We propose a conceptual framework for understanding the relationship between observables and operators in mechanics. To do so, we introduce a postulate that establishes a correspondence between the objective properties permitting to identify physical states and the symmetry transformations that modify their gauge dependant properties. We show that the uncertainty principle results from a faithful—or equivariant—realization of this correspondence. It is a consequence of the proposed postulate that the quantum notion of objective physical states is not incomplete, but rather that (...) the classical notion is overdetermined. (shrink)

We analyze the geometric foundations of classical Yang-Mills theory by studying the relationships between internal relativity, locality, global/local invariance, and background independence. We argue that internal relativity and background independence are the two independent defining principles of Yang-Mills theory. We show that local gauge invariance -heuristically implemented by means of the gauge argument- is a direct consequence of internal relativity. Finally, we analyze the conceptual meaning of BRST symmetry in terms of the invariance of the gauge fixed theory under general (...) local gauge transformations. (shrink)

We shall address from a conceptual perspective the duality between algebra and geometry in the framework of the refoundation of algebraic geometry associated to Grothendieck’s theory of schemes. To do so, we shall revisit scheme theory from the standpoint provided by the problem of recovering a mathematical structure A from its representations \ into other similar structures B. This vantage point will allow us to analyze the relationship between the algebra-geometry duality and the structure-semiotics duality. Whereas in classical algebraic geometry (...) a certain kind of rings can be recovered by considering their representations with respect to a unique codomain B, Grothendieck’s theory of schemes permits to reconstruct general rings by considering representations with respect to a category of codomains. The strategy to reconstruct the object from its representations remains the same in both frameworks: the elements of the ring A can be realized—by means of what we shall generally call Gelfand transform—as quantities on a topological space that parameterizes the relevant representations of A. As we shall argue, important dualities in different areas of mathematics can be understood as particular cases of this general pattern. In the wake of Majid’s analysis of the Pontryagin duality, we shall propose a Kantian-oriented interpretation of this pattern. We shall use this conceptual framework to argue that Grothendieck’s notion of functor of points can be understood as a “relativization of the a priori” that generalizes the relativization already conveyed by the notion of domain extension to more general variations of the corresponding domains. (shrink)

We propose a group-theoretical interpretation of the fact that the transition from classical to quantum mechanics entails a reduction in the number of observables needed to define a physical state and \ to \ or \ in the simplest case). We argue that, in analogy to gauge theories, such a reduction results from the action of a symmetry group. To do so, we propose a conceptual analysis of formal tools coming from symplectic geometry and group representation theory, notably Souriau’s moment (...) map, the Mardsen–Weinstein symplectic reduction, the symplectic “category” introduced by Weinstein, and the conjecture according to which “quantization commutes with reduction”. By using the generalization of this conjecture to the non-zero coadjoint orbits of an abelian Hamiltonian action, we argue that phase invariance in quantum mechanics and gauge invariance have a common geometric underpinning, namely the symplectic reduction formalism. This stance points towards a gauge-theoretical interpretation of Heisenberg indeterminacy principle. We revisit this principle in the light of the difference between the set-theoretic points of a phase space and its category-theoretic symplectic points. (shrink)

We propose the conjecture according to which the fact that quantum mechanics does not admit sharp value attributions to both members of a complementary pair of observables can be understood in the light of the symplectic reduction of phase space in constrained Hamiltonian systems. In order to unpack this claim, we propose a quantum ontology based on two independent postulates, namely the phase postulate and the quantum postulate. The phase postulate generalizes the gauge correspondence between first-class constraints and gauge transformations (...) to the observables of unconstrained Hamiltonian systems. The quantum postulate specifies the relationship between the numerical values of the observables that permit us to individualize a physical system and the symmetry transformations generated by the operators associated to these observables. We argue that the quantum postulate and the phase postulate are formally implemented by the two independent stages of the geometric quantization of a symplectic manifold, namely the prequantization formalism and the election of a polarization of pre-quantum states respectively. (shrink)

