricist would claim to be the places where such approaches to theory are in serious want of further explication and justification.
  7. Finally, on a few matters — for example, the entropic account of time asymmetry — there were substantial doubts on my own part that the treatment given in the earlier book did full justice to the philosophical issues involved. On this particular topic, some preliminary moves are made here to move in the direction of a fuller and fairer discussion of the issues involved, although much more remains to be done.
  8. In the remainder of this introductory essay, I will in turn take up the three major areas of the epistemology of geometry, the ontology of geometric theories, and the nature of causal theories of space-time structure in the hopes of providing for the reader a brief survey of the background discussion in both physics and philosophy which provides the context in which the detailed arguments of the various papers find their place. Again, it should be noted that each essay will be preceded by its own short preface to fix its place in the general scheme even more closely.
  9. The Epistemology of Geometry
    • For two millennia geometry provided philosophers with the paradigm of a science whose propositions could, allegedly, be known to be true with certainty and independently of reliance upon observation and experiment. The discovery of the axiomatic non-Euclidean geometries, and of the far more general n-dimensional generalizations of Gauss's theory of surfaces propounded by Riemann, cast grave doubts on this traditional view of geometry as an a priori discipline. The obvious direction in which to go was to suggest that geometry was just one more theory of the world whose epistemic basis rested on inductive generalization from the data of experience.
    • While there is plainly something correct about this empiricist view, the need for a more subtle approach was emphasized by Poincare's demonstration that, were one willing to make sufficient modifications elsewhere in one's physical theory of the world, any geometry could be held as undisconfirmed by any body of observational data whatever. Most of the interesting work on the epistemology of geometry since his time has been in the varying responses to this alleged underdetermination of geometric theory by all possible observational evidence.
    • One important response is that of the positivist. Offering an account of theory as being nothing but a summary of lawlike regularity among the observables, he counters the threat of skepticism implicit in the underdetermination argument by adopting a notion of theoretical equivalence which is such that any two theory expressions which give rise to the same observational consequences are taken as merely formalistic variants, each expressing one and the same underlying theory. If this is so, then there is no longer an epistemic puzzle regarding alternative theories saving the same phenomena, since there are no such genuine alternatives.
    • But, taken seriously and rigorously, this positivist solution has consequences too irrealist for many to swallow. In the geometric case it seems that we must dispense with spacetime itself as an entity in the world, since equivalent (positivistically) to any space-time theory will be the mere set of its observational consequences, and if these refer only to material objects and their relations, then since this new expression of the theory is equivalent to the old, we ought not to have taken the theoretical ontology of the older expression at face value at all. Worse yet, if, as is frequently the case in geometric underdetermination arguments, we restrict the observable to the local relations among material measuring instruments, then, even relationistically construed, the global geometry of the world becomes a mere fiction.
    • One way to avoid these consequences would be to deny the common presupposition of the underdetermination argument and of the positivist reply to it. Both presuppose that it makes coherent sense to distinguish among the totality of consequences of a theory its proper subset of observational consequences. But many arguments have been advanced to try and convince us that such a notion of an in-principle delimitation of the realm of the observable is an empiricist mistake. Of course if we accept such a claim the problem as posed by Poincare cannot be coherently framed.
    • But, at least in the geometric case, we have reason to be somewhat suspicious of this "way out." Far too many of the accomplishments of the best physical science which deals with the geometry of the world themselves rest upon an implicit assumption of an observational / nonobservational distinction, or, rather, one at least strong enough to assure us that some of the consequences of some of our theories must be considered in-principle nonobservable. Einstein's denial of the aether frame in the theory of special relativity, and his denial of the discriminability of a gravitational field from the metric of spacetime in general relativity, both rest, I believe, on such an assumption. So it certainly behooves us to take the possibility of such a distinction seriously enough to explore what alternatives are available to us assuming it to be a legitimate one.
    • One approach to the problem avoids the threat of skepticism by adopting some form or other of a permissive notion of rationality. Here it is argued that in the case of theoretical underdetermination we are rational to believe any one of the empirically well-confirmed theories. Which one? Any one we choose. In sophisticated versions such a notion of rationality may be combined with an elaborated pragmatist critique of the very notion of truth itself, and with a denial of the legitimacy of doubt except as internal to one's adopted way of "getting on in the world." But to some, myself included, such an approach seems to be merely skepticism sugar-coated so as to make its consequences appear more palatable.
