The Theory of Relativity and A Priori Knowledge will hereafter be cited as "RAK. " The German edition is out of print. 2 H. Reichenbach, The Philosophy of ...

Several variant "Newtonian" theories of inertia and gravitation are described, and their scientific usefulness discussed. An examination of these theories is used to throw light on traditional epistemological and metaphysical questions about space and time. Finally these results are examined in the light of the changes induced by the transition from "Newtonian" to general relativistic spacetime.

In a number of publications, John Earman has advocated a tertium quid to the usual dichotomy between substantivalism and relationism concerning the nature of spacetime. The idea is that the structure common to the members of an equivalence class of substantival models is captured by a Leibniz algebra which can then be taken to directly characterize the intrinsic reality only indirectly represented by the substantival models. An alleged virtue of this is that, while a substantival interpretation of spacetime theories falls (...) prey to radical local indeterminism, the Leibniz algebras do not. I argue that the program of Leibniz algebras is subject to radical local indeterminism to the same extent as substantivalism. In fact, for the category of topological spaces of interest in spacetime physics, the program is equivalent to the original spacetime approach. Moreover, the motivation for the program--that isomorphic substantival models should be regarded as representing the same physical situation--is misguided. (shrink)

Where modern formulations of relatively theory use differentiable manifolds to space-time, Einstein simply used open sets of R 4 , following the then current methods of differential geometry. This fact aids resolution of a number of outstanding puzzles concerning Einstein's use of coordinate systems and covariance principles, including the claimed physical significance of covariance principles, their connection to relativity principles, Einstein's apparent confusion of coordinate systems and frames of reference, and his failure to distinguish active and passive transformations, especially in (...) the context of his hole and point-coincidence arguments. (shrink)

We here present explicit relational theories of a class of geometrical systems (namely, inner product spaces) which includes Euclidean space and Minkowski spacetime. Using an embedding approach suggested by the theory of measurement, we prove formally that our theories express the entire empirical content of the corresponding geometric theory in terms of empirical relations among a finite set of elements (idealized point-particles or events) thought of as embedded in the space. This result is of interest within the general phenomenalist tradition (...) as well as the theory of space and time, since it seems to be the first example of an explicit phenomenalist reconstruction of a realist theory which is provably equivalent to it in observational consequences. The interesting paper "On the Space-Time Ontology of Physical Theories" by Ken Manders, Philosophy of Science, vol. 49, number 4, December 1982, p. 575-590, has significant affinities to this one. We both, in a sense, try to formally vindicate Leibniz's notion of a relational theory of space, by constructing theories of spatial relations among physical objects which are provably equivalent to the standard absolutist theories. The essential difference between our approaches is that Manders retains Leibniz's explicitly modal framework, whereas I do not. Manders constructs a spacetime theory which explicitly characterizes the totality of possible configurations of physical objects, using a modal language in which the notion of a possible configuration occurs as a primitive. There is no doubt that this is a more accurate realization of Leibniz's own conception of space than the embedding-based approach developed here. However, it also remains open to objections (such as those cited here from Sklar) on account of the special appeal to modal notions. Our approach here, by contrast, aims to avoid the special appeal to modal notions by giving directly a set of laws which are satisfied by a configuration individually, if and only if it is one of the allowable ones. One thus avoids the need for reference to possible but not actual configurations or objects, in the statement of the spacetime laws. We may then take this alternative set of laws as the actual geometric theory, and do away with the hypothetical entity called 'space'. Yet at the same time there is no invocation of modality, except in the ordinary sense in which every physical theory constrains what is possible. So that a relationalist is not forced to utilize a modal language (though Leibniz certainly does.). (shrink)

This paper sketches a taxonomy of forms of substantivalism and relationism concerning space and time, and of the traditional arguments for these positions. Several natural sorts of relationism are able to account for Newton's bucket experiment. Conversely, appropriately constructed substantivalism can survive Leibniz's critique, a fact which has been obscured by the conflation of two of Leibniz's arguments. The form of relationism appropriate to the Special Theory of Relativity is also able to evade the problems raised by Field. I survey (...) the effect of the General Theory of Relativity and of plenism on these considerations. (shrink)

In the correspondence with Clarke, Leibniz proposes to construe physical theory in terms of physical (spatio-temporal) relations between physical objects, thus avoiding incorporation of infinite totalities of abstract entities (such as Newtonian space) in physical ontology. It has generally been felt that this proposal cannot be carried out. I demonstrate an equivalence between formulations postulating space-time as an infinite totality and formulations allowing only possible spatio-temporal relations of physical (point-) objects. The resulting rigorous formulations of physical theory may be seen (...) to follow Leibniz' suggestion quite closely. On the other hand, physical assumptions implicit in the postulation of space-time totalities are made explicit in the reconstruction of the space-time versions from the physical-relation versions. (shrink)

I argue that Earman and Norton's familiar "hole argument" raises questions as to whether GTR is a deterministic theory only given a certain assumption about determinism: namely, that to ask whether a theory is deterministic is to ask about the physical situations described by the theory. I think this is a mistake: whether a theory is deterministic is a question about what sentences can be proved within the theory. I show what these sentences look like: for interesting theories, a harmless (...) bit of infinitary logic puts in an appearance. (shrink)

By extending geometrodynamical phase space by embeddings and their conjugate momenta, one can homomorphically map the Lie algebra of space-time diffeomorphisms into the Poisson algebra of dynamical variables on the extended phase space.