En este artículo, se introducirá el formalismo de cuantificación canónica denominado "cuantificación geométrica". Dado que dicho formalismo permite entender la mecánica cuántica como una extensión geométrica de la mecánica clásica, se identificarán las insuficiencias de esta última resueltas por dicha extensión. Se mostrará luego como la cuantificación geométrica permite explicar algunos de los rasgos distintivos de la mecánica cuántica, como, por ejemplo, la noconmutatividad de los operadores cuánticos y el carácter discreto de los espectros de ciertos operadores. In this article, (...) We shall introduce the formalism of canonical quantization called "geometric quantization". Since this formalism let us understand quantum mechanics as a geometric extension of classical mechanics, we shall identify the insufficiencies of the latter that are resolved by such an extension. We shall show that geometric quantization permits us to explain some fundamental features of quantum mechanics, such as the non-commutativity of quantum operators and the discrete spectrum of some operators describing physical quantities. (shrink)

We analyze the notions of indiscernibility and indeterminacy in the light of the Galois theory of field extensions and the generalization to \(K\) -algebras proposed by Grothendieck. Grothendieck’s reformulation of Galois theory permits to recast the Galois correspondence between symmetry groups and invariants as a Galois–Grothendieck duality between \(G\) -spaces and the minimal observable algebras that discern (or separate) their points. According to the natural epistemic interpretation of the original Galois theory, the possible \(K\) -indiscernibilities between the roots of a (...) polynomial \(p(x)\in K[x]\) result from the limitations of the field \(K\) . We discuss the relation between this epistemic interpretation of the Galois–Grothendieck duality and Leibniz’s principle of the identity of indiscernibles. We then use the conceptual framework provided by Klein’s Erlangen program to propose an alternative ontologic interpretation of this duality. The Galoisian symmetries are now interpreted in terms of the automorphisms of the symmetric geometric figures that can be placed in a background Klein geometry. According to this interpretation, the Galois–Grothendieck duality encodes the compatibility condition between geometric figures endowed with groups of automorphisms and the ‘observables’ that can be consistently evaluated at such figures. In this conceptual framework, the Galoisian symmetries do not encode the epistemic indiscernibility between individuals, but rather the intrinsic indeterminacy in the pointwise localization of the figures with respect to the background Klein geometry. (shrink)

We propose a definition of physical objects that aims to clarify some interpretational issues in quantum mechanics. We claim that the transformations generated by the objective properties of a physical system must be strictly interpreted as gauge transformations. We will argue that the uncertainty principle is a consequence of the mutual intertwining between objective properties and gauge-dependant properties. The proposed definition implies that in classical mechanics gauge-dependant properties are wrongly considered objective. We will conclude that, unlike classical mechanics, quantum mechanics (...) provides a complete objective description of physical systems. (shrink)

Can there be two things that are completely indistinguishable? This simple question has raised numerous debates throughout the history of philosophy and science. The principle of the identity of indiscernibles claims that no two things can be completely indiscernible. But this thesis has been challenged in quantum physics and continues to be a hot topic in cutting edge areas of mathematics. The question has gained a renewed interest with the possibility of harnessing indistinguishability as a resource in quantum information tasks. (...) This theme issue is devoted to understanding identity and indistinguishability in philosophy and science, gathering an interdisciplinary group of experts in the field. It will allow readers of diverse disciplines to have an updated introduction to the topic. (shrink)

We analyze the notion of indiscernibility in the light of the Galois theory of field extensions and the generalization to K-algebras proposed by Grothendieck. Grothendieck's reformulation of Galois theory permits to recast the Galois correspondence between symmetry groups and invariants as a duality between G-spaces and the minimal observable algebras that separate theirs points. In order to address the Galoisian notion of indiscernibility, we propose what we call an epistemic reading of the Galois-Grothendieck theory. According to this viewpoint, the Galoisian (...) notion of indiscernibility results from the limitations of the `resolving power' of the observable algebras used to discern the corresponding `coarse-grained' states. The resulting Galois-Grothendieck duality is rephrased in the form of what we call a Galois indiscernibility principle. According to this principle, there exists an inverse correlation between the coarsegrainedness of the states and the size of the minimal observable algebra that discern these states. (shrink)