    • It is worthwhile, in any case, to see just how far one can get in trying to simultaneously maintain a realist notion of truth, an antipositivist and antireductionist approach to theory, and an acceptance of the claim that our body of potential empirical evidence is outrun by the full contents of theory. Much contemporary "realist" work on the epistemology of space and time tries to do just that, and a good deal of the epistemological content of the essays in this volume is devoted to explicating ways in which this approach might go, and to pointing out pitfalls in the path of the philosopher trying to solve the problem in this way.
    • All such realist views will deny the fundamental positivist thesis that observational equivalence is a sufficient condition for full equivalence of theories. All will demand the possibility that two theories, although inequivalent, can equally well save all possible phenomena. What condition they will impose, over and above observational equivalence, for full equivalence will depend on the attitude they take toward the meaning of the nonobservational terms of the theories.
    • One view will argue that the nonobservational terms of a theory cannot have their meaning fully accounted for solely in terms of the role the terms play in the theory. One such approach, for example, will argue that terms which appear in observational contexts can appear, meaning exactly the same thing, in nonobservational contexts as well. Thus, it will be said, we mean the same thing by ‘length' whether we are speaking of the length of a table or the length of the interatomic bond in a molecule. Such a "semantic analogy" approach to the meaning of terms designating nonobservables, or indeed any other approach which takes meaning attribution to outrun that which can be captured by examining the role played in the theory itself by the theoretical term, runs into many difficulties, both in offering a coherent account of meaning accrual for such terms and in offering a systematic account of what it takes, over and above observational equivalence, to make two theory expressions genuinely fully equivalent.
    • The alternative approach, which attempts to reconcile realism with a "role played in theory" approach to the meaning of the nonobservational terms of a theory, is quite a bit more theoretically tractable, and it is an approach which has appealed to many in recent years. This approach is frequently associated with a favorable attitude toward Ramsey's claim that we should properly view theories as adequately represented by the result obtained by (1) conjoining their axioms into a single assertion, and (2) replacing the nonobservational terms with existentially quantified predicate variables. From this point of view "charm" in physics simply is that property which the theory says exists, and which has whatever features the theory says charm has. Relations of charm to observable features are captured by the terms referring to these features staying intact in the Ramsey sentence, but relations to other non-observable features are captured by the appearance in the Ramsey sentence of other existentially quantified predicate variables.
    • Common to this approach to theories is the assertion that what is required for full equivalence, over and above observational equivalence, is that the theories in question bear some appropriate structural isomorphism to one another at the nonobservational level. Theories which can be transformed into one another by term-by-term interdefinitions of theoretical terms, for example, we ought to hold genuinely equivalent, but theories whose theoretical structures are not sufficiently structurally similar ought not to be taken as fully equivalent even if they are observationally equivalent.
    • Such an approach to theories is well worth pursuing in detail, for, if successful, it might very well do justice to the legitimate epistemic and semantic claims of the positivist without being forced into his too generous notion of theoretical equivalence with its irrealist consequences. But there are many problems, both of detail and of principle, in such an approach, and much of the epistemological material in the essays in this volume is devoted to following some of these problems up. Most crucial to such an approach is the question how it is to handle the skepticism latent in any view which lets theoretical content outrun empirical determinability.
    • A number of suggestions have been made which propose to solve this epistemic problem for the realist by invoking grounds for theory choice which outrun conformity with even all possible empiirical data. Some invoke various notions of a priori plausibility for theories, taking, for example, ontologically simpler theories to be more worthy of belief. Here problems of characterization and of justification arise, as well as problems engendered by the plausibility of such claims as that the simplest theory is, ultimately, the Positivist reduction of the theory which does away with nonobservational ontology altogether. Other moves focus on the alleged dependence of our principles for theory acceptance on the best available antecedent theory we have accepted to date. In this context such "reliabilist" views about justification of theory choice frequently cash-out as the view that one ought to believe the theory which saves the phenomena and is the most conservative change from our previously accepted theory. Here again serious problems arise, for it is not at all clear that such a notion will serve to coherently or consistently make a theory choice possible, nor that having done so an adequate rationalization of such a rule for choice from the realist perspective is possible.
