Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. In effect, they follow the same logical paradigm as (multi-particle) interferometers. We show how most known quantum algorithms for factorising and counting, may be cast in this manner. Quantum searching is described as inducing a desired relative phase between two eigenvectors to yield constructive interference on the sought elements and destructive interference on the remaining terms.

David Lewis’s analysis of “can” in “The Paradoxes of Time Travel” (Lewis, American Philosophical Quarterly, 13, 145–52, 1976) has been widely accepted both as a definitive analysis of “can” and as a successful resolution of the Grandfather Paradox for time travel. I argue that the central feature of his analysis puts it on all fours with a fallacy frequently imputed to fatalists such as Richard Taylor. I go on to consider two moves that might be made to avoid the (...) fallacy, arguing that one of them leads to the unavailability of an all-things-considered “can” and the other to a new primitive modality, not analyzable in Lewis’s way. (shrink)

David Lewis’s analysis of “can” in “The Paradoxes of Time Travel” has been widely accepted both as a definitive analysis of “can” and as a successful resolution of the Grandfather Paradox for time travel. I argue that the central feature of his analysis puts it on all fours with a fallacy frequently imputed to fatalists such as Richard Taylor. I go on to consider two moves that might be made to avoid the fallacy, arguing that one of them leads (...) to the unavailability of an all-things-considered “can” and the other to a new primitive modality, not analyzable in Lewis’s way. (shrink)

My aim in what follows is to expound and (if possible) resolve two problems in Spinoza’s theory of mind. The first problem is how Spinoza can accept a key premise in Descartes’s argument for dualism—that thought and extension are separately conceivable, “one without the help of the other”—without accepting Descartes’s conclusion that no substance is both thinking and extended. Resolving this problem will require us to consider a crucial ambiguity in the notion of conceiving one thing without another, the credentials (...) of Descartes’s principle that each substance has a principal attribute, and the prospect of neutral monism as a theory of the mind. The second problem is how Spinoza can maintain that each mental event is identical with some physical event (and conversely) while denying that there is ever any causal interaction between mental and physical events. If one mental event causes another and the first is identical with some physical event, must that physical event not cause the mental event? Resolving this problem will require looking into the reach of opacity in Spinoza’s philosophy and considering whether there are ever any legitimate exceptions to Leibniz’s Law. (shrink)

James Van Cleve examines the main topics from Kant's Critique of Pure Reason, such as transcendental idealism, necessity and analyticity, space and time, substance and cause, noumena and things-in-themselves, problems of the self, and rational theology. He also discusses the relationship between Kant's thought and that of modern anti-realists, such as Putnam and Dummett. Because Van Cleve focuses upon specific problems rather than upon entire passages or sections of the Critique, he makes Kant's work more accessible to the (...) serious student and scholar. (shrink)

A selection of speeches and essays from the author's second decade as president of Yale University.

Descartes's view that the eternal truths of mathematics and logic have been established by God and depend on his will does not merely commit him (as some commentators have suggested) to denying that such truths are necessarily necessary; it abolishes their necessity altogether. For similar reasons, some contemporary views also unwittingly abolish necessity.

In a brief but remarkable section of the Inquiry into the Human Mind, Thomas Reid argued that the visual field is governed by principles other than the familiar theorems of Euclid—theorems we would nowadays classify as Riemannian. On the strength of this section, he has been credited by Norman Daniels, R. B. Angell, and others with discovering non-Euclidean geometry over half a century before the mathematicians—sixty years before Lobachevsky and ninety years before Riemann. I believe that Reid does indeed have (...) a fair claim to have discovered a non-Euclidean geometry. However, the real basis of Reid’s geometry of visibles is subtle and easy to misidentify. My main aim in what follows is to make clear what the real basis is, separating it from several fallacious or irrelevant considerations on which Reid may seem to be relying. A secondary aim is to air the worry that Reid’s case for his geometry can succeed only at the cost of compromising the achievement for which Reid is best known—his direct realist theory of perception. (shrink)

INTRODUCTION TO THE ARGUMENT OF 1768 Some ordinary facts about the world we live in can be readily explained by other ordinary facts. One can, for example, explain the fact that when we are facing north the sun rises on the right and ...

In a brief but remarkable section of the Inquiry into the Human Mind, Thomas Reid argued that the visual field is governed by principles other than the familiar theorems of Euclid—theorems we would nowadays classify as Riemannian. On the strength of this section, he has been credited by Norman Daniels, R. B. Angell, and others with discovering non-Euclidean geometry over half a century before the mathematicians—sixty years before Lobachevsky and ninety years before Riemann. I believe that Reid does indeed have (...) a fair claim to have discovered a non-Euclidean geometry. However, the real basis of Reid’s geometry of visibles is subtle and easy to misidentify. My main aim in what follows is to make clear what the real basis is, separating it from several fallacious or irrelevant considerations on which Reid may seem to be relying. A secondary aim is to air the worry that Reid’s case for his geometry can succeed only at the cost of compromising the achievement for which Reid is best known—his direct realist theory of perception. (shrink)

Two notable thought experiments are discussed in this article: Reid's thought experiment about whether a being supplied with tactile sensations alone could acquire the conception of extension and Strawson's thought experiment about whether a being supplied with auditory sensations alone could acquire the conception of mind-independent objects. The experiments are considered alongside Campbell's argument that only on the so-called relational view of experience is it possible for experiences to make available to their subjects the concept of mind-independent objects. I consider (...) how the three issues ought to be construed as raising questions about woulds, coulds, or shoulds. (shrink)

