This book is available either individually, or as part of the specially-priced Arguments of the Philosphers Collection.

Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of operator algebras, category theory, etc.. Given the rigor and generality of AQFT, it is a particularly apt tool for studying the foundations of QFT. This paper is a survey of AQFT, with an orientation towards foundational topics. In addition to covering the basics of the theory, (...) we discuss issues related to nonlocality, the particle concept, the field concept, and inequivalent representations. We also provide a detailed account of the analysis of superselection rules by Doplicher, Haag, and Roberts (DHR); and we give an alternative proof of Doplicher and Robert's reconstruction of fields and gauge group from the category of physical representations of the observable algebra. The latter is based on unpublished ideas due to J. E. Roberts and the abstract duality theorem for symmetric tensor *-categories, a self-contained proof of which is given in the appendix. (shrink)

Ludwig Wittgenstein is one of the most important, influential, and often-cited philosophers of the twentieth century, yet he remains one of its most elusive and least accessible. The essays in this volume address central themes in Wittgenstein's writings on the philosophy of mind, language, logic, and mathematics. They chart the development of his work and clarify the connections between its different stages. The contributors illuminate the character of the whole body of work by keeping a tight focus on some key (...) topics: the style of the philosophy, the conception of grammar contained in it, rule-following, convention, logical necessity, the self, and what Wittgenstein called, in a famous phrase, 'forms of life'. (shrink)

The central aim of this paper is to present a Boolean algebraic approach to the classical Aristotelian Relations of Opposition, namely Contradiction and (Sub)contrariety, and to provide a 3D visualisation of those relations based on the geometrical properties of Platonic and Archimedean solids. In the first part we start from the standard Generalized Quantifier analysis of expressions for comparative quantification to build the Comparative Quantifier Algebra CQA. The underlying scalar structure allows us to define the Aristotelian relations in Boolean terms (...) and to propose a 3D visualisation by transforming a cube into an octahedron. In part two, the architecture of the CQA is shown to carry over, both to the classical quantifiers of Predicate Calculus and to the modal operators—which are given a Generalized Quantifier style re-interpretation. In this way we provide an algebraic foundation for Blanché’s Aristotelian hexagon as well as a 3D alternative to his 2D star-like visualisation. In a final part, a richer scalar structure is argued to underly the realm of Modality, thus generalizing the 3D algebra with eight (2 3 ) operators to a 4D algebra with sixteen (2 4 ) operators. The visual representation of the latter structure involves a transformation of the hypercube to a rhombic dodecahedron. The resulting 3D visualisation allows a straightforward embedding, not only of the classical Blanché star of Aristotelian relations or the paracomplete and paraconsistent stars of Béziau (Log Investig 10, 218–232, 2003) but also of three additional isomorphic Aristotelian constellations. (shrink)

Wittgenstein's remarks about family resemblance in the Philosophical Investigations should not be construed as implying a comprehensive theory of universals. They possess, rather, a defensive function in his exposition. The remarks allow one, nevertheless, to draw certain general conclusions about how Wittgenstein thought about concepts. Reflection on the notion of family resemblance reveals that kinship and similarity considerations intersect in it in a problematic fashion.

This book presents an innovative reading of Daoist philosophy that highlights the critical and therapeutic functions of satire and humor. Moeller and D'Ambrosio show how the Zhuangzi expounds the Daoist art of "genuine pretending" the paradoxical skill of enacting social roles without submitting to them or letting them define one's identity.

Introduces contemporary American philosophy of technology through six of its leading figures. The six American philosophers of technology whose work is profiled in this clear and concise introduction to the field—Albert Borgmann, Hubert Dreyfus, Andrew Feenberg, Donna Haraway, Don Ihde, and Langdon Winner—represent a new, empirical direction in the philosophical study of technology that has developed mainly in North America. In place of the grand philosophical schemes of the classical generation of European philosophers of technology, the contemporary American generation addresses (...) concrete technological practices and the co-evolution of technology and society in modern culture. Six Dutch philosophers associated with Twente University survey and critique the full scope and development of their American colleagues’ work, often illustrating shifts from earlier to more recent interests. Individual chapters focus on Borgmann’s engagement with technology and everyday life; Dreyfus’s work on the limits of artificial intelligence; Feenberg’s perspectives on the cultural and social possibilities opened by technologies; Haraway’s conception of the cyborg and its attendant blurring of boundaries; Ihde’s explorations of the place of technology in the lifeworld; and Winner’s fascination with the moral and political implications of modern technologies. American Philosophy of Technology offers an insightful and readable introduction to this new and distinctly American philosophical turn. Contributors are Hans Achterhuis, Philip Brey, René Munnik, Martijntje Smits, Pieter Tijmes, and Peter-Paul Verbeek. (shrink)