    • Finally, there are those who seek the resolution of the realist's epistemic problems in the characterization of models of confirmation theory. Such, for example, is Glymour's "bootstrap" model of confirmation (expounded in his Theory and Evidence) which offers an account of confirmation in which the alternatives to the standard relativistic spacetimes receive no confirmation, and Friedman's invocation of notions of consiliance of inductions (in, for example, his Foundations of Space-Time Theories), which tries to explain why we ought, if we are seeking for highest confirmation, to understand the Ramsey sentence version of a theory physically-realistically instead of merely as an instrumentalistic device whose existential quantifications are only indicative of abstract representations.
    • Again these realist approaches to obviating the threat of skepticism are fraught with problems both of detail and of principle, and some of the critical possibilities are explored here in those chapters and portions of chapters which focus on the epistemological status of spacetime theories. Of course many open questions remain. Some of these are problems in the epistemology of theories in general. Other problems remain centering around the question of the degree to which spacetime theories present special and idiosyncratic epistemological problems which differentiate them from the ordinary run of naturalistic theories.
  10. The Ontology of Spacetime Theories and Their Explanatory Role
    • A persistent controversy rages in the philosophy of space and time between those who claim that spacetime ought to be taken as an entity which exists in its own right, and which could exist even were there no ordinary matter in the universe, and those who maintain that talk about spacetime ought to be considered as nothing but a misleading way of representing the fact that there is ordinary matter and that there are spatiotemporal relations among material happenings. Call the former doctrine substantivalism and the latter relationism.
    • Early philosophical debate on this issue frequently hinged on the substantivalist's claim that the relationist was unable to account for the legitimacy of all reasonably assertible propositions about spacetime — for example, about empty regions of it or what it would be like even if totally empty of matter; and the relationist claim that the substantivalist allowed for too prolific a language in which the illegitimate could be expressed — for example, that in substantivalist terms it made sense to ask where in space itself the material universe was located. Much of this debate can be found in the famous correspondence between Leibniz and the Newtonian Clarke.
    • But along with some of the best traditional philosophical argumentation on this issue which can be found there, especially in the form of Leibniz's ingenious formulation of relationism and his brilliant marshalling of the most effective antisubstantivalist arguments, we also find Newton's surprising attempt to demonstrate the truth of substantivalism from the experimental observation of the existence of the so-called inertial forces. According to Newton the distinction between real acceleration, relative to space itself, and mere relative acceleration, of one material object with respect to another, is one demonstrable by the observable causal effects of the real change of motion.
    • While the early relationist replies to Newton were uniformly ineffective, the centuries following Newton's seminal work saw numerous, quite varied, attempts to make the issues clearer. Some were attempts to make Newton's substantivalism more respectable by showing that if nonmechanical phenomena were taken into account features with no empirical consequence on the original view could be found to have observational consequences. For example, the aether theories of light could be taken to show, among other things, that uniform motion with respect to space itself, as well as accelerated motion, had empirical consequences.
    • Other approaches — not actually forthcoming until imaginations had been spurred by the invention of spacetimes appropriate for the new non-Newtonian theories of special and general relativity — were designed to show that we could construct spacetimes more appropriate to Newton's data than was Newton's absolute space. Neo-Newtonian spacetime is one which gives rise to the same empirical results as does Newton's space-through-time, but which is relationistically more acceptable, as within it such notions as absolute place through time and absolute velocity cannot be defined. A curved version of such a spacetime provides an arena for Newtonian gravitation again more relationistically acceptable than Newton's original spacetime. Yet both theories are, of course, substantivalist theories in the sense of taking spacetime to be an entity over and above the material inhabitants of the spacetime.
    • Finally, some approaches tried to reconcile the Newtonian observational data with a genuinely relationist theory. Mach, for example, tried to account for the inertial forces as forces arising from the acceleration of test systems not with respect to space itself, but, rather, with respect to the remaining averaged-out matter of the universe. Alternatively, one could offer a relationistically acceptable account by simply denying that absolute acceleration exists or that an explanation of inertial forces is called for. In such an account we can explain differences in inertial forces by relative motions of material objects, but we simply offer no explanation at all as to why some objects (the inertial ones) suffer no such forces at all.