We argue that the classical description of a symplectic manifold endowed with a Hamiltonian action of an abelian Lie group G and the corresponding quantum theory can be understood as different aspects of the unitary representation theory of G. To do so, we propose a conceptual analysis of formal tools coming from symplectic geometry and group representation theory. The proposed argumentative line strongly relies on the conjecture proposed by Guillemin and Sternberg according to which ``quantization commutes with reduction''. By using (...) the generalization of this conjecture to non-zero coadjoint orbits, we argue that phase invariance in quantum mechanics and gauge invariance have a common geometric underpinning, namely the symplectic reduction formalism. This fact points towards a gauge-theoretic interpretation of Heisenberg indeterminacy principle. (shrink)

We revisit Heisenberg indeterminacy principle in the light of the Galois–Grothendieck theory for the case of finite abelian Galois extensions. In this restricted framework, the Galois–Grothendieck duality between finite K-algebras split by a Galois extension \ and finite \\) -sets can be reformulated as a Pontryagin duality between two abelian groups. We define a Galoisian quantum model in which the Heisenberg indeterminacy principle can be understood as a manifestation of a Galoisian duality: the larger the group of automorphisms \ of (...) the states in a G-set \ , the smaller the “conjugate” algebra of observables that can be consistently evaluated on such states. Finally, we argue that states endowed with a group of automorphisms \ can be interpreted as squeezed coherent states, i.e. as states that minimize the Heisenberg indeterminacy relations. (shrink)

We revisit Heisenberg indeterminacy principle in the light of the Galois-Grothendieck theory for the case of finite abelian Galois extensions. In this restricted framework, the Galois-Grothendieck duality between finite K-algebras split by a Galois extension L and finite Gal-sets can be reformulated as a Pontryagin-like duality between two abelian groups. We then define a Galoisian quantum theory in which the Heisenberg indeterminacy principle between conjugate canonical variables can be understood as a form of Galoisian duality: the larger the group of (...) automorphisms H of the states in a G-set O = G/H, the smaller the ``conjugate'' observable algebra that can be consistently valuated on such states. We then argue that this Galois indeterminacy principle can be understood as a particular case of the Heisenberg indeterminacy principle formulated in terms of the notion of entropic indeterminacy. Finally, we argue that states endowed with a group of automorphisms H can be interpreted as squeezed coherent states, i.e. as states that minimize the Heisenberg indeterminacy relations. (shrink)

Bd. 1. A-B -- Bd. 2. C-F -- Bd. 3. G-Inn -- Bd. 4. Ins-Loc.

This important collection of lectures and essays was regarded by Gabriel Marcel as the best introduction to his thought.

v. 1. Reflection & mystery -- v. 2. Faith & reality.

The Simple Counterfactual Analysis (SCA) was once considered the most promising analysis of disposition ascriptions. According to SCA, disposition ascriptions are to be analyzed in terms of counterfactual conditionals. In the last few decades, however, SCA has become the target of a battery of counterexamples. In all counterexamples, something seems to be interfering with a certain object’s having or not having a certain disposition thus making the truth-values of the disposition ascription and of its associated counterfactual come apart. Intuitively, however, (...) it would seem that, if all interferences were absent, the disposition ascription and its associated conditional would have the same truth-value. Although this idea may seem obvious, it is far from obvious how to implement it. In fact, it has become widely assumed that the content of qualifying ceteris paribus clauses (such as ‘if all interferences were absent’) cannot be specified in a clear and non-circular manner. In this paper, I will argue that this assumption is wrong. I will develop an analysis of disposition ascriptions, the Interference-Free Counterfactual Analysis, which relies on a clear and non-circular definition of the notion of interference and avoids the standard counterexamples to SCA while vindicating the intuition that disposition ascriptions and counterfactual conditionals are intimately related. (Please note that an erratum has been issued for the published version of this paper. It is recommended to read the self-archived version of the paper.). (shrink)

Famously, in the essay Inquiry Concerning the Distinctness of the Principles of Natural Theology and Morality (Prize Essay), Kant attempts to distance himself from the Wolffian model of philosophical inquiry. In this respect, Kant scholars have pointed out Kant’s claim that philosophy should not imitate the method of mathematics and his appeal to Newton’s “analytic method.” In this article, I argue that there is an aspect of Kant’s critique of the Wolffian model that has been neglected. Kant presents a powerful (...) attack of the idea that philosophy should proceed through the analysis of concepts and argues that we should give up the aim of arriving at “complete” concepts as one of its fundamental desiderata. Importantly, this attack of philosophy conceived as conceptual analysis is distinctive and original if one compares it with Kant’s critique of analysis in the Critique of Pure Reason, which rests on the idea that analysis is insufficient to ground substantial metaphysical truths. I also make an additional point: Scholars have debated whether the appeal to Newton’s analytic method involves a form of empiricism. I submit that this debate is ill-conceived because Kant uses a notion of “given concepts” that is indeterminate with respect to their a priori or a posteriori status. (shrink)

