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 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 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 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 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 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)

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 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)

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)

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 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)

In two often neglected passages of the Critique of Pure Reason, Kant submits that the Critique is a 'treatise' or a 'doctrine of method'. These passages are puzzling because the Critique is only cursorily concerned with identifying adequate procedures of argument for philosophy. In this book, Gabriele Gava argues that these passages point out that the Critique is the doctrine of method of metaphysics. Doctrines of method have the task of showing that a given science is indeed a science because (...) it possesses 'architectonic unity' – which happens when it realizes the 'idea' of a science. According to Gava's novel approach, the Critique establishes that metaphysics is capable of this unity, and his reading of the Critique from this perspective not only illuminates the central role of the Transcendental Doctrine of Method within it, but also clarifies the relationship between the different parts of the work. (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)

In this chapter, I investigate a problem for Kant’s claim that metaphysics can reach the status of science. The problem arises when one considers Kant’s account of the “architectonic unity” of metaphysics in the Architectonic of Pure Reason. Attaining architectonic unity is a condition for becoming a science for any body of cognitions that purports to be such. This is achieved when the cognitions belonging to a science are systematically organized according to the “idea of reason” which lies at the (...) basis of that science. However, Kant suggests that nobody can ever legitimately claim to have matched the idea of the philosopher, where this appears to imply that nobody can justifiably claim that she has fully grasped the idea of metaphysics. This generates a problem. I suggest that when Kant claims that the idea of the philosopher must remain an ideal or an archetype, he has a particular conception of philosophy in mind, that is, philosophy as a doctrine of wisdom. According to this understanding, philosophy must provide an example of how one can become virtuous. However, this is only a partial solution to our problem, for reasons that will be illustrated. (shrink)

This paper takes a close look at the thought that mereological relations on material objects mirror, and are mirrored by, parallel mereological relations on their exact locations. This hypothesis is made more precise by means of a battery of principles from which more substantive consequences are derived. Mereological harmony turns out to entail, for example, that atomistic space is an inhospitable environment for material gunk or that Whiteheadian space is not a hospitable environment for unextended material atoms.

Five hundred years after his death, Niccolò Machiavelli still draws an astonishing range of contradictory characterizations. Was he a friend of tyrants? An ardent republican loyal to Florence’s free institutions? The father of political realism? A revolutionary populist? A calculating rationalist? A Renaissance humanist? A prophet of Italian unification? A theorist of mixed government? A forerunner to authoritarianism? The master of the dark arts of intrigue? This book provides a vivid and engaging introduction to Machiavelli’s life and works that sheds (...) new light on his originality and relevance. Gabriele Pedullà—a leading Italian expert and acclaimed writer—offers fresh readings of the Florentine thinker’s most famous writings, The Prince and the Discourses on Livy, as well as lesser-known texts. A new and often surprising Machiavelli emerges: one closer to his time but also better suited to inform our own. Pedullà’s portrait of Machiavelli highlights his close attention to social and emotional bonds, staunch opposition to oligarchy, keen awareness of the economic side of power dynamics, and strong preference for history over philosophy as a guide for leaders. This book recovers the excitement Machiavelli roused in his first readers for a twenty-first-century audience, capturing his capacity to provoke, both then and now, with unconventional ideas and startling insights. (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)

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)

The goal of this paper is to provide an account of the role played by logic in the context of what Husserl names the “crisis of European sciences.” Presupposing the analyses offered in the Krisis, I look at Formale und Transzendentale Logik to demonstrate that the crisis of logic stems from the deviation of its original meaning as a “theory of science” and from its restriction to a mere “theoretical technique.” Through a comparison between Aristotelian syllogistic and modern logic, I (...) show why the modern discovery of the purely formal dimension of knowledge which makes possible such a mathematical technization is a positive achievement that hinders at the same time the disclosure of the truly philosophical nature of logic. The correct appraisal of this ambiguous phenomenon will explain why the rise of modern logic represents a decisive challenge for the success of Husserl’s late phenomenological project. (shrink)

Many consider the nature of human consciousness to be one of the last great unsolved mysteries. Why should the light turn on, so to speak, in human beings at all? And how is the electrical storm of neurons under our skull connected with our consciousness? Is the self only our brain's user interface, a kind of stage on which a show is performed that we cannot freely direct? In this book, philosopher Markus Gabriel challenges an increasing trend in the (...) sciences towards neurocentrism, a notion which rests on the assumption that the self is identical to the brain. Gabriel raises serious doubts as to whether we can know ourselves in this way. In a sharp critique of this approach, he presents a new defense of the free will and provides a timely introduction to philosophical thought about the self – all with verve, humor, and surprising insights. Gabriel criticizes the scientific image of the world and takes us on an eclectic journey of self-reflection by way of such concepts as self, consciousness, and freedom, with the aid of Kant, Schopenhauer, and Nagel but also Dr. Who, The Walking Dead, and Fargo. (shrink)

Schelling entwirft in seiner Spätphilosophie einen neuen Philosophietypus, der in Konkurrenz zu Hegels Metaphysik tritt. Dabei greift er Hegel nicht nur auf dem Gebiet fundamentaler theoretischen Annahmen an, sondern sucht ihn insbesondere durch einen neuen Begriff von Religion zu überbieten. Die Arbeit untersucht dies im Ausgang von Schellings "Philosophie der Mythologie".