The centerpiece of Jeffrey Bub's book Interpreting the Quantum World is a theorem (Bub and Clifton 1996) which correlates each member of a large class of no-collapse interpretations with some 'privileged observable'. In particular, the Bub-Clifton theorem determines the unique maximal sublattice L(R,e) of propositions such that (a) elements of L(R,e) can be simultaneously determinate in state e, (b) L(R,e) contains the spectral projections of the privileged observable R, and (c) L(R,e) is picked out by R and e alone. In (...) this paper, we explore the issue of maximal determinate sets of observables using the tools provided by the algebraic approach to quantum theory; and we call the resulting algebras of determinate observables, "maximal *beable* subalgebras". The capstone of our exploration is a generalized version of Bub and Clifton's theorem that applies to arbitrary (i.e., both mixed and pure) quantum states, to Hilbert spaces of arbitrary (i.e., both finite and infinite) dimension, and to arbitrary observables (including those with a continuous spectrum). Moreover, in the special case covered by the original Bub-Clifton theorem, our theorem reproduces their result under strictly weaker assumptions. This added level of generality permits us to treat several topics that were beyond the reach of the original Bub-Clifton result. In particular: (a) We show explicitly that a (non-dynamical) version of the Bohm theory can be obtained by granting privileged status to the position observable. (b) We show that Clifton's (1995) characterization of the Kochen-Dieks modal interpretation is a corollary of our theorem in the special case when the density operator is taken as the privileged observable. (c) We show that the 'uniqueness' demonstrated by Bub and Clifton is only guaranteed in certain special cases -- viz., when the quantum state is pure, or if the privileged observable is compatible with the density operator. We also use our results to articulate a solid mathematical foundation for certain tenets of the orthodox Copenhagen interpretation of quantum theory. For example, the uncertainty principle asserts that there are strict limits on the precision with which we can know, simultaneously, the position and momentum of a quantum-mechanical particle. However, the Copenhagen interpretation of this fact is not simply that a precision momentum measurement necessarily and uncontrollably disturbs the value of position, and vice-versa; but that position and momentum can never in reality be thought of as simultaneously determinate. We provide warrant for this stronger 'indeterminacy principle' by showing that there is no quantum state that assigns a sharp value to both position and momentum; and, a fortiori, that it is mathematically impossible to construct a beable algebra that contains both the position observable and the momentum observable. We also prove a generalized version of the Bub-Clifton theorem that applies to "singular" states (i.e., states that arise from non-countably-additive probability measures, such as Dirac delta functions). This result allows us to provide a mathematically rigorous reconstruction of Bohr's response to the original EPR argument -- which makes use of a singular state. In particular, we show that if the position of the first particle is privileged (e.g., as Bohr would do in a position measuring context), the position of the second particle acquires a definite value by virtue of lying in the corresponding maximal beable subalgebra. But then (by the indeterminacy principle) the momentum of the second particle is not a beable; and EPR's argument for the simultaneous reality of both position and momentum is undercut. (shrink)

