Since the late 1960s, Roger Penrose has had the ambition to develop a new theory that rethinks the foundations of quantum mechanics. His twistor theory aims to carry out this difficult task. Although today the theory is still in development, it is no less true that it is finding more and more followers and its results are beginning to seem not as far-fetched as initially believed. The goal is still far away, but his impetus for wanting (...) to change things is still valid. (shrink)

A detailed outline is presented of several convergent points of view connecting the self-dual and anti-self-dual fields with their free data. This is done for the Maxwell and for linearized gravity as exemplifying the approaches. The Sparling equation provides one tool of great power and characterizes one approach. The twistor theory of Penrose yields another equally powerful point of view. The links between these two basic approaches given in this paper provide a unification that allows workers and others (...) with interest in this area to proceed more readily toward the goal of understanding the full nonlinear Einstein equations. (shrink)

An assessment is offered of the progress that the major approaches to quantum gravity have made towards the goal of constructing a complete and satisfactory theory. The emphasis is on loop quantum gravity and string theory, although other approaches are discussed, including dynamical triangulation models (euclidean and lorentzian) regge calculus models, causal sets, twistor theory, non-commutative geometry and models based on analogies to condensed matter systems. We proceed by listing the questions the theories are expected to (...) be able to answer. We then compile two lists: the first details the actual results so far achieved in each theory, while the second lists conjectures which remain open. By comparing them we can evaluate how far each theory has progressed, and what must still be done before each theory can be considered a satisfactory quantum theory of gravity. We find there has been impressive recent progress on several fronts. At the same time, important issues about loop quantum gravity are so far unresolved, as are key conjectures of string theory. However, there is a reasonable expectation that experimental tests of lorentz invariance at Planck scales may in the near future make it possible to rule out one or more candidate quantum theories of gravity. (shrink)

We construct the Extended Relativity Theory in Born-Clifford-Phase spaces with an upper R and lower length λ scales (infrared/ultraviolet cutoff). The invariance symmetry leads naturally to the real Clifford algebra Cl (2, 6, R) and complexified Clifford Cl C (4) algebra related to Twistors. A unified theory of all Noncommutative branes in Clifford-spaces is developed based on the Moyal-Yang star product deformation quantization whose deformation parameter involves the lower/upper scale $$(\hbar \lambda / R)$$. Previous work led us to (...) show from first principles why the observed value of the vacuum energy density (cosmological constant) is given by a geometric mean relationship $$\rho \sim L_{\rm Planck}^{-2}R^{-2} = L_{P}^{-4} (L_{\rm Planck} / R)^{2} \sim 10^{-122}M_{\rm Planck}^4$$, and can be obtained when the infrared scale R is set to be of the order of the present value of the Hubble radius. We proceed with an extensive review of Smith’s 8D model based on the Clifford algebra Cl (1, 7) that reproduces at low energies the physics of the Standard Model and Gravity, including the derivation of all the coupling constants, particle masses, mixing angles,....with high precision. Geometric actions are presented like the Clifford-Space extension of Maxwell’s Electrodynamics, and Brandt’s action related to the 8D spacetime tangent-bundle involving coordinates and velocities (Finsler geometries). Finally we outline the reasons why a Clifford-Space Geometric Unification of all forces is a very reasonable avenue to consider and propose an Einstein-Hilbert type action in Clifford-Phase spaces (associated with the 8D Phase space) as a Unified Field theory action candidate that should reproduce the physics of the Standard Model plus Gravity in the low energy limit. (shrink)

In this essay, I consider the ontological status of spacetime from the points of view of the standard tensor formalism and three alternatives: twistor theory, Einstein algebras, and geometric algebra. I briefly review how classical field theories can be formulated in each of these formalisms, and indicate how this suggests a structural realist interpretation of spacetime.

"An important contribution to contemporary jurisprudential debate and to legal thought more generally, Just Interpretations is far ahead of currently available work."--Peter Goodrich, author of Oedipus Lex "I was struck repeatedly by the clarity of expression throughout the book. Rosenfeld's description and criticism of the recent work of leading thinkers distinguishes his work within the legal theory genre. Furthermore, his own theory is quite original and provocative."--Aviam Soifer, author of Law and the Company We Keep.