The discussion of good and evil must not be confined to the sterile lecture halls of academics but related instead to ordinary human feelings, needs, and desires, says noted philosopher Richard Taylor. Efforts to understand morality by exploring human reason will always fail because we are creatures of desire as well. All morality arises from our intense and inescapable longing. The distinction between good and evil is always clouded by rationalists who convert the real problems of ethics into complex (...) philosophical puzzles. In the first part of Good and Evil, Taylor looks for a more meaningful conception by reexamining and rejecting the whole rationalistic tradition that dominates philosophical ethics. The second part provides an empirical explanation of good and evil, noting that one does not have to look too far to find prime examples of the failure of fixed moral rules. Including important commentary on Joseph Fletcher's groundbreaking situation ethics, and Aristotle's virtues (e.g., magnanimity and pride), Taylor rounds out the book by developing a philosophy of aspiration--personal worth as an ethical ideal--to replace the morality of duty. He offers a modified form of situation ethics to fit the contemporary problems we face. (shrink)

Orientalism and Religion offers us a timely discussion of the implications of contemporary post-colonial theory for the study of religion. Drawing on a variety of post-structuralist and post-colonial thinkers, including Foucault, Gadamer, Said, and Spivak, Richard King examines the way in which notions such as mysticism, religion, Hinduism and Buddhism are taken for granted, and shows us how religion needs to be redescribed along the lines of cultural studies.

This is the third edition of a classic book first published in 1960, which has sold thousands of copies in two paperback edition and has been translated into several foreign languages. Popkin's work ha generated innumerable citations, and remains a valuable stimulus to current historical research. In this updated version, he has revised and expanded throughout, and has added three new chapters, one on Savonarola, one on Henry More and Ralph Cudworth, and one on Pascal. This authoritative treatment of the (...) theme of scepticism and its historical impact will appeal to scholars and students of early modern history now as much as ever. (shrink)

James Van Cleve here shows why Thomas Reid (1710-96) deserves a place alongside the other canonical figures of modern philosophy. He expounds Reid's positions and arguments on a wide range of topics, taking interpretive stands on points where his meaning is disputed and assessing the value of his contributions to issues philosophers are discussing today. -/- Among the topics Van Cleve explores are Reid's account of perception and its relation to sensation, conception, and belief; his nativist account of (...) the origin of the concepts of space and power; his attempt to clear the way for the belief that the things we directly perceive are external things, not ideas in our minds; his stand on the distinction between primary and secondary qualities; his account of his externalist reply to philosophical skepticism, his volitional theory of action, his use of the distinction between event causation and agent causation to understand freedom of the will, and his criticism of Hume and anticipation of Moore on the analysis of moral judgment. -/- The most comprehensive work on Reid in a quarter century, this book will be welcomed by students of early modern philosophy, epistemology, the philosophy of perception, and the philosophy of action. (shrink)

Thinking through the body: educating for the humanities -- The body as background -- Self-knowledge and its discontents: from Socrates to somaesthetics -- Muscle memory and the somaesthetic pathologies of everyday life -- Somaesthetics in the philosophy classroom: a practical approach -- Somaesthetics and the limits of aesthetics -- Somaesthetics and Burke's sublime -- Pragmatism and cultural politics: from textualism to somaesthetics -- Body consciousness and performance -- Somaesthetics and architecture: a critical option -- Photography as performative process -- Asian (...) ars erotica and the question of sexual aesthetics -- Philosophy as awakened life : everyday aesthetics of embodiment in American transcendentalism and Japanese Zen practice -- Somatic style. (shrink)

Most foundationalists allow that relations of coherence among antecedently justified beliefs can enhance their overall level of justification or warrant. In light of this, some coherentists ask the following question: if coherence can elevate the epistemic status of a set of beliefs, what prevents it from generating warrant entirely on its own? Why do we need the foundationalist's basic beliefs? I address that question here, drawing lessons from an instructive series of attempts to reconstruct within the probability calculus the classical (...) problem of independent witnesses who corroborate each other's testimony. Starred section headings indicate sections omitted here, but available on the author's USC website. (shrink)

According to certain normative theories in epistemology, rationality requires us to be logically omniscient. Yet this prescription clashes with our ordinary judgments of rationality. How should we resolve this tension? In this paper, I focus particularly on the logical omniscience requirement in Bayesian epistemology. Building on a key insight by Hacking :311–325, 1967), I develop a version of Bayesianism that permits logical ignorance. This includes: an account of the synchronic norms that govern a logically ignorant individual at any given time; (...) an account of how we reduce our logical ignorance by learning logical facts and how we should update our credences in response to such evidence; and an account of when logical ignorance is irrational and when it isn’t. At the end, I explain why the requirement of logical omniscience remains true of ideal agents with no computational, processing, or storage limitations. (shrink)

Conditionalization is one of the central norms of Bayesian epistemology. But there are a number of competing formulations, and a number of arguments that purport to establish it. In this paper, I explore which formulations of the norm are supported by which arguments. In their standard formulations, each of the arguments I consider here depends on the same assumption, which I call Deterministic Updating. I will investigate whether it is possible to amend these arguments so that they no longer depend (...) on it. As I show, whether this is possible depends on the formulation of the norm under consideration. (shrink)