    • With the discovery of special and general relativity the discussion must shift somewhat. Now it is the question of the appropriateness of substantivalist or relationist ontologies for spacetime to these new accounts of the world which is at issue, rather than to the discredited Newtonian account. While some early writers thought that special relativity was the long-awaited appropriately relationist theory, further reflection showed that in this account of the world the distinction between inertial and noninertial motion, with which the Newtonian underpinned his substantivalism, is just as strong (rather, stronger) in this account than in the Newtonian. And while Einstein was originally motivated to discover general relativity at least in part by the hope that he was coming up with a theory which was relationist in the Machian vein, further thought showed that this was not a very plausible reading of what the theory implied.
    • Indeed, on a surface reading, the general theory of relativity certainly has the appearance of a substantivalist account. Of course there is no Newtonian space-itself through time, nor Newtonian absolute position or velocity. Nor are there the global inertial frames of Newtonian, neo-Newtonian or Minkowski spacetime. But there is the geodesic structure of a curved spacetime, a structure whose observable effects on the motion of material objects is plain. And there is the variable metric of this curved spacetime which, on at least a surface reading of the theory, exists whether or not measuring rods and clocks are there to determine it. Again, on general relativistic grounds the notion of spacetime itself, even if devoid entirely of ordinary matter, with its own structural features seems to make perfectly coherent sense and sounds substantivalist indeed.
    • But we cannot be satisfied with such a surface reading of the metaphysics of the theory. We must, instead, probe more deeply into the philosophical sources of the arguments relied on by substantivalists and relationists. Much of the impetus behind the relationist attack on substantivalism is, of course, motivated by that same skepticism regarding the unobservable which constituted the basis of the epistemological debates about geometry. Relationism is plainly a doctrine akin to other "instrumentalistic" doctrines regarding theories, doctrines which attribute genuine reference only to the names and predicates of the theory which aim to denote observable entities and properties, and which treat the apparently denoting terms which allegedly refer to nonobservable entities and properties as not really referring in nature at all. Instead, the linguistic apparatus of a theory which superficially refers to the unobservable is taken to function rather as an intermediary device allowing us to move inferentially from observation to observation, but not as making genuine existential claims of its own at all. Much of the argumentation here is familiar from the positivist epistemic critique of theoretical realism discussed earlier.
    • But the relationist argument against substantivalism has curious idiosyncratic elements of its own, elements which differentiate it from the usual epistemically motivated attacks against allegedly otiose ontology. These special arguments rest upon various symmetry considerations concerning space and time. Essentially, the arguments go, since the points of space (or spacetime) are everywhere alike and since all directions in space (or spacetime) are alike, that is, because space (or spacetime) is, allegedly, homogeneous and isotropic, the substantivalist view commits us to distinctions between possible worlds which are not real distinctions, and is, hence, an illegitimate doctrine. Consider, for example, Leibniz's famous arguments to the effect that if substantival space existed, there would be a difference between the actual world and a world which differed from it only in the place of the material universe in space itself. But such a difference would not be a genuine qualitative difference. Hence, by a version of the principle of the identity ofindiscernibles, the two possible worlds would have to be the same possible world, refuting the .substantivalist's claim that they are genuine alternatives.
    • Some characteristic objections of the substantivalist to the relationist, and of the relationist to the substantivalist, come as no surprise. Crudely, many substantivalists, besides supporting their doctrine on the kinds of positive grounds which are the modernizations of Newton's important argument, criticize relationism for its tendency to lead us to an extreme irrealism, the result of following out the relationists' arguments against substantival spacetime to, by parity of reasoning, arguments against a world of independent (of mind) existence at all. On the other hand, the relationist will frequently argue that one is forced to the full-fledged relationist denial of substantival spacetime by exactly the same sort of reasoning which, within natural science, leads us to deny the existence of otiose theoretical postulates — for example, the denial of the aether frame in special relativity or the denial of global inertial frames in the general theory of relativity. The relationist will frequently claim that it is only a failure of nerve on the part of the substantivalist which allows him not to see that exactly the same sorts of thinking which leads us to eschew the aether frame ought to lead us, by consistency of reasoning, to eschew substantival spacetime altogether.
