Michael Cuffaro

Works in progress or under review

  • Quantum Theory is About Open Systems (with Stephan Hartmann). To appear in Cuffaro & Hartmann (eds.), Open Systems: Physics, Metaphysics, and Methodology
  • Kantianism with a Human Face: Grete Hermann's Critical Philosophy (with Guido Bacciagaluppi and Elise Crull)
  • Complete positivity and relatively local operations in algebraic quantum field theory (working title – with Stephan Hartmann and Giovanni Valente)


    Articles, book chapters, and book reviews
  • The Open Systems View (with Stephan Hartmann). Philosophy of Physics, 2(1) (2024), 6: 1-27.
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    • There is a deeply entrenched view in philosophy and physics, the closed systems view, according to which isolated systems are conceived of as fundamental. On this view, when a system is under the influence of its environment this is always described in terms of a coupling between it and a separate system, which taken together are isolated. There is an alternative, the open systems view, according to which systems interacting with their environment are conceived of as fundamental, and the environment’s influence is represented via the dynamical equations that govern the system of interest’s evolution. In this paper we propose (although the formalism is not original to us) a theoretical framework which we call the general quantum theory of open systems (GT), within which one can make sense of the dynamics of open quantum systems in fundamental terms, and we argue that the open systems view, as formalized in GT, is fundamental in quantum theory.
  • The Measurement Problem is a Feature, Not a Bug – Schematising the Observer and the Concept of an Open System on an Informational, or (neo-)Bohrian, Approach. Entropy, 25 (2023), 1410.
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    • I flesh out the sense in which the informational approach to interpreting quantum mechanics, as defended by Pitowsky and Bub and lately by a number of other authors, is (neo-)Bohrian. I argue that on this approach, quantum mechanics represents what Bohr called a "natural generalisation of the ordinary causal description" in the sense that the idea (which philosophers of science like Stein have argued for on the grounds of practical and epistemic necessity), that understanding a theory as a theory of physics requires that one be able to "schematise the observer" within it, is elevated in quantum mechanics to the level of a postulate in the sense that interpreting the outcome of a measurement interaction as providing us with information about the world, requires as a matter of principle the specification of a schematic representation of an observer in the form of a `Boolean frame'---the Boolean algebra representing the yes-or-no questions associated with a given observable representative of a given experimental context. I argue that the approach's central concern is with the methodological question of how to assign physical properties to what one takes to be a system in a given experimental context, rather than the metaphysical question of what a given state vector represents independently of any context, and I show how the quantum generalisation of the concept of an open system may be used to assuage Einstein's complaint that the orthodox approach to quantum mechanics runs afoul of the supposedly fundamental methodological requirement to the effect that one must always be able, according to Einstein, to treat spatially separated systems as isolated from one another.
  • Review of Slobodan Perovic's From Data to Quanta: Niels Bohr’s Vision of Physics. Philosophy of Science, 91(2) (2023), pp. 525-529.
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  • The Open Systems View and the Everett Interpretation (with Stephan Hartmann). Quantum Reports, 5(2) (2023), 418-425.
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    • It is argued that those who defend the Everett, or ‘many-worlds’, interpretation of quantum mechanics should embrace what we call the general quantum theory of open systems (GT) as the proper framework in which to conduct foundational and philosophical investigations in quantum physics. GT is a wider dynamical framework than its alternative, standard quantum theory (ST). This is true even though GT makes no modifications to the quantum formalism. GT rather takes a different view, what we call the open systems view, of the formalism; i.e., in GT, the dynamics of systems whose physical states are fundamentally represented by density operators are represented as fundamentally open as specified by an in general non-unitary dynamical map. This includes, in principle, the dynamics of the universe as a whole. We argue that the more general dynamics describable in GT can be physically motivated, that there is as much prima facie empirical support for GT as there is for ST, and that GT could be fully in the spirit of the Everett interpretation—that there might, in short, be little reason for an Everettian not to embrace the more general theoretical landscape that GT allows one to explore.
  • Transcendental Idealism and its influence on Nineteenth Century Science. Forthcoming in History and Philosophy of Modern Science: 1750-1900, Crull, E., and Peterson, E. (eds.), Bloomsbury.
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    • In this chapter we motivate and introduce the doctrine of transcendental idealism as expounded by Immanuel Kant (1724--1804), the general theory of matter and principle of natural purpose that he took it to ground, as well as the influence of transcendental idealism, via its various philosophical (re-)interpretations, on some of the more important conceptual developments in mathematical physics and in the life sciences over the course of nineteenth century.
  • Grete Hermann, Quantum Mechanics, and the Evolution of Kantian Philosophy. In Women in the History of Analytic Philosophy (Springer-Verlag), J. Peijnenburg and S. Verhaegh eds. (2022).
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    • 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-Kantianism was Neo-Friesian. Jakob Friedrich Fries, like Kant, had understood critical philosophy to be an essentially epistemic project. Fries departed from Kant in his account of the elements involved in our cognition. In this chapter it is discussed how, beginning from a neo-Friesian understanding of critical philosophy, Hermann is led to conclude that quantum mechanics shows us that physical knowledge is fundamentally split; that the objects of quantum mechanics are only objects from a particular perspective and in the context of a particular physical interaction. It will be seen how Hermann's solution to the problem of objectivity in quantum mechanics is a natural one from a neo-Friesian point of view, even though it disagrees with those offered by more orthodox versions of Kantian doctrine.
  • The Philosophy of Quantum Computing. In Quantum Computing in the Arts and Humanities: An Introduction to Core Concepts, Theory and Applications (Springer-Verlag), Eduardo Miranda, ed. (2022).