Professor Sir Roger Penrose's work, spanning fifty years of science, with over five thousand pages and more than three hundred papers, has been collected together for the first time and arranged chronologically over six volumes, each with an introduction from the author. Where relevant, individual papers also come with specific introductions or notes. Many important realizations concerning twistor theory occurred during the short period of this third volume, providing a new perspective on the way that mathematical features of (...) the complex geometry of twistor theory relate to actual physical fields. Following on from the nonlinear graviton construction, a twistor construction was found for (anti-)self-dual electromagnetism allowing the general (anti-)self-dual Yang-Mills field to be obtained. It became clear that some features of twistor contour integrals could be understood in terms of holomorphic sheaf cohomology. During this period, the Oxford research group founded the informal publication, Twistor Newsletter. This volume also contains the influential Weyl curvature hypothesis and new forms of Penrose tiles. (shrink)

Professor Sir Roger Penrose's work, spanning fifty years of science, with over five thousand pages and more than three hundred papers, has been collected together for the first time and arranged chronologically over six volumes, each with an introduction from the author. Where relevant, individual papers also come with specific introductions or notes. Publication of The Emperor's New Mind (OUP 1989) had caused considerable debate and Penrose's responses are included in this volume. Arising from this came the idea that large-scale (...) quantum coherence might exist within the conscious brain, and actual conscious experience would be associated with a reduction of the quantum state. Within this collection, Penrose also proposes that a twistor might usefully be regarded as a source (or 'charge') for a massless field of spin 3/2, suggesting that the twistor space for a Ricci-flat space-time might actually be the space of such possible sources. Towards the end of the volume, Penrose begins to develop a quite different approach to incorporating full general relativity into twistor theory. This period also sees the origin of the Diósi-Penrose proposal. (shrink)

Professor Sir Roger Penrose's work, spanning fifty years of science, with over five thousand pages and more than three hundred papers, has been collected together for the first time and arranged chronologically over six volumes, each with an introduction from the author. Where relevant, individual papers also come with specific introductions or notes. Developing ideas sketched in the first volume, twistor theory is now applied to genuine issues of physics, and there are the beginnings of twistor diagram (...) theory (an analogue of Feynman Diagrams). This collection includes joint papers with Stephen Hawking, and uncovers certain properties of black holes. The idea of cosmic censorship is also first proposed. Along completely different lines, the first methods of aperiodic tiling for the Euclidean plane that come to be known as Penrose tiles are described. This volume also contains Penrose's three prize-winning essays for the Gravity Foundation (two second places with both Ezra Newman and Steven Hawking, and a solo first place for 'The Non-linear graviton'). (shrink)

Professor Sir Roger Penrose's work, spanning fifty years of science, with over five thousand pages and more than three hundred papers, has been collected together for the first time and arranged chronologically over six volumes, each with an introduction from the author. Where relevant, individual papers also come with specific introductions or notes. The first volume covers the beginnings of a career that is ground-breaking from the outset. Inspired by courses given by Dirac and Bondi, much of the early published (...) work involves linking general relativity with tensor systems. Among his early works is the seminal 1955 paper, 'A Generalized Inverse for Matrices', his previously unpublished PhD and St John's College Fellowship theses, and from 1967, his Adam's Prize-winning essay on the structure of space-time. Add to this his 1965 paper, 'Gravitational collapse and space-time singularities', and the 1967 paper that introduced a remarkable new theory, 'Twistor algebra', and this becomes a truly stellar procession of works on mathematics and cosmology. (shrink)

Literary Theory and Criminology demonstrates the significance of contemporary literary theory to the discipline of criminology, particularly to those criminologists who are primarily concerned with questions of power, inequality, and harm. Drawing on innovations in philosophical, narrative, cultural, and pulp criminology, it sets out a deconstructive framework as part of a critical criminological critique-praxis. -/- This book comprises eight essays – on globalisation, criminological fiction, poststructuralism, patriarchal political economy, racial capitalism, anthropocidal ecocide, critical theory, and critical praxis (...) – that argue for the value of contemporary literary theory to a critical criminology concerned with the construction of a just and sustainable reality in the face of climate change and other mass harms. This is the first criminology book to engage with literary theory from the perspective of criminology and provides a guide for criminologists who want to deploy literary theory as part of their research programmes. It supersedes existing engagements with poststructuralism in the philosophical criminological tradition because it entails neither a constructionist ontology nor a relativist epistemology. It shows criminologists how literary theory offers the tools to first deconstruct and then reconstruct meaning and value. -/- Literary Theory and Criminology is essential reading for all critical criminological theorists. (shrink)