    • It is at this point in the argument that the differential attitude toward scientific explanation of the substantivalist and the relationist frequently becomes crucial. The substantivalist will often argue that the need for a residual substantivalist spacetime in our conceptual theory is the need for the postulation of features of the world which explain the observational data. Just as Newton requires space itself to explain the inertial forces observed, so in general relativity we need the geodesic structure and metric of spacetime itself to explain the mechanical, optical, and metrical facts available to us in our empirical data. The relationist counter to this is to critique the substantivalist's notion of explanation in several important ways. A careful examination of the interrelation of epistemic, semantic, and ontological views about theories with models of just what constitutes an explanation in science is needed here. For it is no trivial matter to resolve the debate between the substantivalist, who tells us that the relationist can only summarize the observational data and not explain it, and the relationist, who tells us that the substantivalist's alleged explanatory apparatus is only pseudoexplanatory and a redundant inflation of our reasonable scientifically established ontology of the world.
    • While most modern substantivalists argue for their doctrine as being necessary in the light of the ontological commitments of our best available spacetime theories, in particular as implied by the general theory of relativity, there are other characteristic substantivalist arguments as well. One version of substantivalism, for example, argues to the necessity of this ontologically realist doctrine from the existence of global topological facts, such as the orientability (or nonorientability) of the spacetime. Here the style of the argument traces back in its historical origins to Kant's well-known, but enigmatic, remarks about handedness and space. Once again the relationist has a body of counterarguments to this "outside the mainstream" argument for the existence of spacetime itself as an entity over and above the ordinary material constituents of the world.
    • There are special features of the substantivalist-relationist debate which arise out of the specific nature of our current best spacetime theory, the general theory of relativity. While some of these issues are touched on in the essays in this volume, I believe that profitable further exploration of them is called for and can be expected in the future.
    • One issue arises because the implicit distinction between ordinary matter and spacetime itself, a distinction simply assumed in the classical substantivalist-relationist debate of earlier years, is a distinction it is hard to maintain coherently in the face of general relativity. The identification of gravity with curvature of spacetime itself in the general theory of relativity leads to the conclusion that spacetime itself can embody mass-energy (although the lack of symmetry in the general spacetime model of the theory leads to grave questions of the global definability of the energy of the spacetime field). In the light of this, it simply isn't clear how the distinction between spacetime itself and "ordinary matter," a distinction so frequently utilized by the ordinary relationist, can be maintained. This problem for the relationist becomes even more crucial if one moves to some kind of "geometrodynamic" style of theory in which ordinary matter is identified with curved spacetime itself, rather than as an autonomous "inhabitant" of a spacetime arena. Further, traditional relationism relies quite heavily on Leibnizian arguments which rest on presupposed symmetries of spacetime. But in general relativity, where the models for the theories are, in general, nonsymmetric, these arguments lose much of their force. The older relationist arguments which tell us that, matter aside, each place in spacetime and each direction in it is just like every other are dubious indeed, in a theory in which intrinsically space-time features, like the magnitude of curvature, can discriminate pure spacetime event locations from one another.
    • I think that both of these issues require the relationist to carefully study how his arguments against substantival spacetime fit into broader philosophical schemes. While not inevitable, a predictable relationist response to the first problem above will be to move ordinary matter into the same dispensable category as substantival spacetime, accepting the substantivalist's claim that a consistent relationism ultimately results in a phenomenalistic approach to theories in general.
    • Responding to the second problem noted above will require the relationist to think through issues concerning identity and diversity with greater thoroughness. Even without symmetry, he will argue, the idea of spacetime itself is illegitimate. While structural features, indeed those with observable causal consequences, will, in a non-symmetric spacetime world, differentiate event-locations from one another by their purely spacetime features alone, the possibility of saving the phenomena by moving to an alternative world where the structure is the same but the identity of the spacetime locations having the structure is changed by a permutation of locations through structure will, he argues, show the illegitimacy of the substantivalist viewpoint. Here the consistent relationist will be led to consider the claim that just such a change, which keeps structure the same but which changes the identity of entity suffering the structure, is possible in the world of material things as well. And, once again, the consistent relationist will probably acknowledge that his antisubstantivalism vis-a-vis spacetime must, to be coherent, be generalized to an antirealism regarding ordinary matter as well.
