The usual representation of quantum algorithms is limited to the process of solving the problem. We extend it to the process of setting the problem. Bob, the problem setter, selects a problem-setting by the initial measurement. Alice, the problem solver, unitarily computes the corresponding solution and reads it by the final measurement. This simple extension creates a new perspective from which to see the quantum algorithm. First, it highlights the relevance of time-symmetric quantum mechanics to quantum computation: the problem-setting and (...) problem solution, in their quantum version, constitute pre- and post-selection, hence the process as a whole is bound to be affected by both boundary conditions. Second, it forces us to enter into relational quantum mechanics. There must be a representation of the quantum algorithm with respect to Bob, and another one with respect to Alice, from whom the outcome of the initial measurement, specifying the setting and thus the solution of the problem, must be concealed. Time-symmetrizing the quantum algorithm to take into account both boundary conditions leaves the representation to Bob unaltered. It shows that the representation to Alice is a sum over histories in each of which she remains shielded from the information coming to her from the initial measurement, not from that coming to her backwards in time from the final measurement. In retrospect, all is as if she knew in advance, before performing her problem-solving action, half of the information that specifies the solution of the problem she will read in the future and could use this information to reach the solution with fewer computation steps. This elucidates the quantum computational speedup in all the quantum algorithms examined. (shrink)

This article aims at reconstructing the logic and assessing the force of Socrates' argument against Protagoras' 'Measure Doctrine' at Theaetetus 171a–c. I examine and criticise some influential interpretations of the passage, according to which, e.g., Socrates is guilty of ignoratio elenchi by dropping the essential Protagorean qualifiers or successfully proves that md is self-refuting provided the missing qualifiers are restored by the attentive reader. Having clarified the meaning of MD, I analyse in detail the broader section 170a–171d and argue, against (...) an extensive scholarly consensus, that it contains two slightly different formulations of the same argument, and not two distinct arguments, that Socrates does not highlight his own strategy at 171a–c as especially clever, and that his argument successfully shows that md turns out to be untenable for Protagoras himself when submitted to scrutiny in dialectical contexts, without aiming at proving its absolute falsehood. Finally, I clarify the philosophical import of the final image of Protagoras' momentary return from the underworld. (shrink)

A 'self-refutation argument' is any argument which aims at showing that a certain thesis is self-refuting. This study was the first book-length treatment of ancient self-refutation and provides a unified account of what is distinctive in the ancient approach to the self-refutation argument, on the basis of close philological, logical and historical analysis of a variety of sources. It examines the logic, force and prospects of this original style of argumentation within the context of ancient philosophical debates, dispelling various misconceptions (...) concerning its nature and purpose and elucidating some important differences which exist both within the ancient approach to self-refutation and between that approach, as a whole, and some modern counterparts of it. In providing a comprehensive account of ancient self-refutation, the book advances our understanding of influential and debated texts and arguments from philosophers like Democritus, Plato, Aristotle, Epicurus, the Stoics, the Academic sceptics, the Pyrrhonists and Augustine. (shrink)

This Companion provides a comprehensive guide to ancient logic. The first part charts its chronological development, focussing especially on the Greek tradition, and discusses its two main systems: Aristotle's logic of terms and the Stoic logic of propositions. The second part explores the key concepts at the heart of the ancient logical systems: truth, definition, terms, propositions, syllogisms, demonstrations, modality and fallacy. The systematic discussion of these concepts allows the reader to engage with some specific logical and exegetical issues and (...) to appreciate their transformations across different philosophical traditions. The intersections between logic, mathematics and rhetoric are also explored. The third part of the volume discusses the reception and influence of ancient logic in the history of philosophy and its significance for philosophy in our own times. Comprehensive coverage, chapters by leading international scholars and a critical overview of the recent literature in the field will make this volume essential for students and scholars of ancient logic. (shrink)

When in classical formal logic the notions of deduction, valid inference and logical consequence are defined, causal language plays no role. The founder of western logic, Aristotle, identified ‘non-cause’, or ‘positing as cause what is not a cause’, as a logical fallacy. I argue that a systematic re-examination of Aristotle's analysis of NCF, and the related language of logical causality, in the Sophistical Refutations, Topics, Analytics and Rhetoric, helps us to understand his conception of. It reveals that Aristotle's syllogismhood is (...) non-monotonic, and thus narrower than classical validity as consisting in, or coextensive with, necessary truth-preservation. It also supports the conclusion that a syllogism is a form of relevant consequence: the premisses must be causes of the conclusion in the sense that they are not only sufficient but also necessary for the conclusion to follow. Close analysis of NCF also suggests that syllogistic relevance is not a semantic matter, but a syntactic.. (shrink)