This paper develops and defends three related forms of relationism about spacetime against attacks by contemporary substantivalists. It clarifies Newton's globes argument to show that it does not bear on relations that fail to determine geodesic motions, since the inertial effects on which Newton relies are not simply correlated with affine structure, but must be understood in dynamical terms. It develops remarks by Sklar and van Fraassen into relational versions of Newtonian mechanics, and argues that Earman does not show them (...) to trivialize the debate. (shrink)

Foundations of Space-Time Theories, by Michael Friedman, falls naturally into two parts. In the first, he presents the general framework within which he will characterize and discuss space-time theories, and then he devotes a chapter each to Newtonian physics, special relativity, and general relativity. Although there is some rich philosophical discussion along the way, these chapters are, of necessity, somewhat technical expositions of the general framework in action. It is in the second part, consisting of two substantial chapters, one on (...) relationalism, the other on conventionalism, that more general philosophical issues are addressed. (shrink)

This paper represents an attempt to clarify a number of long-standing issues concerning the nature and status of the special and general principles of relativity in particular and symmetry or invariance principles in general. An analysis of the active and passive interpretations of symmetry operations is offered. This analysis yields an evaluation of the old covariance-invariance issue. It also demonstrates that the passive interpretation, insofar as it is not trivial, is parasitic on the active picture. Finally, the analysis shows that (...) grave difficulties lie in the way of any attempt to generalize the special principle of relativity in a manner like the one Einstein originally proposed. (shrink)

Kant's argument from incongruent counterparts for substantival space is examined; it is concluded that the argument has no force against a relationist. The argument does suggest that a relationist cannot give an account of enantiomorphism, incongruent counterparts and orientability. The prospects for a relationist account of these notions are assessed, and it is found that they are good provided the relationist is some kind of modal relationist. An illustration and interpretation of these modal commitments is given.

In this paper Modern Essentialism is used to solve a problem of individuation of spacetime points in General Relativity that has been raised by a New Leibnizian Argument against spacetime substantivalism, elaborated by Earman and Norton. An earlier essentialistic solution, proposed by Maudlin, is criticized as being against both the spirit of metrical essentialism and the fundamental principles of General Relativity. I argue for a modified essentialistic account of spacetime points that avoids those obstacles.

Although Leibniz's writing forms an enormous corpus, no single work stands as a canonical expression of his whole philosophy. In addition, the wide range of Leibniz's work--letters, published papers, and fragments on a variety of philosophical, religious, mathematical, and scientific questions over a fifty-year period--heightens the challenge of preparing an edition of his writings in English translation from the French and Latin.

FIRST DAY INTERLOCUTORS: SALVIATI, SA- GREDO AND SIMPLICIO ALV. The constant activity which you Venetians display in your famous arsenal suggests to the ...

Part four of the Proceedings of the fifth International Congress of Logic, Methodology and Philosophy of Science, London, Ontario, Canada, August 27-September 2, 1975.

Skeptics have cast doubt on the idea that scientific theories give us a true picture of an objective world. Lawrence Sklar examines three kinds of skeptical arguments about scientific truth, and explores the important role they play within foundational science itself. Sklar demonstrates that these kinds of philosophical critique are employed within science, and reveals the clear difference between how they operate in a scientific context and more abstract philosophical contexts. The underlying theme of Theory and Truth is that science (...) and philosophy are essential to one another. Sklar advances the claim that one cannot understand the methods of science without a comprehension of philosophy, and one cannot fruitfully pursue philosophy of science without understanding fundamental science as well. (shrink)

The paper is about the physical theories which result when one identifies points in phase space related by symmetries; with applications to problems concerning gauge freedom and the structure of spacetime in classical mechanics.

We discuss the relationship between the interpretative problems of quantum gravity and those of general relativity. We argue that classical and quantum theories of gravity resuscitate venerable philosophical questions about the nature of space, time, and change; and that the resolution of some of the difficulties facing physicists working on quantum theories of gravity would appear to require philosophical as well as scientific creativity.

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This paper is concerned with the debate between substantival and relational theories of space-time, and discusses two difficulties that beset the relationalist: a difficulty posed by field theories, and another difficulty called the problem of quantities. A main purpose of the paper is to argue that possibility can not always be used as a surrogate of ontology, and that in particular that there is no hope of using possibility to solve the problem of quantities.