    • At this point the relationist will need also to carefully examine his notion of identity and diversity, and, given his bent toward critiquing semantics2 from an epistemic point of view, probably look toward our basic notion of self-identity as the phenomenal origin of the notions of identity as projected onto the world of matter and of spacetime itself by the substantivalist.
    • On both these issues, taking the debate about spacetime as they do into some of the most intractable of general philosophical debates, we need far more clarity and enlightenment than is available to date, and, I believe, further work on these problems in the general philosophical context, and in the context of the specific issues governing the substantivalist-relationist debate about spacetime, will interact in ways which will be mutually clarificatory.
  11. Causal Order and Spatiotemporal Order
    • A persistently recurring theme in the philosophy of space and time is that there is an intimate connection between the spatiotemporal order of events in the world and the causal order among these events. Sometimes it is alleged that the connection is so fundamental that we ought to view the spatiotemporal structure of the world not as a primitive feature of it, but, rather, as a feature which ought, in some sense, to be "defined away" in terms of, or "reduced to," the causal order.
    • The thesis is frequently maintained in an ontological vein, for example, with claims to the effect that spatiotemporal structure is "nothing but" causal structure. Or that we ought to take as the genuine, or real, spatiotemporal structure of the world only that spatiotemporal structure which can, in some appropriate sense, be identified with causal structure. Frequently the doctrine of the ultimately causal nature of spatiotemporal structure is also alleged to have important consequences of an epistemological sort as well, as in, for example, claims to the effect that insofar as spatiotemporal structure is not fully determined by some appropriate causal structure, the attribution of the spatiotemporal structure to the world ought to be taken as merely "conventional" in some important sense.
    • Before one can judge the plausibility of a causal theory of spatiotemporal order, however, one first must have a clear idea of what claims the alleged causal reducibility thesis is actually making. As a number of essays in this volume attempt to show, this is none too easy a thing to do. For, as these essays argue, there is a wide variety of quite different, and indeed sometimes incompatible, claims that different theses of causal reducibility are making. Sometimes the differences between these claims can be seen as forthright components of the doctrine. But in other cases various exponents of causal theses seem not to have been clear in their own minds about just which version of a causal theory of spacetime they want to expound and defend.
    • Sometimes causal theses are being offered as a kind of reduction of the spatiotemporal order to the causal which parallels that alleged in phenomenalism as a reduction of material-object language to the language of immediate content of perception. In theories of this kind it is usually claimed that our entire epistemic access into spacetime structure is through causal structure. It is for this reason that we ought to take assertions about spatiotemporal structure to reduce to assertions about causal structure in their very meaning.
    • Sometimes, rather, the claim is that spatiotemporal structure reduces to causal structure in the sense that the theory of matter reduces to that of atoms or the theory of light reduces to that of electromagnetism. In these cases the claim is that structure of one kind reduces to that of the other because it is a fact of nature, discovered by the progress of empirical science, that the entities discussed at one level of discourse are simply identical to those referred to by the other theory. So, it is sometimes claimed, tables are just arrays of atoms, light waves are just electromagnetic waves, and, in a similar vein, spatiotemporal relations are just causal relations.
    • Various causal theories of spacetime are also differentiated by what they take the appropriate causal relations to be which constitute the basis of the causal structure to which the spacetime structure is to be reduced. For some authors the basic causal notion is that of one event having a determining influence on the occurrence of another. For others it is the possibility, rather than the actuality, of determining influence which is crucial. Other accounts rely in a fundamental way on the fact that in a relativistic world causation3 is taken to be mediated by the connection of the events by a continuous causal signal. Here it might be connection or connectability which is the basic causal notion. Or, rather, it might be the structure of the causal propagations themselves which is essential. These distinctions may sound trivial, but they are not, and quite different causal theories of spacetime result, depending on which of these options one adopts in one's theory. Finally, for other authors it is the algebraic structure among quantum measurements which constitutes the real causal order to which spacetime order is to be reduced.