The volume deals with the history of logic, the question of the nature of logic, the relation of logic and mathematics, modal or alternative logics (many-valued, relevant, paraconsistent logics) and their relations, including translatability, to classical logic in the Fregean and Russellian sense, and, more generally, the aim or aims of philosophy of logic and mathematics. Also explored are several problems concerning the concept of definition, non-designating terms, the interdependence of quantifiers, and the idea of an assertion sign. The contributions (...) concerned with Wittgenstein's investigations into the philosophy of logic and mathematics pursue issues relating to logical necessity, the undeniability of the law of the excluded middle, and the source of self-evidence, often characterized in the literature as the "rule-following considerations". Additionally, they examine Wittgenstein's attitudes towards the very idea of set-theory as a possible foundation for arithmetic. The volume also includes a number of contributions on specific issues concerning Wittgenstein's views on moral and religious judgements. (shrink)

The primary objective of this book is to open space for rethinking the relationship between art and politics. It seeks to combat one of the fundamental assumptions that has plagued many of the previous debates on this issue: that art and politics are distinct entities definable in terms of common properties, and that they have privileged points of intersection, which can be determined once and for all in terms of an established formula. This common sense assumption is rooted in a (...) transcendent illusion according to which there are more or less fixed characteristics that unify our terms, concepts, and practices in such a way as to guarantee their meaning. Against this substantialist approach, Radical History & the Politics of Art argues for a praxeological account that begins the other way around by analyzing specific cultural practices without presupposing a conceptual unity behind them. Such an orientation is radically historicist in the sense that it recognizes that all of our practices—be they linguistic, theoretical, aesthetic or political—are historically constituted and that they are necessarily part of a temporal dynamic. Hence the contingent nature of the labels used to classify various practices or even identify ‘practice’ as such. Radical history thereby proposes a significant departure from the extant debates on art and politics by maintaining that there is no ‘art’ or ‘politics’ in general, nor a singular relation between them. There are only historically constituted practices in various conjunctures, some of which have been labeled, through practical acts of denomination, as ‘artistic’ or ‘political.’ Instead of proposing one more response to the oft-repeated question ‘what is the relationship between Art and Politics?’ this book seeks to overcome the presuppositions that plague such a question. It thereby changes the very nature of the investigation by asking: ‘how do the diverse aspects of practices identified as ‘aesthetic’ and ‘political’ overlap, intertwine and sometimes merge in precise socio-historical force fields of action? (shrink)

This edition of Marcel's inspiring Homo Viator has been updated to includle fifty-seven pages of new material available for the first time in English, making this the first English-language edition to conform to the standard French edition. Here, Christianity's foremost existentialist of the twentieth century gives us a prodigious personal insight on 'man on the way' that will reinforce and commend our own pilgrimages in hope. Book jacket.

The intellectual resistance to totalitarian regimes can take many forms. This remarkable volume portrays one such story of resistance in Romania during the reign of Ceausescu: that of Constantin Noica, one of the country's foremost intellectuals. The Paltinis Diary is a wonderful homage to an intellectual master and to the power of intellect and freedom. The book will be of interest to philosophers, non-philosophers alike, and to anyone who seeks to grasp the true meaning of survival under totalitarian conditions.

