The authors of the Rainich-Misner-Wheeler theory no longer believe that everything physical can be accounted for in terms of the topological-geometrical structure of ordinary spacetime. However, many physicists and philosophers entertain the possibility that a geometrodynamics (a theory which accounts for sources as well as fields in terms of topological-geometrical structure) may be feasible in the context of a more general topology. In this dissertation I consider two topological-geometrical models (based upon a single suggestive formalism) in which a geometrodynamics is both feasible and pedagogically advantageous. Specifically I consider the topology which is constituted by the real domains of the two broad classes of rotation groups: those characterized by the commutator and anti-commutator algebras. I then adopt a Riemannian geometric structure and show that the monistically geometric interpretation of this formalism restricts displacements on the proposed manifold to integral multiples of a universal constant. Secondly I demonstrate that in the context under consideration, this constraint affects a very interesting ontological reduction: the unification of quantum mechanics with a discrete, multidimensional extension of general relativity. A particularly interesting feature of this unification is that it includes and (for the world which is characterized by energy levels which range in magnitude from low to intermediately high) requires the choice cf an SL(2,R)xSU(3)-symmetric realization of the proposed, generic formalism which is a lattice of spins π and π/2. (This is in the context of the same universally constant scale factor as that which yields the quantization conditions described above.) If the vertices of this lattice are associated with the fundamental particles, then the resulting theory predicts and precludes the same interactions as the standard supersymmetry theory. In addition to the ontological reduction which is provided, and the restriction to supersymmetry, the proposed theory may also represent a scientifically useful extension of conventional theory in that it suggests a means of understanding the apparently large energy productions of the quasars and relates Planck's constant to the size of the universe.

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A program for advancing a new philosophical account of physical laws is presented. The program is non-reductive in that it maintains that any correct account of physical laws must recognize law sentences as irreducible--that is, as not admitting of an analysis which does not invoke any unanalyzed nomic facts (i.e. causal statements, law statements, subjunctive conditionals, etc.). The program has the unusual attraction of being consistent with Nominalism and epistemically in the spirit of Empiricism. Initially motivating my program is a two-stage attack in chapters two and three on all reductive accounts. The first stage of the attack is on traditional reductive accounts. Traditional reductive accounts are those accounts which do not invoke abstract entities in addressing nomic modality, i.e. in distinguishing universal laws from accidentally true generalizations or in explaining the relationship between statements of probability and statements of relative frequency. These accounts include those of Brian Skyrms, David Lewis, and Bas van Fraassen. The second stage of the attack is on all non-traditional reductive accounts. These accounts include David Armstrong's Nomic Realism. The two-stage attack exhausts the ontological ground for a reduction of laws. It is concluded that no reductive accounts of physical laws is possible. Chapter four spells out the details of my positive program. The program calls for (i) statement of the basic philosophical truths about nomic modality, (ii) the specification of axiomatic principles governing physical laws, and (iii) the analysis of nomic facts in terms of other nomic facts. The basic truths about nomic modality are stated in full. Foremost among these is the Irreducibility Thesis which states that law sentences are irreducible. Some examples of axiomatic principles governing physical laws are specified and one example of an analysis of nomic facts in terms of other nomic facts is given. The analysis is of general causal statements. Time is also spent in chapter four critically reviewing other accounts in the history of philosophy which have recognized law sentences as irreducible. The final chapter addresses the most common and the most significant objection to my positive program. That objection is the epistemological challenge of Empiricism. I argue that my program and, in particular, the Irreducibility Thesis are epistemologically innocuous.

Thesis (Ph. D.)--Columbia University, 1931. / Vita.