A framework for the mind-matter problem in a holistic universe which has no parts is outlined. The conceptual structure of modern quantum theory suggests to use complementary Boolean descriptions as elements for a more comprehensive non-Boolean description of a world without an a priori mind-matter distinction. Such a description in terms of a locally Boolean but globally non-Boolean structure makes allowance for the fact that Boolean descriptions play a privileged role in science. If we accept the insight that there are (...) no ultimate building blocks, the existence of holistic correlations between contextually chosen parts is a natural consequence. The main problem of a genuinely non-Boolean description is to find an appropriate partition of the universe of discourse. If we adopt the idea that all fundamental laws of physics are invariant under time translations, then we can consider a partition of the world into a tenseless and a tensed domain.In the sense of a regulative principle, the material domain is defined as the tenseless domain with its homogeneous time. The tensed domain contains the mental domain with a tensed time characterized by a privileged position, the Now. Since this partition refers to two complementary descriptions which are not given a priori we have to expect correlations between these two domains. In physics it corresponds to Newton 's separation of universal laws of nature and contingent initial conditions Both descriptions have a non-Boolean structure and can be encompassed into a single non-Boolean description. Tensed and tenseless time can be synchronized by holistic correlations. (shrink)

This essay traces the roots of Wittgenstein’s Pyrrhonism to Mauthner, and argues that Wittgenstein’s later views moved even closer to those of Mauthner, although Wittgenstein never became as thoroughgoing a Pyrrhonian as Mauthner had been. It is argued that Mauthner’s neo-Pyrrhonian view of language was “responsible for the linguistic turn in Wittgenstein’s thinking and thereby indirectly also for the whole linguistic turn in 20th-century analytic philosophy”.

Current radical democratic politics is characterized by new participatory spaces for citizens’ engagement, which aim at facilitating the democratic ideals of freedom and equality. These spaces are, however, situated in the context of deep societal inequalities. Modes of discrimination are carried over into participatory interaction. The democratic subject is judged by its physically embodied appearance, which replicates external hierarchies and impedes the freedom of self-expression. To tackle this problem, this article seeks to identify ways to increase the freedom of the (...) subject to explore its multiple self. Understanding the self as inherently fugitive, the article investigates participatory, deliberative and agonistic concepts of self-transformation. As all of them appear limited, it introduces a transformative perspective in democratic thought. Enriching the transformative perspective with queer and gender theory, the article generates the concept of a politics of becoming, which, through radical democratic practices of disidentification, advances the freedom of the subject to change. (shrink)

Michael Dummett, following an established line of reasoning, has interpreted Frege as a realist. But his claim that Frege was arguing against a dominant idealism is untenable. While there are passages in Frege's writings that seem to support a realistic interpretation, others are irreconcilable with it. The issue can be resolved only by examining the historical context. Frege's thought is, in fact, related to the philosophy of Hermann Lotze. Frege is best regarded as a transcendental idealist in the Lotze-Kant tradition. (...) His contextual principle is a linguistic version of Kant's principle of the transcendental unity of judgment. By ignoring the historical context Dummett has been led to misinterpret the precise role of the contextual principle in Frege's thought. (shrink)

Radical democratic thinking is becoming intrigued by the material situatedness of its political agents and by the role of nonhuman participants in political interaction. At stake here is the displacement of narrow anthropocentrism that currently guides democratic theory and practice, and its repositioning into what we call ‘the nonhuman condition’. This Critical Exchange explores the nonhuman condition. It asks: What are the implications of decentering the human subject via a new materialist reading of radical democracy? Does this reading dilute political (...) agency? Or should this be seen, on the contrary, as an invitation for new voices and demands to enter into democratic assemblages? How might engagement with the more-than-human disrupt or extend theories of radical democracy? Hans Asenbaum and Amanda Machin discuss the human democratic subject both through radical democratic and new materialist lenses. They suggest that a new materialist decentred subject does not lose agency but further gains political responsibility in radical democracy. Jean-Paul Gagnon highlights the possibility of becoming through loss. In losing our anthropocentric arrogance—our understanding of being other and better than animal—we become more connected and discover our place in human-nonhuman assemblages. Melissa Orlie agrees that something can be gained through renouncing dominant human fantasies and presents a ‘radical democratic naturalism’. By renouncing land violence and acknowledging nature’s subjectivity, we can further nonexploitative radical democratic politics. This is where the notion of ‘tidalectic’ processes introduced by James L. Smith is helpful. Focusing on water and the Indigenous knowledges around rivers, he considers how democracy and community can be reimagined as plural, cyclical and attentive to the nonhuman with which the human is inevitably entangled. Diana Leong offers a different approach. Considering the nonhuman from the perspective of Black Studies demands an awareness to how blackness has long been constituted as non- or partially human. (shrink)

Inter-theoretical reduction has always been a major topic in the structuralist philosophy of science. This paper reviews criteria of adequacy which were put forward by Adams, Sneed, Stegmuller, Mayr, Pearce, Kamlah, and Mormann. The criteria are formalized in a simplified structuralist model, and the logical relations between them are investigated. It turns out that various parts of these criteria are incompatible.