The usual representation of quantum algorithms, limited to the process of solving the problem, is physically incomplete. We complete it in three steps: extending the representation to the process of setting the problem, relativizing the extended representation to the problem solver to whom the problem setting must be concealed, and symmetrizing the relativized representation for time reversal to represent the reversibility of the underlying physical process. The third steps projects the input state of the representation, where the problem solver is (...) completely ignorant of the setting and thus the solution of the problem, on one where she knows half solution. Completing the physical representation shows that the number of computation steps required to solve any oracle problem in an optimal quantum way should be that of a classical algorithm endowed with the advanced knowledge of half solution. (shrink)

The article examines Aristotle’s seminal discussion of the fallacy of begging the question, reconstructing its complex articulation within a variety of different, but related, contexts. I suggest that close analysis of Aristotle’s understanding of the fallacy should prompt critical reconsideration of the scope and articulation of the fallacy in modern discussions and usages, suggesting how begging the question should be distinguished from a number of only partially related argumentative faults.

This is a comprehensive introduction to the two great logical systems of antiquity, Aristotelian logic and Stoic logic. Although advanced undergraduate and graduate students are the intended primary readership, classical and philosophy scholars with non-specialist interests in the subject will find the fresh approach useful and stimulating. A conscious effort has been made to create a fruitful dialogue between the Aristotelian and Stoic systems both in terms of theoretical content and in terms of methodological issues and approaches. In all sections (...) emphasis is placed on broader questions concerning the distinctive nature of ancient logic, its relation with modern logic and the study of the history of logic, and the methodological difficulties posed by the reconstruction, analysis and assessment of ancient views, both in themselves and in the light of modern logic. (shrink)

Greek Memories aims to identify and examine the central concepts underlying the theories and practices of memory in the Greek world, from the archaic period to Late Antiquity, across all the main literary genres, and to trace some fundamental changes in these theories and practices. It explores the interaction and development of different 'disciplinary' approaches to memory in Ancient Greece, which will enable a fuller and deeper understanding of the whole phenomenon, and of its specific manifestations. This collection of papers (...) contributes to enriching the current scholarly discussion by refocusing it on the question of how various theories and practices of memory, recollection, and forgetting play themselves out in specific texts and authors from Ancient Greece, within a wide chronological span, and across a broad range of genres and disciplines. (shrink)

Bob hides a ball in one of four drawers. Alice is to locate it. Classically she has to open up to three drawers, quantally just one. The fundamental reason for this quantum speedup is not known. The usual representation of the quantum algorithm is limited to the process of solving the problem. We extend it to the process of setting the problem. The number of the drawer with the ball becomes a unitary transformation of the random outcome of the preparation (...) measurement. This extended, time-symmetric, representation brings in relational quantum mechanics. It is with respect to Bob and any external observer and cannot be with respect to Alice. It would tell her the number of the drawer with the ball before she opens any drawer. To Alice, the projection of the quantum state due to the preparation measurement should be retarded at the end of her search; in the input state of the search, the drawer number is determined to Bob and undetermined to Alice. We show that, mathematically, one can ascribe any part of the selection of the random outcome of the preparation measurement to the final Alice’s measurement. Ascribing half of it explains the speedup of the present algorithm. This leaves the input state to Bob unaltered and projects that to Alice on a state of lower entropy where she knows half of the number of the drawer with the ball in advance. The quantum algorithm turns out to be a sum over histories in each of which Alice knows in advance that the ball is in a pair of drawers and locates it by opening one of the two. In the sample of quantum algorithms examined, the part of the random outcome of the initial measurement selected by the final measurement is one half or slightly above it. Conversely, given an oracle problem, the assumption it is one half always corresponds to an existing quantum algorithm and gives the order of magnitude of the number of oracle queries required by the optimal one. (shrink)

Through a close reading of Plutarch’s Against Colotes 3-9, the paper reconstructs and interprets the original Epicurean criticism against Democritean epistemology and ontology, and in particular against Democritus’ theory of sensible qualities, and Plutarch’s twofold criticism of Epicurean epistemology, on similar grounds, and of the questionable exegetical and argumentative manoeuvres used by the Epicurean Colotes. In the process of interpreting Plutarch’s text, the paper reflects on the nature, motivation and plausibility of Plutarch’s own exegetical and argumentative strategies. Finally, the paper (...) suggests that a careful reading of Against Colotes will help us to put into focus the important question of whether, independently of their apparently opposite claims about the “reality” of secondary qualities, Democritus and Epicurus shared either a form of radical relativism or a form of commonsense “intersubjectivism” in their evaluations of ascriptions of such qualities to macroscopic objects. (shrink)

This is a welcome reprint of a book that continues to grow in importance.

