•  209
    Kant's Views on Non-Euclidean Geometry
    Proceedings of the Canadian Society for History and Philosophy of Mathematics 25 42-54. 2012.
    Kant's arguments for the synthetic a priori status of geometry are generally taken to have been refuted by the development of non-Euclidean geometries. Recently, however, some philosophers have argued that, on the contrary, the development of non-Euclidean geometry has confirmed Kant's views, for since a demonstration of the consistency of non-Euclidean geometry depends on a demonstration of its equi-consistency with Euclidean geometry, one need only show that the axioms of Euclidean geometry ha…Read more
  •  202
    The Kantian framework of complementarity
    Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 41 (4): 309-317. 2010.
    A growing number of commentators have, in recent years, noted the important affinities in the views of Immanuel Kant and Niels Bohr. While these commentators are correct, the picture they present of the connections between Bohr and Kant is painted in broad strokes; it is open to the criticism that these affinities are merely superficial. In this essay, I provide a closer, structural, analysis of both Bohr's and Kant's views that makes these connections more explicit. In particular, I demonstrate…Read more
  •  188
    Wittgenstein on Prior Probabilities
    Proceedings of the Canadian Society for History and Philosophy of Mathematics 23 85-98. 2010.
    Wittgenstein did not write very much on the topic of probability. The little we have comes from a few short pages of the Tractatus, some 'remarks' from the 1930s, and the informal conversations which went on during that decade with the Vienna Circle. Nevertheless, Wittgenstein's views were highly influential in the later development of the logical theory of probability. This paper will attempt to clarify and defend Wittgenstein's conception of probability against some oft-cited criticisms that s…Read more
  •  184
    Many worlds, the cluster-state quantum computer, and the problem of the preferred basis
    Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 43 (1): 35-42. 2012.
    I argue that the many worlds explanation of quantum computation is not licensed by, and in fact is conceptually inferior to, the many worlds interpretation of quantum mechanics from which it is derived. I argue that the many worlds explanation of quantum computation is incompatible with the recently developed cluster state model of quantum computation. Based on these considerations I conclude that we should reject the many worlds explanation of quantum computation.
  •  177
    Of the many and varied applications of quantum information theory, perhaps the most fascinating is the sub-field of quantum computation. In this sub-field, computational algorithms are designed which utilise the resources available in quantum systems in order to compute solutions to computational problems with, in some cases, exponentially fewer resources than any known classical algorithm. While the fact of quantum computational speedup is almost beyond doubt, the source of quantum speedup is s…Read more
  •  167
    Kant and Frege on Existence and the Ontological Argument
    History of Philosophy Quarterly 29 (4): 337-354. 2012.
    I argue that Kant's and Frege's refutations of the ontological argument are more similar than has generally been acknowledged. As I clarify, for both Kant and Frege, to say that something exists is to assert of a concept that it is instantiated. With such an assertion one expresses that there is a particular relation between the instantiating object and a rational subject - a particular mode of presentation for the object in question. By its very nature such a relation cannot be the property of …Read more
  •  157
    On the Significance of the Gottesman–Knill Theorem
    British Journal for the Philosophy of Science 68 (1): 91-121. 2017.
    According to the Gottesman–Knill theorem, quantum algorithms that utilize only the operations belonging to a certain restricted set are efficiently simulable classically. Since some of the operations in this set generate entangled states, it is commonly concluded that entanglement is insufficient to enable quantum computers to outperform classical computers. I argue in this article that this conclusion is misleading. First, the statement of the theorem is, on reflection, already evident when we …Read more
  •  138
    There has been a long-standing and sometimes passionate debate between physicists over whether a dynamical framework for quantum systems should incorporate not completely positive (NCP) maps in addition to completely positive (CP) maps. Despite the reasonableness of the arguments for complete positivity, we argue that NCP maps should be allowed, with a qualification: these should be understood, not as reflecting ‘not completely positive’ evolution, but as linear extensions, to a system’s entire …Read more
  •  138
    On the Physical Explanation for Quantum Computational Speedup
    Dissertation, The University of Western Ontario. 2013.
    The aim of this dissertation is to clarify the debate over the explanation of quantum speedup and to submit, for the reader's consideration, a tentative resolution to it. In particular, I argue, in this dissertation, that the physical explanation for quantum speedup is precisely the fact that the phenomenon of quantum entanglement enables a quantum computer to fully exploit the representational capacity of Hilbert space. This is impossible for classical systems, joint states of which must always…Read more
  •  137
    How-Possibly Explanations in (Quantum) Computer Science
    Philosophy of Science 82 (5): 737-748. 2015.
    A primary goal of quantum computer science is to find an explanation for the fact that quantum computers are more powerful than classical computers. In this paper I argue that to answer this question is to compare algorithmic processes of various kinds and to describe the possibility spaces associated with these processes. By doing this, we explain how it is possible for one process to outperform its rival. Further, in this and similar examples little is gained in subsequently asking a how-actua…Read more
  •  118
    On Thomas Hobbes's Fallible Natural Law Theory
    History of Philosophy Quarterly 28 (2): 175-190. 2011.
    It is not clear, on the face of it, whether Thomas Hobbes's legal philosophy should be considered to be an early example of legal positivism or continuous with the natural-law tradition. On the one hand, Hobbes's command theory of law seems characteristically positivistic. On the other hand, his conception of the "law of nature," as binding on both sovereign and subject, seems to point more naturally toward a natural-law reading of his philosophy. Yet despite this seeming ambiguity, Hobbes schol…Read more
  •  108
    Quantum computing
    with Amit Hagar
    Stanford Encyclopedia of Philosophy. 2019.