The book also sheds new light on many important allegories by showing how modern translations often conceal the wit and humor of the Chinese original.

This volume outlines a model of language that can be characterized as functionalist, usage-based, dynamic, and complex-adaptive. The core idea is that linguistic structure is not stable and uniform, but continually refreshed by the interaction between three components: usage, the communicative activities of speakers; conventionalization, the social processes triggered by these activities and feeding back into them; and entrenchment, the individual cognitive processes that are also linked to these activities in a feedback loop. Hans-Joerg Schmid explains how this multiple (...) feedback system works by extending his Entrenchment-and-Conventionalization Model, showing how the linguistic system is created, sustained, and continually adapted by the ongoing interaction between usage, conventionalization, and entrenchment. Fulfilling the promise of usage-based accounts, the model explains how exactly usage is transformed into collective and individual grammar and how these two grammars in turn feed back into usage.0The book is exceptionally broad in scope, with insights from a wide range of linguistic subdisciplines. It provides a coherent account of the role of multiple factors that influence language structure, variation, and change, including frequency, economy, identity, multilingualism, and language contact. (shrink)

In this paper we provide an analysis of the logical relations within the conceptual or lexical field of angles in 2D geometry. The basic tripartition into acute/right/obtuse angles is extended in two steps: first zero and straight angles are added, and secondly reflex and full angles are added, in both cases extending the logical space of angles. Within the framework of logical geometry, the resulting partitions of these logical spaces yield bitstring semantics of increasing complexity. These bitstring analyses allow a (...) straightforward account of the Aristotelian relations between angular concepts. In addition, also relational concepts such as complementary and supplementary angles receive a natural bitstring analysis. (shrink)

In recent years the mushrooming power, functionality and ubiquity of computers and the Internet have outstripped early forecasts about technology's rate of advancement and usefulness in everyday life. Alert pundits now foresee a world saturated with powerful computer chips, which will increasingly insinuate themselves into our gadgets, dwellings, apparel and even our bodies.

This paper presents a generalization of the standard notions of left monotonicity (on the nominal argument of a determiner) and right monotonicity (on the VP argument of a determiner). Determiners such as “more than/at least as many as” or “fewer than/at most as many as”, which occur in so-called propositional comparison, are shown to be monotone with respect to two nominal arguments and two VP-arguments. In addition, it is argued that the standard Generalized Quantifier analysis of numerical determiners such as (...) “more than three/at least three” is a simplification which ignores the fundamental parallellism with the propositional comparatives. Furthermore, the symmetric monotonicity configurations of the existential “some” and “no” are shown to be straightforwardly related to those of numerical comparatives with the limit numeral zero, whereas the asymmetric configurations of universal “all” and “not all” involve the extra complicating mechanism of polarity reversal, which is related to Keenan's notion of co-intersectivity (as opposed to intersectivity). A second aim of the paper is to investigate some of the factors reducing the inferential potential of determiners. Different types of comparative determiners and their modification will be considered in detail. In addition, a systematic interaction will be revealed between the monotonicity properties of the determiners in propositional comparatives and the differ ent types of ellipsis in the “than”-complement. Different degrees of ellipsis are defined in terms of informational dependencies between the “than”-complement and the main clause. A general balancing mechanism is observed by virtue of which an increase in informational dependency is compensated by a reduction of the inferential potential of the comparative determiner. The structure of the paper is as follows. Part two deals with propositional comparison and introduces the two basic monotonicity configurations. Part three distinguishes three types of informational dependencies or ellipsis between the “than”-complement and the main clause. In Section 3.1 the “than”-complement only contains a VP constituent, whereas in Section 3.2. it only consists of a nominal constituent. Section 3.3 considers more complex instances of multiple dependencies. Section 3.4 then looks at the interaction of these three types with the modifier “proportionally”. Part four presents the two basic monotonicity configurations for numerical comparison, whereas part five deals with more complex numerical determiners. Bounding determiners, such as “between five and ten”, and other boolean combinations are discussed in Section 5.1, whereas Section 5.2 goes into approximative determiners involving modifiers such as “only” or “almost”. Section 5.3. is devoted to proportional determiners such as “more than two out of three”. Part six then considers the standard existential and universal quantifiers. Section 6.1 reformulates the standard Generalized Quantifier analysis in comparative terms, whereas Section 6.2 deals with exception determiners of the form “all but five”. (shrink)