This dissertation gives a general account of the properties of unitarily inequivalent representations (UIRs) in both canonical quantum field theory and algebraic quantum field theory. A simple model is constructed and then used to show how to build a broad spectrum of UIRs including a version of Haag’s theorem. Haag and Kastler,P, two of the founding fathers of algebraic quantum field theory, argue that the problems posed by UIRs are solved by adopting a notion of equivalence that is weaker than unitary equivalence, which they refer to as physical equivalence. In the dissertation, it is shown that their notion does not provide a suitable classificatory schema. Some of the most important physical representations fail to satisfy the mathematical conditions of their notion. However, Haag and Kastler's notion has an unexpected connection with classical observables. A theorem is proven in which two representations make the same predictions with respect to all classical observables if and only if they satisfy their notion of physical equivalence. Following Haag and Kastler's lead, it was claimed by most proponents of algebraic quantum field theory that all physical content resides in a specific class of observables. It is shown in the dissertation that such claims are exaggerated and misleading. UIRs are used to elucidate the nature of quantum field theory by showing that UIRs have different expectation values for some classical observables of the system, such as temperature and chemical potential, which are not in Haag and Kastler’s specific class. It is shown how UIRs may be used to construct classical observables. To capture the physical content of quantum field theory it is shown that a much larger algebra than that of Haag and Kastler is necessary. Finally, the arguments that UIRs are incommensurable theories are shown to be flawed. The lesson of UIRs is that the mathematical structures in both canonical quantum field theory and Haag and Kastler’s version of algebraic quantum field theory are not sufficient to capture all of the physical content that UIRs represent. A suitable algebraic structure for quantum field theory is provided in the dissertation. / text

The thesis focuses on what impact the use of idealizations has on the realism/anti-realism debate concerning the fundamental laws of physics. My aim is modest. It is not to present an argument for either the realist or the anti-realist position but rather to show where the debate stands once we have considered recent arguments by Laymon and Cartwright which have made use of the notion of idealization assumptions. My intent is to point out the difficulties of Laymon's argument for realism in the hope of showing what must be accomplished in providing a more convincing argument for realism. I will also suggest that although Laymon's proposal is problematic, it still poses a serious problem for van Fraassen's form of anti-realism, constructive empiricism.

This thesis examines the idea that when a physical theory contains symmetries, the theory should be interpreted in such a way that symmetry-related models represent the same physical state of affairs. It argues that we can best do so by drawing on analogies to ideas in philosophy of logic and language: specifically, by thinking of symmetries as a means of translating a theory into itself. It consists of six chapters, together with an introduction and conclusion. In Chapter 1, I set up the main ideas needed to more precisely frame the question at hand: namely, the notions of symmetry, interpretation, and possibility. I make some remarks about how I take these to be connected. In Chapter 2, I argue that isomorphic models should be interpreted as equivalent. After giving some motivations for doing so, I consider the main obstruction: how to provide an account of de re modality. I review how counterpart theory may be used to overcome this obstruction, and clarify how counterpart theory relates to other positions in the debate over modality de re. In Chapter 3, I show that the metaphysical debate over quidditism can be made precise by drawing on notions of translation from model theory, and argue in favour of an anti-quidditist attitude towards interpreting theories. I then consider the special case of translating a theory into itself: how such a theory should be interpreted, and what reformulations of the theory such an interpretation suggests. In Chapter 4, I turn my attention to physics. I define the notion of an internal symmetry for a theory, and argue that they may be regarded as translations from a theory into itself (in the sense of Chapter 3); and, hence, that symmetry-related models should be interpreted as equivalent. Drawing on the analogy further, I look at how the theory may be reformulated to take this interpretation into account. In Chapter 5, I look at external symmetries. I argue, drawing on ideas from Chapters 2 and 3, that models related by external symmetries should also be interpreted as equivalent. I discuss how implementing this interpretational lesson bears on finding the spacetime structure appropriate to a theory. In Chapter 6, I consider a specific external symmetry: the accelerative symmetry of Newtonian gravitation. I show that one can reformulate the theory to take this into account, setting gravitation on a spacetime structure that has absolute rotation but no absolute acceleration.

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