The author presents and defends three theses: (1) "the first is that it is not profitable for us at present to do moral philosophy; that should be laid aside at any rate until we have an adequate philosophy of psychology." (2) "the second is that the concepts of obligation, And duty... And of what is morally right and wrong, And of the moral sense of 'ought', Ought to be jettisoned if this is psychologically possible...." (3) "the third thesis is that (...) the differences between the well-Known english writers on moral philosophy from sidgwick to the present day are of little importance." (staff). (shrink)

The relations between reason, motivation and value present problems which, though ancient, remain intractable. If values are objective and rational how can they move us and if they are dependent on our contingent desires how can they be rational? E. J. Bond makes a bold attack on this dilemma. The widespread view among philosophers today is that judgements contain an irreducible element of personal commitment. To this Professor Bond proposes an account of values as objective and value judgements as true (...) or false, employing a distinction between grounding and motivating reasons to establish their connection with action. He defines and tests his position against a number of recent theories, providing in the process forceful criticism of Williams, Wiggins, Foot, Narveson and Nagel, among others. A distinctive contribution to the subject, it will stimulate interest and worthwhile debate among philosophers, while also serving as an introduction to this vital topic. (shrink)

Derek Parfit’s view of personal identity raises questions about whether advance decisions refusing life-saving treatment should be honored in cases where a patient loses psychological continuity; it implies that these advance decisions would not be self-determining at all. However, rather than accepting that an unknown metaphysical ‘further fact’ underpins agential unity, one can accept Parfit’s view but offer a different account of what it implies morally. Part II of this article argues that contractual obligations provide a moral basis for honoring (...) advance decisions refusing life-saving and/or life-sustaining medical treatment; advance decisions have similarities to contracts, such as life insurance policies and will-contracts, that come into effect when the psychological discontinuity is through death. (shrink)

The aim of this study is to explore how nurses perceive patient participations of patients over 75 years old undergoing hemodialysis treatment in dialysis units, and of their next of kin. Ten nurses told stories about what happened in the dialysis units. These stories were analyzed with critical discourse analysis. Three discursive practices are found: (1) the nurses’ power and control; (2) sharing power with the patient; and (3) transferring power to the next of kin. The first and the predominant (...) discursive practice can be explained with an ideology of paternalism, in which the nurses used biomedical explanations and the ethical principle of benefice to justify their actions. The second can be explained with an ideology of participation, in which the nurses used ethical narratives as a way to let the patients participate in the treatment. The third seemed to involve autonomous decision-making and the ethical principle of autonomy for the next of kin in the difficult end-of-life decisions. (shrink)

Arguing that psychologists and their predecessors have invariably relied on metaphors in articulation, the contributors to this volume offer a new "key" to understanding a critically important area of human knowledge by specifying the major metaphors.

Released in 1984, Steven E. Rhoads' classic was considered by many to be among the best introductions to the economic way of thinking and its applications. This anniversary edition has been updated to account for political and economic developments - from the greater interest in redistributing income and the ascendancy of behaviorism to the Trump presidency. Rhoads explores opportunity cost, marginalism, and economic incentives and explains why mainstream economists - even those well to the left - still value free markets. (...) He critiques economics for its unbalanced emphasis on narrow self-interest as controlling motive and route to happiness, highlighting philosophers and positive psychologists' findings that happiness is far more dependent on friends and family than on income or wealth. This thought-provoking tour of the economist's mind is a must read for our times, providing a clear, lively, non-technical insight into how economists think and why they shouldn't be ignored. (shrink)

We have identified a sample of 53 societies outside of the classical Himalayan and Marquesean area that permit polyandrous unions. Our goal is to broadly describe the demographic, social, marital, and economic characteristics of these societies and to evaluate some hypotheses of the causes of polyandry. We demonstrate that although polyandry is rare it is not as rare as commonly believed, is found worldwide, and is most common in egalitarian societies. We also argue that polyandry likely existed during early human (...) history and should be examined from an evolutionary perspective. Our analysis reveals that it may be a predictable response to a high operational sex ratio favoring males and may also be a response to high rates of male mortality and, possibly, male absenteeism. Other factors may contribute, but our within-polyandry sample limits analysis. (shrink)

Big Ideas for Little Kids includes everything a teacher, a parent, or a college student needs to teach philosophy to elementary school children from picture books. Written in a clear and accessible style, the book explains why it is important to allow young children access to philosophy during primary-school education. Wartenberg also gives advice on how to construct a "learner-centered" classroom, in which children discuss philosophical issues with one another as they respond to open-ended questions by saying whether they agree (...) or disagree with what others have said. (shrink)

A dialogue between a foreign philosopher and a powerful statesman outline Plato's reflections on the family, the status of women, property rights, and criminal law.