In Kant’s Critique of Pure Reason and the Method of Metaphysics (CUP 2023), I argue that the first Critique is not only a ‘propaedeutic’ to metaphysics, but actually already establishes parts of metaphysics. These parts belong to what Kant calls transcendental philosophy. Additionally, I also provide an account of Kant’s critique of dogmatism and Wolff as its main defender. In this paper, I take up Luigi Filieri’s and Davide Dalla Rosa’s invitation to further develop my characterization of transcendental philosophy and (...) I respond to Michael Walschots’s objections against my interpretation of Kant’s critique of Wolff’s dogmatism. (shrink)

This chapter analyzes two short texts in which Peirce sketches out an anti-skeptical argument inspired by Kant’s refutation of idealism. The chapter will first consider why Peirce found Kant’s argument interesting and promising, given that it is often regarded as problematic and unsuccessful. It will then briefly reconstruct Kant’s refutation, highlighting its most problematic passages. Moreover, since Peirce’s own version of the argument relies on Kant’s views regarding the temporal structure of consciousness, the chapter will explain how Peirce tackles this (...) issue in “The Law of Mind.” Finally, the chapter considers Peirce’s own anti-skeptical argument and examines whether and how it can be seen as appropriating Kant’s strategy. (shrink)

This discussion of pride, shame, and guilt centers on the beliefs involved in the experience of any of these emotions. Through a detailed study, the author demonstrates how these beliefs are alike--in that they are all directed towards the self--and how they differ. The experience of these three emotions are illustrated by examples taken from English literature. These concrete cases supply a context for study and indicate the complexity of the situations in which these emotions usually occur.

In this paper I examine the relation between modern transhumanism and Nietzsche’s philosophy of the superhuman. Following Loeb, I argue that transhumanists cannot claim affinity to Nietzsche’s philosophy until they incorporate the doctrine of eternal recurrence to their project of technological enhancement. This doctrine liberates us from resentment against time by teaching us reconciliation with time and something higher than all reconciliation. Unlike Loeb, however, I claim that this “something higher” is not a new skill (prospective memory), but rather a (...) love for the past in the form of loving that aspect of it that is still with us, namely, the will to power itself, which is the engine of all life. Love of the past is thus equivalent to love of life. Since human beings are conscious incarnations of the will to power, in our case, love of life manifests itself as love of our humanity or love for that aspect of ourselves that connects us to each other, for we recognize it to be the same in all of us. Thus, learning this kind of love enables us to joyfully coordinate our wills in the pursuit of Zarathustra’s superhuman ideal without turning it into a destructive mockery of itself. While learning this kind of love would facilitate a joyful version of transhumanism, I conclude by suggesting that it is unlikely to be achieved through technological interventions of the sort envisioned by transhumanists. Instead, it requires the kind of participatory pedagogical program that Nietzsche thought his Zarathustra would fulfill. (shrink)

O objetivo deste trabalho é investigar a natureza ontológica e epistemológica do conceito de informação, focalizando inicialmente a Filosofia e Ética da Informação (EI), propostas por Floridi (1999; 2002; 2004; 2011; 2016), cujo fundamento teórico servirá de suporte para reflexões acerca da inteligência artificial generativa (IAGen), mais especificamente, o ChatGPT. O conceito de informação será abordado a partir de três vertentes na perspectiva filosófico-interdisciplinar: (1) realismo informacional, (2) ecologia informacional e (3) semântica informacional, segundo Gonzalez, Nascimento & Haselager (2004). A (...) partir dessa abordagem, direcionamos nosso estudo para propostas de Floridi (2004), indicando os seus possíveis problemas. Procuraremos entender a Filosofia da Informação, a partir da perspectiva da Ética da Informação (EI), analisando como a EI pode contribuir para reflexões acerca do uso de IA generativa. Problematizamos a EI a fim de construir uma ponte com a Ética Intercultural da Informação (EII) proposta por Capurro (2010). (shrink)

Sexualpolitik ist eine Machttechnik. Sie reguliert Verhaltensweisen oder schliesst Gruppen aus - das Feld Sexualität ist dabei besonders skandalisierbar. Angeblich problematische Sexualitäten werden nicht nur mit Geschlecht, sondern auch mit Ethnizität und Religion verflochten. Gabriele Dietze diskutiert diesen Zusammenhang in historischer, theoretischer und gegenwartsanalytischer Perspektive von feministischen Orientalismen der Ersten Frauenbewegung bis hin zu den Ereignissen von Köln in der Silvesternacht 2015.