In this impressive second edition of Theory of Knowledge, Keith Lehrer introduces students to the major traditional and contemporary accounts of knowing. Beginning with the traditional definition of knowledge as justified true belief, Lehrer explores the truth, belief, and justification conditions on the way to a thorough examination of foundation theories of knowledge,the work of Platinga, externalism and naturalized epistemologies, internalism and modern coherence theories, contextualism, and recent reliabilist and causal theories. Lehrer gives all views careful examination and concludes (...) that external factors must be matched by appropriate internal factors to yield knowledge. This match of internal and external factors follows from Lehrer’s new coherence theory of undefeated justification. In addition to doing justice to the living epistemological traditions, the text smoothly integrates several new lines that will interest scholars. Also, a feature of special interest is Lehrer’s concept of a justification game.This second edition of Theory of Knowledge is a thoroughly revised and updated version that contains several completely new chapters. Written by a well-known scholar and contributor to modern epistemology, this text is distinguished by clarity of structure, accessible writing, and an elegant mix of traditional material, contemporary ideas, and well-motivated innovation. (shrink)

Though the revised edition of A Theory of Justice, published in 1999, is the definitive statement of Rawls's view, so much of the extensive literature on Rawls's theory refers to the first edition. This reissue makes the first edition once again available for scholars and serious students of Rawls's work.

This comprehensive monograph is a cornerstone in the area of mathematical logic and related fields. Focusing on Gentzen-type proof theory, the book presents a detailed overview of creative works by the author and other 20th-century logicians that includes applications of proof theory to logic as well as other areas of mathematics. 1975 edition.

This paper starts by characterising moral requirements and everyday thought. Then ways in which moral requirements shape everyday thought are identified, including the way internalised moral requirements prevent some possible actions from even being considered. The paper then explains that everyday moral thought might be structured by dispositions to which there are corresponding principles even if these principles do not usually appear in the conscious thoughts of agents while they are engaged in everyday moral decision-making. Nevertheless, especially when conflicts between (...) moral considerations arise, alternative possible resolutions are typically framed in terms of principles. The paper pushes on to discuss how everyday moral thought is pushed to consider principles, engage in moral theorising, and even consider abstract moral theories. (shrink)

The foundation for a system of morals, this 1749 work is a landmark of moral and political thought. Its highly original theories of conscience, moral judgment, and virtue offer a reconstruction of the Enlightenment concept of social science, embracing both political economy and theories of law and government.

Though the revised edition of A Theory of Justice, published in 1999, is the definitive statement of Rawls's view, so much of the extensive literature on Rawls's theory refers to the first edition.

« Pourquoi les choses tiennent-elles ensemble ? » (Traité d'ontologie, 2009, p. 237). Cette citation me sert de départ à une réflexion sur la nature des relations liantes souvent appelées relations de comprésence à la suite de Russell, ces bundling relations qui nouent les propriétés ensembles pour constituer les objets ordinaires (tables, chaises, individus biologiques) selon la théorie du faisceau. De même que Frédéric Nef, je suis séduit par les nombreuses vertus philosophiques de ces relations liantes. Ma contribution ne portera (...) pas sur une critique ou une défense de ces relations mais sur l'étude de leur nature, et en particulier, de leur possible nature méréologique. Je vais esquisser rapidement certains aspects de la théorie classique du faisceau que je qualifierai de réaliste pour opposer ensuite les variantes réalistes à deux autres versions méréologiques de la théorie, que je qualifierai d'éliminativistes. (shrink)

La theorie physique? Ce titre, qui fut au debut de notre siecle celui d'un ouvrage controverse, suggere bien une question, celle de savoir si en matiere de science la theorie doit se qualifier en fonction d'un domaine plus particulier d'application. L'auteur, Pierre Duhem, n'aurait pas hesite, semble-t-il, a repondre par l'affirmative en ce qui concerne le vaste champ de la recherche que l'on peut signifier sous le nom de physique. Son ouvrage est en fait construit comme une preparation rigoureuse a (...) une telle reponse et bien que les annees aient modifie considerablement le contexte du champ sus-dit, les analyses proposees ont ete jugees suggestives par de nombreux epistemologues d'aujourd'hui. (shrink)