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    • From the philosopher's perspective, the interest in quantum computation stems primarily from the way that it combines fundamental concepts from two distinct sciences: physics (especially quantum mechanics) and computer science, each long a subject of philosophical speculation and analysis in its own right. Quantum computing combines both of these more traditional areas of inquiry into one wholly new (if not quite independent) science. There are philosophical questions that arise from this merger, and philosophical lessons to be learned. Over the course of this chapter we discuss what I take to be some of the most important.
  • Essay review (with Emerson P. Doyle) of Bub & Bub's Totally Random. Foundations of Physics, 51 (2021), 28:1-28:16.
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    • 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 Random is a beautiful expression and illustration of the information-theoretic interpretation and its value.
  • "Information Causality, the Tsirelson Bound, and the 'Being-Thus' of Things." Studies in History and Philosophy of Modern Physics 72 (2020), 266-277
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    • 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. To date, however, it has not been sufficiently motivated to play such a foundational role. The motivations that have so far been given are, as I argue, either unsatisfactorily vague or appeal to little if anything more than intuition. Thus in this paper I consider whether some way might be found to successfully motivate the principle. And I propose that a compelling way of so doing is to understand it as a methodological generalisation of Einstein's principle of the mutually independent existence—the `being-thus'—of spatially distant things. In particular I first describe an argument, due to Demopoulos, to the effect that the so-called `no-signalling' condition can be viewed as a generalisation of Einstein's principle that is appropriate for an irreducibly statistical theory such as quantum mechanics. I then argue that a compelling way to motivate information causality is to in turn consider it as a further generalisation of the Einsteinian principle that is appropriate for a theory of communication. I describe, however, some important conceptual obstacles that must yet be overcome if the project of establishing information causality as a foundational principle of nature is to succeed.
  • "String of PURLs – Frugal Migration and Maintenance of Persistent Identifiers." Data Science 3 (2020), 3-13 (with James A. Overton and Chris Mungall)
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    • FAIR data requires unique and persistent identifiers. Persistent Uniform Resource Locators (PURLs) are one common solution, introducing a mapping layer from the permanent identifier to a target URL that can change over time. Maintaining a PURL system requires long-term commitment and resources, and this can present a challenge for open projects that rely heavily on volunteers and donated resources. When the PURL system used by the Open Biological and Biomedical Ontologies (OBO) community suffered major technical problems in 2015, OBO developers had to migrate quickly to a new system. We describe that migration, the new OBO PURL system that we built, and the key factors behind our design. The OBO PURL system is low-cost and low-maintenance, built on well-established open source software, customized to the needs of the OBO community, and shows how key FAIR principles can be supported on a tight budget.
  • "Quantum Computing" (with Amit Hagar), The Stanford Encyclopedia of Philosophy (Winter 2019 Edition), Edward N. Zalta (ed.).
    Link to online version
  • "Universality, Invariance, and the Foundations of Computational Complexity in the light of the Quantum Computer." In Technology and Mathematics: Philosophical and Historical Investigations (Springer-Verlag), Sven Ove Hansson, ed. (2018).
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    • 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 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 radically revise the foundations of the theory. For model-independence never has been essential to those foundations. The fundamental aim of complexity theory is to describe what is achievable in practice under various models of computation for our various practical purposes. Reflecting on quantum computing illuminates complexity theory by reminding us of this, too often under-emphasised, fact.
  • "Reconsidering No-Go Theorems from a Practical Perspective." The British Journal for the Philosophy of Science, 69 (2018), 633-655
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    • I argue that our judgements regarding the locally causal models which are compatible with a given quantum no-go theorem implicitly depend, in part, on the context of inquiry. It follows from this that certain 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 the possible implications of this for our understanding of the limits of classical description, and for our understanding of the fundamental aim of physical investigation.
  • "On the Significance of the Gottesman-Knill Theorem." The British Journal for the Philosophy of Science, 68 (2017), 91-121.
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    • According to the Gottesman-Knill theorem, quantum algorithms which utilise 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 paper that this conclusion is misleading. First, the statement of the theorem (that the particular set of quantum operations in question can be simulated using a classical computer) is, on reflection, already evident when we consider Bell's and related inequalities in the context of a discussion of computational machines. This, in turn, helps us to understand that the appropriate conclusion to draw from the Gottesman-Knill theorem is not that entanglement is insufficient to enable a quantum performance advantage, but rather that if we limit ourselves to the operations referred to in the Gottesman-Knill theorem, we will not have used the resources provided by an entangled quantum system to their full potential.
  • "How-Possibly Explanations in (Quantum) Computer Science." Philosophy of Science, 82 (2015), 737-748.
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    • 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 in so doing 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-actually question. Once one has explained how-possibly there is little left to do.
  • Review of "Quantum Information Theory and the Foundations of Quantum Mechanics", by Christopher G. Timpson. Philosophy of Science, 81 (2014), 681-684.
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  • "On the Debate Concerning the Proper Characterisation of Quantum Dynamical Evolution." Philosophy of Science, 80 (2013), 1125-1136 (with Wayne C. Myrvold).
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    • 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 state space, of CP maps that are only partially defined. Beyond the domain of definition of a partial-CP map, we argue, much may be permitted.
  • "Many Worlds, the Cluster-state Quantum Computer, and the Problem of the Preferred Basis." Studies in History and Philosophy of Modern Physics 43 (2012), 35-42.