From mass murder to genocide, slavery to colonial suppression, acts of atrocity have lives that extend far beyond the horrific moment. They engender trauma that echoes for generations, in the experiences of those on both sides of the act. Gabriele Schwab reads these legacies in a number of narratives, primarily through the writing of postwar Germans and the descendents of Holocaust survivors. She connects their work to earlier histories of slavery and colonialism and to more recent events, such as South (...) African Apartheid, the practice of torture after 9/11, and the "disappearances" that occurred during South American dictatorships. Schwab's texts include memoirs, such as Ruth Kluger's _Still Alive_ and Marguerite Duras's _La Douleur_; second-generation accounts by the children of Holocaust survivors, such as Georges Perec's _W_, Art Spiegelman's _Maus_, and Philippe Grimbert's _Secret_; and second-generation recollections by Germans, such as W. G. Sebald's _Austerlitz_, Sabine Reichel's _What Did You Do in the War, Daddy?_, and Ursula Duba's _Tales from a Child of the Enemy_. She also incorporates her own reminiscences of growing up in postwar Germany, mapping interlaced memories and histories as they interact in psychic life and cultural memory. Schwab concludes with a bracing look at issues of responsibility, reparation, and forgiveness across the victim/perpetrator divide. (shrink)

Recent epidemiological research on the social determinants of health has been used to attack an important framework, associated with Norman Daniels, that depicts healthcare as special. My aim is to rescue the idea that healthcare has special importance in society, although specialness will turn out to be mainly limited to clinical care. I build upon the link between Daniels's theory and the work of John Rawls to develop a conception of public justification liberalism that is suitable to the field of (...) justice and health. I argue that, from the perspective of public justification liberalism, (clinical) healthcare deserves special status. (shrink)

In this paper, I distinguish three general approaches to public trust in science, which I call the individual approach, the semi-social approach, and the social approach, and critically examine their proposed solutions to what I call the problem of harmful distrust. I argue that, despite their differences, the individual and the semi-social approaches see the solution to the problem of harmful distrust as consisting primarily in trying to persuade individual citizens to trust science and that both approaches face two general (...) problems, which I call the problem of overidealizing science and the problem of overburdening citizens. I then argue that in order to avoid these problems we need to embrace a (thoroughly) social approach to public trust in science, which emphasizes the social dimensions of the reception, transmission, and uptake of scientific knowledge in society and the ways in which social forces influence both positively and negatively the trustworthiness of science. (shrink)

Intimacy: From Transformation to Transmutation The paper reflects the historical and current dynamism of the concept of intimacy. Besides differences between scientific disciplines in understanding what the substance of intimacy is, the recent discourse on change in intimacy has been dominated by the transformation theme introduced by Anthony Giddens (1992). Led by reflections of Richard Sennett (1986) the author draws attention to the opposite aspect of change in intimacy—the change in content, or the "transmutation" of intimacy. Transmutation of intimacy—the substitution (...) of the satisfaction of intimate needs with identity creation—not only contests the very essence of intimacy, but also constitutes a significant challenge for the project of intimate citizenship (Plummer 2003). (shrink)

In this paper, I develop Mauricio Suárez’s distinction between denotation, epistemic representation, and faithful epistemic representation. I then outline an interpretational account of epistemic representation, according to which a vehicle represents a target for a certain user if and only if the user adopts an interpretation of the vehicle in terms of the target, which would allow them to perform valid (but not necessarily sound) surrogative inferences from the model to the system. The main difference between the interpretational conception I (...) defend here and Suárez’s inferential conception is that the interpretational account is a substantial account—interpretation is not just a “symptom” of representation; it is what makes something an epistemic representation of a something else. (shrink)

Carnap’s seminal ‘Empiricism, Semantics and Ontology’ makes important use of the notion of a framework and the related distinction between internal and external questions. But what exactly is a framework? And what role does the internal/external distinction play in Carnap’s metaontology? In an influential series of papers, Matti Eklund has recently defended a bracingly straightforward interpretation: A Carnapian framework, Eklund says, is just a natural language. To ask an internal question, then, is just to ask a question in, say, English. (...) To try to ask an external question is to try, absurdly, to ask a question in no language at all. Finding that so trivial an I/e distinction can’t help to explain Carnap’s deflationary metaontology, Eklund is led to attribute to Carnap a view he calls ontological pluralism. In this paper, I show that Eklund misreads Carnap, and I argue that this misreading obscures fundamental features of Carnap’s philosophy. I then defend an account of frameworks as what Carnap called semantical systems, and I place this account in the context of Carnap’s philosophical program of explication. Finally, I discuss the role that frameworks and the I/e distinction play in ESO, showing that ESO provides no reason to attribute the doctrine of ontological pluralism to Carnap. (shrink)

Per una sociosemiotica della comunicazione musicale -- Per una sociosemiotica dei generi musicali -- Per una sociosemiotica della novità in musica -- Per una sociosemiotica del dubstep.