이 글은 들뢰즈가 주장했던 개념에 대한 분명한 이해를 목적으로 기획되었다. 일찍이 들뢰즈는 사르트르의 타인-구조에 대해 구조주의의 선구자로서의 면모를 갖추었다고 상찬한 바 있지만, 그것을 ‘시선’을 통해 정의함으로써 결국 타자를 또 다시 주체와 대상의 범주로 떨어지게 만들었다며 아쉬워했다. 부정과 모순 을 기반으로 하고 있는 주체철학의 구도에서 축조된 사르트르의 타인이론은 결국 에 머물 수밖에 없기 때문이다. 게다가 능동적인 의 재인능력은 만을 가능하도록 이끎으로써 우리의 사유를 치명적으로 제한하는 문제점을 안고 있다. 따라서 들뢰즈는 서양철학에서의 선-철학적 전제로 인해 재현적 사유만이 가능한 인격 적인 주체 개념을 비인격적 (...) 개체인 로 대신하였을 뿐만 아니라, 재인으로부터 를 구하기 위해, 즉 에 관심 을 쏟았고 그러는 가운데 로 을 지목함으로써 의 구도를 벗어나게 된다. 그 과정을 톺아보면 사르트르의 타인-시선 구조는 들뢰즈에게 전 해져 지각장의 한 구조로서의 타인과 절대적 구조인 으로 좀 더 면밀 히 구분되는데, 이 절대적인 구조는 그것을 채우는 항들에 앞서 존재하는 것이 아니라 중 단 없이 연속적으로 변이하며 전개되어 간다. 이처럼 타인-구조와 개체화는 긴밀히 연관 되어 있기에, 만약 우리가 진정 새로워지고 싶다면 우선 재현의 개체화만을 일으키는 기존 의 타인-구조를 와해시킴으로써 창조적 사유자인 로 거듭나기 위한 조건을 만들 어야만 한다. 이는 우리의 사유가 어떻게 재현의 방식을 벗어나 자유로워질 수 있는가 하 는 방법의 문제이기도 하며 뒤집어 말해, 우리 사유의 독특성과 다양성에 대한 설명이기도 하다. 들뢰즈의 이론을 통해 타인은 투쟁의 대상이나 유사함과 감미로움의 대상을 넘어, 이라는 고유한 의미의 타인으로 새롭게 태어난다. (shrink)

The new theory of reference has won popularity. However, a number of noted philosophers have also attempted to reply to the critical arguments of Kripke and others, and aimed to vindicate the description theory of reference. Such responses are often based on ingenious novel kinds of descriptions, such as rigidified descriptions, causal descriptions, and metalinguistic descriptions. This prolonged debate raises the doubt whether different parties really have any shared understanding of what the central question of the philosophical (...) class='Hi'>theory of reference is: what is the main question to which descriptivism and the causal-historical theory have presented competing answers. One aim of the paper is to clarify this issue. The most influential objections to the new theory of reference are critically reviewed. Special attention is also paid to certain important later advances in the new theory of reference, due to Devitt and others. (shrink)

This paper discusses the role of Law and Legal Thinking in Critical Theory with specific reference to the arguments that Michael Hardt and Antonio Negri offer in their book Commonwealth. The core idea is that Critical Theory is no less radical, but much more concrete, when it is performing not only an external, but also an internal critique of the Law. It shows that the role of the law in critical theory emerges as a problem when the (...) latter claims that ‘there is no outside’ and that ‘the legal base of the system structures our lives.’ It then discusses optimistic and pessimistic strategies to overcome the problem, and argue for a demanding strategy which consist in articulating the external and the internal critique of the law. To make this point, the paper goes back to the epistemic context in which critical attitudes are deployed (the ‘Conflict of the Faculties’), describes the four theoretical moves constitutive of the historical moment in which, at the end of the 18th Century, modern law as we know it was conceived of and founded; and sketches the key moments of the history of the internal critique of the law. It then illustrates the demanding strategy with examples taken from the field of Intellectual Property, and concludes that the Law is malleable and open enough to allow the thinking and practicing of radical alternatives from within the legal system and also that alternatives spoken in the language of the law are no less radical, but certainly, more concrete than others. (shrink)

If the world itself is metaphysically indeterminate in a specified respect, what follows? In this paper, we develop a theory of metaphysical indeterminacy answering this question.