These autobiographical reflections by a major contemporary philosopher offer an enjoyable and enlightening tour not only of his own intellectual development but of the rich and fruitful collaboration of minds during a rich period in German cultural history. Hans-Georg Gadamer, the author of Truth and Method, traces his "philosophical apprenticeships" with some of the most important thinkers of the 20th century. Perhaps more than anyone else, Hans-Georg Gadamer, who is Professor Emeritus at the University of Heidelberg, is the (...) doyen of German philosophy and the recognized chief theorist of hermeneutics. His book Reason in the Age of Science (MIT Press paperback) is an ideal introduction to his thought and to the problems of hermeneutics more generally. Philosophical Apprenticeships is included in the series Studies in Contemporary German Social Thought, edited by Thomas McCarthy. (shrink)

The last few years have been good for time machines. Kip Thorne's renowned general relativity group at Caltech invented a new quantum gravitational approach to building a time gate, and, in an international collaboration, gave a plausible rebuttal of "grandfather paradox" arguments against time travel. Another respected group suggested time machines that exploit quantum mechanical time uncertainty. The technical requirements for these suggestions exceed our present capabilities, but each new approach seems less onerous than the last. There is hope yet (...) that time travel will eventually become possible, even cheap. (shrink)

This chapter contains sections titled: A Political Moment Action, Words, and Concepts The Pluralism of the Political Natural Affinities Words and Their Contexts Rules, Decisions, Authority The Unpredictability of Behavior Vision and Choice in Politics Further reading.

Foucault’s political thinking is focused on the concept of power relations. Under the influence of Nietzsche he proposes two different accounts of how power is related to human action. Nietzsche had argued, on the basis of a reading of Kant’s antinomies of pure reason, for two different accounts of that relationship. On the one hand, he had sought to understand action as a phenomenon of the will to power; on the other, he had also spoken of the will to power (...) as an aspect of human agency. On Nietzsche’s views, we need to assert both positions even though they are for us irreconcilable. In his writings on power and action Foucault finds himself driven into adopting a similarly dual view. While he speaks of action in the nineteen seventies as subsidiary to power relations, he reverses himself in the nineteen eighties by treating power as a feature of human action. Just like Nietzsche, he offers us no way of reconciling these two distinct accounts. (shrink)

With reference to Plato and Aristotle, Gadamer discusses the question of what is left of friendship and solidarity in an age of `anonymous responsibility.'.

_Wittgenstein_ presents a concise, comprehensive, and systematic treatment of Ludwig Wittgenstein's thought from his early work, _Tractatus Logico-Philosophicus,_ to the posthumous publication of _On Certainty_, notes written just prior to his death. A substantial scholarly addition to our understanding of one of the most original and influential thinkers of the twentieth century, by renowned Wittgenstein scholar, Hans Sluga Proposes an original new interpretation of Wittgenstein's work Written to also be accessible to readers unfamiliar with Wittgenstein's thought Includes discussion of (...) the social and political background and contemporary relevance of Wittgenstein's thoughts. (shrink)