    Combining physics, mathematics and computer science, quantum computing and its sister discipline of quantum information have developed in the past few decades from visionary ideas to two of the most fascinating areas of quantum theory. General interest and excitement in quantum computing was initially triggered by Peter Shor (1994) who showed how a quantum algorithm could exponentially “speed-up” classical computation and factor large numbers into primes far more efficiently than any (known) cla…Read more
  •  96
    Reconsidering No-Go Theorems from a Practical Perspective
    British Journal for the Philosophy of Science 69 (3): 633-655. 2018.
    I argue that our judgements regarding the locally causal models that are compatible with a given constraint implicitly depend, in part, on the context of inquiry. It follows from this that certain quantum no-go theorems, which are particularly striking in the traditional foundational context, have no force when the context switches to a discussion of the physical systems we are capable of building with the aim of classically reproducing quantum statistics. I close with a general discussion of th…Read more
  •  91
    The conditions of tolerance
    with Ryan Muldoon and Michael Borgida
    Politics, Philosophy and Economics 11 (3): 322-344. 2012.
    The philosophical tradition of liberal political thought has come to see tolerance as a crucial element of a liberal political order. However, while much has been made of the value of toleration, little work has been done on individual-level motivations for tolerant behavior. In this article, we seek to develop an account of the rational motivations for toleration and of where the limits of toleration lie. We first present a very simple model of rational motivations for toleration. Key to this m…Read more
  •  71
    Although computation and the science of physical systems would appear to be unrelated, there are a number of ways in which computational and physical concepts can be brought together in ways that illuminate both. This volume examines fundamental questions which connect scholars from both disciplines: is the universe a computer? Can a universal computing machine simulate every physical process? What is the source of the computational power of quantum computers? Are computational approaches to sol…Read more
  •  51
    Which Rights Are Basic Rights?
    Gnosis 9 (1): 1-11. 2007.
    In this paper I explain and defend the content and justification of John Rawls's conception of human rights, as he outlines it in his major work: The Law of Peoples. I focus, in particular, on the criticisms of Allen Buchanan. Buchanan distinguishes four lines of argument that Rawls uses to derive what, according to Buchanan, is a 'lean' list of human rights : the Political Conception Argument, the Associationist Argument, the Cooperation Argument, and finally the Functionalist Argument. In each…Read more
  •  51
    I argue that Immanuel Kant's critical philosophy—in particular the doctrine of transcendental idealism which grounds it—is best understood as an `epistemic' or `metaphilosophical' doctrine. As such it aims to show how one may engage in the natural sciences and in metaphysics under the restriction that certain conditions are imposed on our cognition of objects. Underlying Kant's doctrine, however, is an ontological posit, of a sort, regarding the fundamental nature of our cognition. This posit, s…Read more
  •  39
    We use Bub's (2016) correlation arrays and Pitowksy's (1989b) correlation polytopes to analyze an experimental setup due to Mermin (1981) for measurements on the singlet state of a pair of spin-12 particles. The class of correlations allowed by quantum mechanics in this setup is represented by an elliptope inscribed in a non-signaling cube. The class of correlations allowed by local hidden-variable theories is represented by a tetrahedron inscribed in this elliptope. We extend this analysis to p…Read more
  •  38
    Computational complexity theory is a branch of computer science dedicated to classifying computational problems in terms of their difficulty. While computability theory tells us what we can compute in principle, complexity theory informs us regarding our practical limits. In this chapter I argue that the science of \emph{quantum computing} illuminates complexity theory by emphasising that its fundamental concepts are not model-independent, but that this does not, as some suggest, force us to rad…Read more
  •  37
    Information causality, the Tsirelson bound, and the ‘being-thus’ of things
    Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 72 266-277. 2020.
    The principle of 'information causality' can be used to derive an upper bound---known as the 'Tsirelson bound'---on the strength of quantum mechanical correlations, and has been conjectured to be a foundational principle of nature. In this paper, however, I argue that the principle has not to date been sufficiently motivated to play this role; the motivations that have so far been given are either unsatisfactorily vague or else amount to little more than an appeal to intuition. I then consider h…Read more
  •  32
    Nativist Models of the Mind
    Gnosis 9 (3): 1-22. 2008.
    I give a defense of the Massive Modularity hypothesis: the view that the mind is composed of discrete, encapsulated, informationally isolated computational structures dedicated to particular problem domains. This view contrasts with Psychological Rationalism: the view that mental structures take the form of unencapsulated representational items, all available as inputs to one domain-general computational processor. I argue that although Psychological Rationalism is in principle able to overcome …Read more
  •  11
    This is an extended essay review of Tanya and Jeffrey Bub’s Totally Random: Why Nobody Understands Quantum Mechanics: A serious comic on entanglement. We review the philosophical aspects of the book, provide suggestions for instructors on how to use the book in a class setting, and evaluate the authors’ artistic choices in the context of comics theory. Although Totally Random does not defend any particular interpretation of quantum mechanics, we find that, in its mode of presentation, Totally Ra…Read more
  • This book offers a thorough technical elaboration and philosophical defense of an objectivist informational interpretation of quantum mechanics according to which its novel content is located in its kinematical framework, that is, in how the theory describes systems independently of the specifics of their dynamics. It will be of interest to researchers and students in the philosophy of physics and in theoretical physics with an interest in the foundations of quantum mechanics. Additionally, part…Read more
  • This chapter is about Grete Hermann, a philosopher-mathematician who productively and mutually beneficially interacted with the founders of quantum mechanics in the early period of that theory's elaboration. Hermann was a neo-Kantian philosopher. At the heart of Immanuel Kant's critical philosophy lay the question of the conditions under which we can be said to know something objectively, a question Hermann found to be particularly pressing in quantum mechanics. Hermann's own approach to Neo-Kan…Read more