    • The kind of relation between spatiotemporal and causal feature which is essential for the correctness of the causal theory again varies from theory to theory. Need the causal and spatiotemporal relations only be coextensive for the "definition" or "reduction" to be counted as established? Or is it lawlike coextensiveness which is demanded? Perhaps some stronger kind of necessity for the coextensiveness is what really is in mind, say the kind of necessity which is the result of an identification of one relation with another. Or, even stronger, is it an analytic meaning reduction among the relations which is being called for? Once again, there is a wide variety of causal theories of spacetime, with differing presuppostions and differing intended claims. They must be carefully sorted out before we can even begin to examine their plausibility and their immediate or remote consequences.
    • Finally, just what aspects of spatiotemporal structure are supposed to be accounted for causally? In some theories it is the topology of spacetime which is reduced to a causal notion. In others it is the metric of spacetime which is also to be accounted for causally. On top of this there is the very special theory which tells us that it is the asymmetry or directionality of time which is to be reduced to a notion not prima facie spatiotemporal. Here the alleged reduction is usually taken to be to the entropic increase of systems in the world in time, a notion not properly thought of as causal at all!
    • Pursuing these issues sometimes requires the careful consideration of a variety of contemporary physical theories in some detail. One example comes from the philosophical examination of the special theory of relativity. It is frequently claimed that simultaneity for distant events in the special theory of relativity is merely a conventional notion. Sometimes it is alleged that this is not true in the prerelativistic spacetime context, and that the ground of the distinction rests upon the fact that simultaneity is causally definable prerelativistically but not in the special theory of relativity. But consideration of the early work of Robb on relativity shows that, in certain senses, simultaneity, and indeed the entire metric of spacetime, is causally definable in the relativistic context. Understanding just what Robb's work does and does not show about the interrelation of causal and spatiotemporal structures in relativistic spacetimes; just what the relevance of his results is for various claims of definability or reducibility of spacetime to causal notions; and just what the relevance of these results to various allegations of conventionality is, is a subtle and difficult task. But it is worth pursuing, for in doing so one learns how many issues can be confounded together, and how much misdirection can result from practicing philosophy by slogans instead of by hard and detailed considerations of physics and philosophy.
    • Another fascinating and difficult test case is the study of the relation of topological structure to causal structure in the general theory of relativity. Here a full understanding of the physics requires that one bring to bear some of the most subtle considerations of the mathematics of spacetime structures. And the relevance of the results obtained to various philosophical questions is, once again, a matter which requires a good deal of thought in its own right. Ultimately, one discovers such results as the implausibility of causal theories of topology, construed in some ways, and the plausibility of other construals of causal theories of spacetime topology. But the plausibility of the latter versions is purchased, perhaps, at the price of realizing that what one called a causal theory really wasn't reasonably so designated at all.
    • Finally, on the alleged reducibility of the asymmetry of time to entropic features of the world, we again discover a host of difficult questions, many of them unresolved at the present time. While the essays in this volume take up some of these issues, in particular asking just what kind of reduction the alleged reduction is supposed to be, many difficult questions regarding the very nature of the concept of entropy, and of the structure of the statistical mechanical theory which defines it and in which it plays its explanatory role, remain to be given the close philosophical scrutiny they deserve.
    • The essays in this volume do pursue, at a certain level of abstraction, the general questions of types of alleged reducibility and definability, and some of the intrinsic difficulties of such claims, irrespective of the details which differentiate them, are brought to light. One issue which is hardly touched on here, and one which again requires far more philosophical attention than it has received, is the fact that almost all of these discussions on causal order and spatiotemporal order take place in a background which assumes the prequantum view of the world. Just what transformation the arguments must take when one accepts the necessity of viewing the whole of physics through the conceptual scheme of quantum theory4 remains to be seen.
  12. Reflections on These Essays
    • The purpose of these essays is not to expound and defend some one particular approach to the philosophy of science, but, rather, to explore in some detail the presuppositions and consequences of several alternative points of view. All too often philosophical debate becomes a matter of sloganeering, with, for example, "realists" opposing "fictionalists" where it hasn't been made clear just what the opposing points of view really amount to. Semantic issues regarding the meaning of the terms which function in our theories, epistemological issues regarding the warrant for belief or disbelief we might have in theories, ontological issues regarding the degree to which we ought to take the apparently referential language of theories as genuinely referential, and such methodological issues as what is to count as explanatory in science, form a complex and tangled whole. Unless we go a good deal further than has been done in disentangling some of the relevant strands, I believe that further progress will be much impeded.