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    • I argue that the many worlds explanation of quantum computation is not licensed by, and in fact is conceptually inferior to, the standard neo-Everettian interpretation of quantum mechanics from which it receives its inspiration. I argue that the many worlds explanation of quantum computation is incompatible with the more 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.
  • "Kant and Frege on Existence and the Ontological Argument." History of Philosophy Quarterly, 29 (2012), 337-354.
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    • 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 an object and thus cannot be included in the concept of that object. Thus the ontological argument, which takes existence to be a part of the concept of the supreme being, cannot, according to Kant and Frege, succeed. A secondary goal of the paper is to illuminate what I take to be a deep affinity between Kant's and Frege's views more generally: that Frege's fundamental distinction between the sense and the referent of a proposition echoes, in an important way, Kant's distinction between concepts and the formal principles for their application to experience.
  • "The Conditions of Tolerance." Politics, Philosophy, and Economics, 11 (2012), 322-344 (with Ryan Muldoon and Michael Borgida).
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    • 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 model is an application of David Ricardo's model of trade to thinking about toleration. This model supports the claim that we always have reasons to be as tolerant as possible. We then explore why we do not always see tolerant attitudes in the actual world, and point to some potential preconditions for toleration that the initial model does not capture. Subsequently, we examine a more detailed model that allows us to investigate more carefully the conditions under which tolerant behavior can be rewarded. We conclude by arguing that a consideration of self-interested motivations for toleration is essential to the success of a robust theory of toleration for a diverse society, but that even this approach has its limitations.
  • "Kant's Views on Non-Euclidean Geometry," Proceedings of the Canadian Society for History and Philosophy of Mathematics, 25 (2012), 42-54.
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    • 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 have 'intuitive content' in order to show that both Euclidean and non-Euclidean geometry are bodies of synthetic a priori truths. Michael Friedman has argued that this defence presumes a polyadic conception of logic that was foreign to Kant. According to Friedman, Kant held that geometrical reasoning itself relies essentially on intuition, and that this precludes the very possibility of non-Euclidean geometry. While Friedman's characterization of Kant's views on geometrical reasoning is correct, I argue that Friedman's conclusion that non-Euclidean geometries are logically impossible for Kant is not. I argue that Kant is best understood as a proto-constructivist and that modern constructive axiomatizations (unlike Hilbert-style axiomatizations) of both Euclidean and non-Euclidean geometry capture Kant's views on the essentially constructive nature of geometrical reasoning well.
  • "On Thomas Hobbes' Fallible Natural Law Theory." History of Philosophy Quarterly, 28 (2011), 175-190.
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    • I focus on two aspects of Hobbes's philosophy of law to argue that it is closer to the natural law tradition than to legal positivism. First, I draw on Ronald Dworkin's analysis of the distinction between legal positivism and natural law theory with respect to the role of principles in judicial decision making to argue that Hobbes's view of principles accords better with the natural law view. Second I show how Hobbes's requirement that the natural law remain unwritten prevents Hobbes's view from becoming a 'for all practical purposes' legal positivist view.
  • "The Kantian Framework of Complementarity." Studies in History and Philosophy of Modern Physics, 41 (2010), 309-317.
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    • 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 the similarities between Bohr's argument, on the one hand, that neither the wave nor the particle description of atomic phenomena pick out an object in the ordinary sense of the word, and Kant's requirement, on the other hand, that both 'mathematical' (having to do with magnitude) and 'dynamical' (having to do with an object's interaction with other objects) principles must be applicable to appearances in order for us to determine them as objects of experience. I argue that Bohr's 'Complementarity interpretation' of quantum mechanics, which views atomic objects as idealizations, and which licenses the repeal of the principle of causality for the domain of atomic physics, is perfectly compatible with, and indeed follows naturally from a broadly Kantian epistemological framework.
  • "Wittgenstein on Prior Probabilities," Proceedings of the Canadian Society for History and Philosophy of Mathematics, 23 (2010), 85-98.
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    • 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 stem from a misunderstanding of his views. Max Black, for instance, criticises Wittgenstein for formulating a theory of probability that is capable of being used only against the backdrop of the ideal language of the Tractatus. I argue that on the contrary, by appealing to the 'hypothetical laws of nature', Wittgenstein is able to make sense of probability statements involving propositions that have not been completely analysed. G.H. von Wright criticises Wittgenstein's characterisation of these very hypothetical laws. He argues that by introducing them Wittgenstein makes what is distinctive about his theory superfluous, for the hypothetical laws are directly inspired by statistical observations and hence these observations indirectly determine the mechanism by which the logical theory of probability operates. I argue that this is not the case at all, and that while statistical observations play a part in the formation of the hypothetical laws, these observations are only necessary, but not sufficient conditions for the introduction of these hypotheses.
  • "Nativist Models of the Mind." Gnosis: A Journal of Philosophic Interest, no. 9.3 (2008)
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    • 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 the `intractability objection', the view must borrow many features of a massively modular architecture in order to do so, that although it can, in principle, overcome the `optimality objection', the way it does so does not correlate with the way we think, and that although it can, in principle, respond to the `argument from biology', it cannot do so without advancing an unrealistic and unsupported account of cognitive evolution.
  • "Which Rights are Basic Rights?" Gnosis: A Journal of Philosophic Interest, no. 9.1 (2007)
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    • 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 case Buchanan proceeds to show how the premises of Rawls's argument lead to absurd consequences if taken to their logical conclusion. It can be shown, however, that the reason these consequences follow is that Buchanan misunderstands and misrepresents Rawls's premises.

