Mechanical and economic considerations are such that the text of this paperback edition differs from the original only in the correction of a number of typographical errors and other minor mistakes redeemable by changing a few words.
Were a new edition to appear, though, I would make a number of substantial revisions and additions. I will use the opportunity of this preface just to indicate the direction in which some of these more important changes might go.
- In (IV, E, 1) a "causal" definition of temporal betweenness is given.
- In (IV, E, 2) it is suggested that this definition breaks down in spacetimes which are causally pathological. As David Malament argues (in his review1 of this book in Journal of Philosophy) the account here is misleading. There exist definitions of temporal betweenness, framed in terms of the same primitives I use, which will hold up in any general relativistic spacetime.
- The situation is, rather, like this. In appropriately non-pathological spacetimes a full definition of the topology in terms of the relation of causal connectibility among events is possible. In pathological spacetimes such a definition breaks down. But the full topology is always at least defined, in a sense which can be made precise, by the class of causal curves of the spacetime.
- Nonetheless, the basic argument of (IV, E, 3) still goes through I believe. The causal theory of time as it is usually meant philosophically still appears to me to be an allegation that from a primitive knowledge of certain causal relationships, without presupposing any "direct awareness" of spatio-temporal relationships, one could reconstruct the spatiotemporal order of the world. But, I would still allege, the kind of causal relationships one would need for such a "reconstruction by definition" of the spacetime topology would be those (knowing the class of continuous causal curves, for example) which we could determine only if we had already the ability to discriminate topological features of the spacetime (the class of continuous timelike or null curves, for example).
- Still, there may be something philosophically important to the fact that knowing a proper subset of the topological features is enough to fix the rest. For one might then argue that it is just those features of the topology which we discover, upon epistemological analysis, to be "immediately apprehendible" that are sufficient to fully determine the topology. So now a kind of "reductionism" seems to have some plausibility. But it is not a "reduction" of spatio-temporal to (prima facie) non-spatio-temporal, but of all the spatio-temporal concepts to an (apparently) proper subset of them.
- These considerations are relevant in another way as well. If these topological aspects of spacetime are really the directly ascertainable root facts upon which our theories are to be constructed, many of Reichenbach's allegations about the conventionality of topology require further scrutiny. In particular one might make a case for certain global features being conventional (depending upon our choices in individuating events) but that certain local aspects (what classes of spacetime points are continuous) are among the non-conventional "brute facts" of experience.
- Despite the skepticism evidenced throughout the book about "necessary" or "analytic" propositions so common in philosophical theories of space and time, it would seem that further exploration of the connections between such concepts as spatio-temporal continuity, genidentity and causal connection is in order. Not in the hopes of reducing all spatiotemporal concepts to those prima facie non-spatio-temporal but, rather, in the hopes of sorting out the spatio-temporal components of the other concepts. Finally, we need to be much clearer about the very fundamentul problem of connecting the "immediately apprehendible" features of our "subjective" spatio-temporal experience with our hypothesized physical spatio-temporal structure of the world.
- In Chapter V I believe a greatly expanded treatment of the problem of the direction of time is necessary. First of all the discussion of the physical aspects of the asymmetry of the world in time requires much supplementation to be adequate. More importantly I think much more needs to be said about just what the content of a philosophical theory of the direction of time is supposed to be and whether the assertions of such a theory could be justified. In particular I think it would be very worthwhile to explore the question as to why a "gravitational theory of up and down" seems obviously correct, why a "weak interaction theory of left and right" seems obviously wrong, and, most importantly, why an entropic theory of the direction of time seems so persistently controversial. I believe that this would require a much more thorough exploration of the notion of our "subjective" sense of time direction and its relation to the "physical direction of time" and of the alleged inter-connections between such varied asymmetries as the subjective, the entropic, the causal, the epistemic, etc. In particular I now think the present treatment is unfair to the subtlety of the Boltzmann-Reichenbach approach, although I am still inclined to believe that that approach leaves many questions to be resolved.
- (III, D, 3) should be supplemented by a treatment of a curved neo-Newtonian spacetime in which the gravitational field is assimilated to the geometry in a completely non-relativistic context just as it is in the relativistic context by the theory of general relativity.
- The treatment of abstractions from Riemannian geometry in (II, B, 6) should be supplemented by a treatment of projective and conformal geometries which lie, in their abstractness, between affine geometry and the theory of differential manifolds in general.
- The treatment of global aspects of spacetime in (IV, D) should be supplemented by a discussion of the hierarchy of notions of causal non-pathology, including the notion of stable causality2, and by a discussion of the notion of a global time function for a spacetime. There should also be treatments of so-called non-predictive and indistinguishable space-times in which interesting consequences of the relativistic limits on the physical possibility of acquiring information are applied to world models for general relativity.
- (II, D, 2) should be supplemented by a discussion of alleged limitations on the principle of equivalence.
- Finally, there are numerous minor errors of mathematics and physics throughout the text which it has been impossible to repair in the present addition. The author would be delighted to have these pointed out to him by readers in the hopes that at some future date a more accurate version may appear.
- Since the manuscript was submitted for publication numerous books and articles of interest have appeared. Some recent works of interest are:
… Lawrence Sklar, February 1976
- Misner, C., Thorne, K., and Wheeler, J., Gravitation3
which, among other things, gives an extensive account of the application of modern mathematics to general relativity;
- Hawking, S., and Ellis, G., The Large Scale Structure of Space-Time,
a brilliant and comprehensive study of global properties of spacetime in general relativity; and
- Davies, P., The Physics of Time Asymmetry,
which is an important study of the physics relevant to the problem of the "direction of time."
- Minnesota Studies in the Philosophy of Science, Vol. VIII.
A sample of recent philosophical work in space and time
Footnote 1: See "Malament (David) - Review of 'Space, Time, and Spacetime' by Lawrence Sklar".
Footnote 3: See "Misner (Charles W.), Thorne (Kip S.) & Wheeler (John Archibald) - Gravitation".
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