Philosophy Theses and Dissertations
Permanent URI for this collectionhttp://hdl.handle.net/1903/2799
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Item Structuralism and Natural Philosophy: Method, Metaphysics and Explanation(2009) Cifone, Michael Christian; Bub, Jeffrey; Philosophy; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This dissertation is an examination of the foundations of what I call a "fourth" tradition of analytical-scientific philosophy, the tradition of "structuralism". It is a disavowal of a metaphysics of substances and/or entities in the pursuit of scientific theory and truth. We look, in particular, at the current manifestation of this tradition, which advances the thesis of "structural realism"; we ask how tenable this thesis is, and whether we can weaken it. I argue that we should focus on methodology--a program for the formulation of scientific hypotheses about the sorts of things there are--rather than on metaphysics per se. We replace "substance" with "relation" as the basic ontic posit, and hold that substances or entities are metaphysically derivative from relational structure. Thus, the thesis is not that "there are no things" (or that "everything must go", as Ladyman et al. suppose); rather, the thesis is that the things (entities or substances) are relational structure, and there is no complete specification of an independent entity that is not itself more relational structure (so a metaphysics of substances is merely secondary to that of relational structure). I also suggest that there is no complete, unitary or monistic theory of what `structure' itself is. That is, I hold that there is no "total" structure of which everything that is relational structure is a "part", on the grounds that this would constitute an "illegitimate totality" in Russell's sense (the claim that "everything is structural" does not mean that there is a single structure which everything has--what a monistic theory of structure seems to demand). We then turn to the question of scientific explanation in light of structural realism: can there be explanation without a metaphysics of substances? I answer affirmatively. I then turn to two cases where, I argue, structuralism (and the specific thesis of structural realism) is in play regarding scientific explanation: quantum information theory, and the recent attempt to render quantum mechanics local by re-interpreting physical law time symmetrically. I conclude with a consideration of some objections to structuralism, and an articulation of the general view of metaphysics that structuralism seems to presuppose.Item Entanglement and Information in Algebraic Quantum Theories(2008) Valente, Giovanni; Bub, Jeffrey; Philosophy; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The algebraic approach to physical theories provides a general framework encompassing both classical and quantum mechanics. Accordingly, by looking at the behaviour of the relevant algebras of observables one can investigate structural and conceptual differences between the theories. Interesting foundational questions can be formulated algebraically and their answers are then given in a mathematically compelling way. My dissertation focuses on some philosophical issues concerning entanglement and quantum information as they arise in the algebraic approach. The se two concepts are connected in that one can exploit the non-local character of quantum theory to construct protocols of information theory which are not realized in the classical world. I first introduce the basic concepts of the algebraic formalism by reviewing von Neumann's work on the mathematical foundations of quantum theories. After presenting the reasons why von Neumann abandoned the standard Hilbert space formulation in favour of the algebraic approach, I show how his axiomatic program remained a mathematical "utopia" in mathematical physics. The Bayesian interpretation of quantum mechanics is grounded in information-theoretical considerations. I take on some specific problems concerning the extension of Bayesian statistical inference in infinite dimensional Hilbert space. I demonstrate that the failure of a stability condition, formulated as a rationality constraint for classical Bayesian conditional probabilities, does not undermine the Bayesian interpretation of quantum probabilities. I then provide a solution to the problem of Bayesian noncommutative statistical inference in general probability spaces. Furthermore, I propose a derivation of the a priori probability state in quantum mechanics from symmetry considerations. Finally, Algebraic Quantum Field Theory offers a rigorous axiomatization of quantum field theory, namely the synthesis of quantum mechanics and special relativity. In such a framework one can raise the question of whether or not quantum correlations are made stronger by adding relativistic constraints. I argue that entanglement is more robust in the relativistic context than in ordinary quantum theory. In particular, I show how to generalize the claim that entanglement across space-like separated regions of Minkowski spacetime would persist, no matter how one acts locally.Item Clifford Algebra: A Case for Geometric and Ontological Unification(2008-04-17) Kallfelz, William Michael; Bub, Jeffrey; Philosophy; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Robert Batterman's ontological insights (2002, 2004, 2005) are apt: Nature abhors singularities. "So should we," responds the physicist. However, the epistemic assessments of Batterman concerning the matter prove to be less clear, for in the same vein he write that singularities play an essential role in certain classes of physical theories referring to certain types of critical phenomena. I devise a procedure ("methodological fundamentalism") which exhibits how singularities, at least in principle, may be avoided within the same classes of formalisms discussed by Batterman. I show that we need not accept some divergence between explanation and reduction (Batterman 2002), or between epistemological and ontological fundamentalism (Batterman 2004, 2005). Though I remain sympathetic to the 'principle of charity' (Frisch (2005)), which appears to favor a pluralist outlook, I nevertheless call into question some of the forms such pluralist implications take in Robert Batterman's conclusions. It is difficult to reconcile some of the pluralist assessments that he and some of his contemporaries advocate with what appears to be a countervailing trend in a burgeoning research tradition known as Clifford (or geometric) algebra. In my critical chapters (2 and 3) I use some of the demonstrated formal unity of Clifford algebra to argue that Batterman (2002) equivocates a physical theory's ontology with its purely mathematical content. Carefully distinguishing the two, and employing Clifford algebraic methods reveals a symmetry between reduction and explanation that Batterman overlooks. I refine this point by indicating that geometric algebraic methods are an active area of research in computational fluid dynamics, and applied in modeling the behavior of droplet-formation appear to instantiate a "methodologically fundamental" approach. I argue in my introductory and concluding chapters that the model of inter-theoretic reduction and explanation offered by Fritz Rohrlich (1988, 1994) provides the best framework for accommodating the burgeoning pluralism in philosophical studies of physics, with the presumed claims of formal unification demonstrated by physicists choices of mathematical formalisms such as Clifford algebra. I show how Batterman's insights can be reconstructed in Rohrlich's framework, preserving Batterman's important philosophical work, minus what I consider are his incorrect conclusions.