    • The method which I primarily apply to gain insight into some of these complexes of issues is to confront philosophical doctrine with contemporary physical theory. The viewpoint held here is most certainly not that one can resolve philosophical issues in a simpleminded way by reference to the results of our best available current scientific theory. Quite the contrary, the essays try to show that the work of theoretical science takes place in a context in which various philosophical presuppositions are, consciously or unconsciously, continuously being utilized to reach theoretical conclusions. The hope is that by seeing how we do behave in resolving open theoretical questions in science, some light will be thrown on the philosophers' questions of how we ought to proceed methodologically, and how such methodological stances ought to reflect underlying semantic, epistemological, and ontological consequences of philosophical standpoints.
    • Once again, the issues will be complex. First, one must realize that at the frontier of theoretical science there is no simple "what science tells us." Rather, what we find is a complex body of theory, including, on occasion, incompatible scientific alternatives between which theoretical science cannot decide. Even when we look back at older results in science we sometimes discover that a kind of "openness" is present which allows us to view the very results of scientific research from several, not obviously compatible, points of view. The myth of a monolithic uncontroversial body of scientific theory, contrasted with the squabbling indecision of the philosophers who never agree on anything, is a myth, although one not without the degree of truth most stereotypes possess.
    • The complexity and fluidity of the issues treated here suggest that a rather "dialectic" means of investigation is the appropriate one, and it is such a method that the reader will discover in these essays. Issues in philosophy are taken up over and over, each time from a somewhat different perspective. Single philosophical controversies are tested against a multiplicity of scientific results on which they bear, and single scientific theories are repeatedly examined from a multitude of philosophical perspectives. Again and again it is emphasized that philosophical issues are highly interdependent, and that one cannot opt for a solution to one problem without accepting the relevant consequences, sometimes unwelcome, which follow in other areas. And, again and again, the necessity for an open-minded attitude with regard to theories in physics is emphasized, with an insistence that we ought not to be satisfied with confronting philosophy by the standard theoretical view understood in the most common way, but, instead, must look at the wide variety of theoretical options possible and must understand that even a single theoretical choice in science might look quite different depending on how one views it philosophically.
    • That the philosophical issues are of such great complexity, forcing us to look at numerous subtly distinguished alternatives and to engage in an intellectual juggling act of treating several interrelated but distinct issues simultaneously, sometimes makes for hard going in following the argument in some of these essays. The work of the reader is not made easier by the fact that the physical theories used as test cases here are themselves of a high level of abstractness. A full understanding of them would require a mastery of large areas of modern mathematics, and even the nontechnical treatment offered here requires the reader to try to grasp some of the subtle ideas of current mathematical physics. The reader shouldn't be discouraged if working through these essays sometimes seems like heavy going indeed.
    • Since topics are taken up again and again and treated in different ways and from different perspectives, a good way to approach this book would be to read through the essays from beginning to end, not worrying about the places where full comprehension is elusive. In this way one will gain an overall perspective on the structure of the problems being attacked and on the author's "dialectical" way of approaching them. A rereading of some of the more difficult essays subsequent to gaining this overview will probably find the reader less adrift in the complexities and better able to keep sight of the overall objectives while trying to sort out the necessary but intrusive details which sometimes tend to force one to lose sight of the overall direction in which the essay is going. I realize that this is asking a lot of the reader, and I can only hope that he will find his efforts rewarded by the understanding gained. The author begs forgiveness of his readers for those difficulties engendered by his inability of laying things out in the clearest and most perspicuous way possible. Suffice it to say that strenuous efforts were made to make the argument as straightforward and transparent as possible. I repeat, the issues are complex and difficult, and the gain in clarity which might result from oversimplification would, I am afraid, require paying too high a price in missing out on what are often crucial and fundamental issues.


Annotated printout filed in "Various - Papers on Identity Boxes: Vol 16 (S1: Sa-Sl)".

In-Page Footnotes

Footnote 1: See "Sklar (Lawrence) - Space, Time and Spacetime".

Text Colour Conventions (see disclaimer)

  1. Blue: Text by me; © Theo Todman, 2020
  2. Mauve: Text by correspondent(s) or other author(s); © the author(s)

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