Gabriel Richardson Lear presents a bold new approach to one of the enduring debates about Aristotle's Nicomachean Ethics: the controversy about whether it coherently argues that the best life for humans is one devoted to a single activity, namely philosophical contemplation. Many scholars oppose this reading because the bulk of the Ethics is devoted to various moral virtues--courage and generosity, for example--that are not in any obvious way either manifestations of philosophical contemplation or subordinated to it. They argue that (...) Aristotle was inconsistent, and that we should not try to read the entire Ethics as an attempt to flesh out the notion that the best life aims at the "monistic good" of contemplation. In defending the unity and coherence of the Ethics, Lear argues that, in Aristotle's view, we may act for the sake of an end not just by instrumentally bringing it about but also by approximating it. She then argues that, for Aristotle, the excellent rational activity of moral virtue is an approximation of theoretical contemplation. Thus, the happiest person chooses moral virtue as an approximation of contemplation in practical life. Richardson Lear bolsters this interpretation by examining three moral virtues--courage, temperance, and greatness of soul--and the way they are fine. Elegantly written and rigorously argued, this is a major contribution to our understanding of a central issue in Aristotle's moral philosophy. (shrink)

Those who wish to claim that all facts about grounding are themselves grounded (“the meta-grounding thesis”) must defend against the charge that such a claim leads to infinite regress and violates the well-foundedness of ground. In this paper, we defend. First, we explore three distinct but related notions of “well-founded”, which are often conflated, and three corresponding notions of infinite regress. We explore the entailment relations between these notions. We conclude that the meta-grounding thesis need not lead to tension with (...) any of the three notions of “well-founded”. Finally, we explore the details of and motivations for further conditions on ground that one might add to generate a conflict between the meta-grounding thesis and a well-founded constraint. We explore these topics by developing and utilizing a formal framework based on the notion of a grounding structure. (shrink)

The central theme of this important book is that we are paying the price of an arrogance that refuses to recognize mystery. The author invites the reader to enter into the argument that he holds with himself on a great number of problems. Written in the early 1950s, Marcel's discussion of these topics are remarkably contemporary, e.g.: * Our crisis is a metaphysical, not merely social, one. * What a man is depends partly on what he thinks he is, and (...) a materialistic philosophy turns men into things. * Can a man be free except in a free country? * Stoicism is no longer a workable philosophy because today pressure can be put on the mind as well as on the body. * Technical progress is not evil in itself, but a technique is a means that, regarded as an end, can become either an idol or an excuse for self-idolatry. State control of scientific research, leading to a concentration on new means of destruction, is a calamity. * Fanaticism is an opinion that refuses to argue, and so the fanatic is an enemy of truth. * The kind of unification that science is bringing about today is really an ironing out of differences, but the only valuable kind of unity is one that implies a respect for differences. * We must beware of thinking in terms of great numbers and so blinding ourselves to the reality of individual suffering. Our philosophical approach to being is made possible only by our practical approach to our neighbor. * We must encourage the spirit of fraternity and distrust the kind of egalitarianism that is based on envy and resentment. * No man however humble should feel that he cannot spread the light among his friends. No easy solution is offered, but the author conveys his own faith that ultimately love and intelligence will triumph. (shrink)

El Estado de Hegel es el Estado de Derecho. Sin embargo en su Filosofía del Derecho se encuentran fundamentos decisivos para una teoría del Estado Social. Siguiendo el hilo de las Líneas fundamentales de la Filosofía del Derecho, se empieza por ver el derecho al bienestar, tal como se formula en la Moralidad (1). En la familia aparece el derecho de los hijos "de ser alimentados y educados" (2). El Derecho al bienestar se concreta en la sociedad civil (3), se (...) hace posible en el sistema de las necesidades (3.1.) y efectivo en la policía y la corporación (3.2 y 3.3), que ejercen funciones de suplencia de la familia. El mayor problema es la pobreza, tanto la que surge por contingencias subjetivas y sociales como por el funcionamiento mismo de la sociedad civil: la plebe. A este problema la sociedad es incapaz de darle una solución. (shrink)