Thesis and dissertation

  • Ph.D. Dissertation (2013): On the Physical Explanation for Quantum Computational Speedup.
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  • M.A. Thesis (2008): A Metaphysically Neutral Theory of Singular Scientific Explanation.
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Other papers on the arXiv or PhilSci-Archive

  • Kantian and Neo-Kantian First Principles for Physical and Metaphysical Cognition (longer version of "Grete Hermann, Quantum Mechanics, and the Evolution of Kantian Philosophy").
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    • 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, sometimes called the `discursivity thesis', while considered to be completely obvious and uncontroversial by some, has nevertheless been denied by thinkers both before and after Kant. One such thinker is Jakob Friedrich Fries, an early neo-Kantian thinker who, despite his rejection of discursivity, also advocated for a metaphilosophical understanding of critical philosophy. As I will explain, a consequence for Fries of the denial of discursivity is a radical reconceptualisation of the method of critical philosophy; whereas this method is a priori for Kant, for Fries it is in general empirical. I discuss these issues in the context of quantum theory, and I focus in particular on the views of the physicist Niels Bohr and the Neo-Friesian philosopher Grete Hermann. I argue that Bohr's understanding of quantum mechanics can be seen as a natural extension of an orthodox Kantian viewpoint in the face of the challenges posed by quantum theory, and I compare this with the extension of Friesian philosophy that is represented by Hermann's view.
  • On the Necessity of Entanglement for the Explanation of Quantum Speedup.
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    • In this paper I argue that entanglement is a necessary component for any explanation of quantum speedup and I address some purported counter-examples that some claim show that the contrary is true. In particular, I address Biham et al.'s mixed-state version of the Deutsch-Jozsa algorithm, and Knill & Laflamme's deterministic quantum computation with one qubit (DQC1) model of quantum computation. I argue that these examples do not demonstrate that entanglement is unnecessary for the explanation of quantum speedup, but that they rather illuminate and clarify the role that entanglement does play.

Papers not freely downloadable via this page are available upon request.