The paper interprets Wittgenstein’s famous call to silence at the end of his Tractatus – that “whereof one cannot speak, thereof one must be silent” – as a critique of philosophy itself. Wittgenstein was concerned throughout his philosophical life with finding a way to delineate the limits of language. These limits, once we have them clearly in view, rob our attempts to put forth philosophical theories of their legitimacy. In order to give a critical assessment of this Wittgensteinian critique of (...) philosophy, the paper primarily focuses on the roots of that critique in Wittgenstein’s earliest writings – his notebooks, his 1913 “Notes on Logic,” the 1914 set of notes dictated to G. E. Moore, and the Tractatus itself. Wittgenstein’s influence by Fritz Mauthner and, mediated through Mauthner, by Kant receive special attention. The conclusion is that, far from Mauthner’s radical anti-philosophical bias, we can come to see a deep appreciation of the power, the draw, and the significance of philosophical problems in Wittgenstein’s writings. The text closes with a short look at how Wittgenstein’s thinking about the limits of language evolved later in his life. (shrink)

The narrative of the Death of Emperor Hundun 混沌, who finally perishes from the seventh hole that his two fellow Emperors have drilled into his formless body to do him the favor of supplying him with a face, famously concludes the seven Inner Chapters of the Zhuangzi 莊子.1 Perhaps the sudden demise of the story’s protagonist is meant to signal paradoxically to the reader that he or she, too, has, unwittingly, now come to an end and reached a stage of (...) no return. With the completion of the seventh chapter, seven deep holes have been drilled into one’s head and have transformed one irredeemably. Zhuangzi, too, may have repaid the kindness of those who took him home with equal kindness and deprived them of their... (shrink)

v. Savigny's commentary is a remarkable achievement and essential reading for all scholars of the Investigations. It brings to the exegetical enterprise something new and important — the challenge of an immanent approach and the tool of German philology. However, some of the potential gains may be lost by his leitmotiv of a tight master-scheme. In my view this ‘central theses’ scheme presses Wittgenstein's multifaceted masterpiece into an unsuitable Procrustean bed and tends to impoverish v. Savigny's account. Nevertheless there remains (...) the palatable pattern-recipe (for me partly spoiled by an overdose of community-views). Most importantly, v. Savigny approaches most of the material in an innovative and illuminating way. He provides good reasons for questioning, although not necessarily overturning, many key claims of recent scholarship. (shrink)

Books reviewed: Donald Davidson, Subjective, Intersubjective, Objective.

This dissertation reconsiders some traditional issues in the foundations of quantum mechanics in the context of relativistic quantum field theory (RQFT); and it considers some novel foundational issues that arise first in the context of RQFT. The first part of the dissertation considers quantum nonlocality in RQFT. Here I show that the generic state of RQFT displays Bell correlations relative to measurements performed in any pair of spacelike separated regions, no matter how distant. I also show that local systems in (...) RQFT are "open" to influence from their environment, in the sense that it is generally impossible to perform local operations that would remove the entanglement between a local system and any other spacelike separated system. The second part of the dissertation argues that RQFT does not support a particle ontology -- at least if particles are understood to be localizable objects. In particular, while RQFT permits us to describe situations in which a determinate number of particles are present, it does not permit us to speak of the location of any individual particle, nor of the number of particles in any particular region of space. Nonetheless, the absence of localizable particles in RQFT does not threaten the integrity of our commonsense concept of a localized object. Indeed, RQFT itself predicts that descriptions in terms of localized objects can be quite accurate on the macroscopic level. The third part of the dissertation examines the so-called observer-dependence of the particle concept in RQFT -- that is, whether there are any particles present must be relativized to an observer's state of motion. Now, it is not uncommon for modern physical theories to subsume observer-dependent descriptions under a more general observer-independent description of some underlying state of affairs. However, I show that the conflicting accounts concerning the particle content of the field cannot be reconciled in this way. In fact, I argue that these conflicting accounts should be thought of as "complementary" in the same sense that position and momentum descriptions are complementary in elementary quantum mechanics. (shrink)

The project is funded by the Office of Naval Research under a contract entiltled Underwater Robots. The effort is interesting in its own right, and complements projects involving underwater vehicles such as those at the University of New Hampshire and the Naval Ocean Systems Center in San Diego. These other efforts are interesting to us, but we feel they are incomplete. Their current control systems are very simple, typically incorporating quite small programs on one or a few microprocessors and implementing (...) simple dead reckoning navigation or terrain following behavior. (shrink)