Vassilios Karakostas

According to various no-go results in the foundations of quantum mechanics, for any system associated to a Hilbert space of dimension higher than two, it is not possible to assign definite truth values to all propositions pertaining to the system without generating a Kochen-Specker contradiction. In this respect, the Bub-Clifton uniqueness theorem is utilized for arguing that truth-value definiteness is consistently restored with respect to a determinate sublattice of propositions defined by the state of the quantum system concerned and a particular observable to be measured. On this basis, a perspectivist/contextual account of truth valuation in the quantum domain is produced that satisfies Tarski’s criterion of material adequacy for a theory of truth. In light of the latter, perspectivist truth conforms to perspective or context-bound correspondence of a de re nature, designating locally an objectively existing state of affairs. Such an account derives by virtue of the microphysical nature of physical reality in displaying a context-dependence of facts; thus, it essentially opposes a non-perspectival, metaphysically fixed point of reference, or a panoptical standpoint from which to state all facts of nature.

The present study investigates the tension between objectivism and perspectivism in light of the conceptual and philosophical implications of quantum theory. The guiding dictum of objectivism posits that science reveals the underlying structure of reality independently of human cognitive activity, that is, in terms of mind-independent, discourse-independent properties and relations occurring at any spatiotemporal location. It is shown that objectivism’s stance fits with the applicability of the bivalence principle as the semantic foundation of scientific discourse. It becomes then apparent that the non-Boolean logical structure of quantum theory systematically disrupts the objectivist framework. Along this vein, we provide succinct argumentation demonstrating quantum theory’s affinity to perspectivist reasoning. It is contended that the ubiquitous phenomenon of quantum contextuality, as established by Kochen-Specker’s celebrated theorem, strongly suggests that measurement values of quantum observables can, in general, be regarded as pertaining to an object under investigation only within a local probing frame or perspective from which the object-system is considered. The last remark is reinforced when considered within the endo-theoretic perspectivist framework of quantum mechanics. The essential philosophical meaning of the latter implies the view that the quantum world can be consistently comprehended through a multilevel structure of overlapping Boolean probing frames, realized as locally variable perspectives on a quantum system, being capable of forming jointly a coherent picture of the whole in a nontrivial way. Finally, in the appendix, the endo-theoretic perspectivist framework of quantum theory is critically compared to the relational interpretation of quantum mechanics, particularly in its recent development involving the postulate of “cross-perspective links”, revealing thereby the profoundly different picture of the quantum world’s architecture between the two proposals.

The logic of a physical theory reflects the structure of the propositions referring to the behaviour of a physical system in the domain of the relevant theory. It is argued in relation to classical mechanics that the propositional structure of the theory allows truth-value assignment in conformity with the traditional conception of a correspondence theory of truth. Every proposition in classical mechanics is assigned a definite truth value, either ‘true’ or ‘false’, describing what is actually the case at a certain moment of time. Truth-value assignment in quantum mechanics, however, differs; it is known, by means of a variety of ‘no go’ theorems, that it is not possible to assign definite truth values to all propositions pertaining to a quantum system without generating a Kochen–Specker contradiction. In this respect, the Bub–Clifton ‘uniqueness theorem’ is utilized for arguing that truth-value definiteness is consistently restored with respect to a determinate sublattice of propositions defined by the state of the quantum system concerned and a particular observable to be measured. An account of truth of contextual correspondence is thereby provided that is appropriate to the quantum domain of discourse. The conceptual implications of the resulting account are traced down and analyzed at length. In this light, the traditional conception of correspondence truth may be viewed as a species or as a limit case of the more generic proposed scheme of contextual correspondence when the non-explicit specification of a context of discourse poses no further consequences.

Contemporary perspectivism is viewed as a framework of scientific inquiry concerning the origin, generation and systematization of scientific knowledge of nature by focusing on the conditions under which such knowledge may arise in perspectivist terms and investigating the essential ramifications of these conditions. To this end, we develop the conceptual, methodological and semantic framework of contemporary perspectivism according to the norms of the proposed endo-theoretic approach. Implementation of the preceding three-fold scheme in quantum mechanics implies that the global structure of a quantum algebra of events can be consistently comprehended through a multilevel structure of locally variable Boolean perspectives, interconnected in a category-theoretic environment, yielding jointly all the information encoded in the former. In this respect, the proposed approach validates the perspectivist/contextual nature of quantum mechanics at a fundamental level of discourse. Furthermore, due to its general character, it may acquire the form of a theoretical pattern of scientific inquiry in the natural sciences, especially when dealing with complex trans-perspectival phenomena, the analysis of which requires the use of information resulting from more than one perspective. Finally, in the appendix, we provide a concise comparative assessment between our perspectivist framework of quantum theory and Rovelli’s relational interpretation of quantum mechanics.

The category-theoretic representation of quantum event structures provides a canonical setting for confronting the fundamental problem of truth valuation in quantum mechanics as exemplified, in particular, by Kochen–Specker’s theorem. In the present study, this is realized on the basis of the existence of a categorical adjunction between the category of sheaves of variable local Boolean frames, constituting a topos, and the category of quantum event algebras. We show explicitly that the latter category is equipped with an object of truth values, or classifying object, which constitutes the appropriate tool for assigning truth values to propositions describing the behavior of quantum systems. Effectively, this category-theoretic representation scheme circumvents consistently the semantic ambiguity with respect to truth valuation that is inherent in conventional quantum mechanics by inducing an objective contextual account of truth in the quantum domain of discourse. The philosophical implications of the resulting account are analyzed. We argue that it subscribes neither to a pragmatic instrumental nor to a relative notion of truth. Such an account essentially denies that there can be a universal context of reference or an Archimedean standpoint from which to evaluate logically the totality of facts of nature.

Contemporary scientific perspectivism is primarily viewed as a methodological framework of how we obtain and form scientific knowledge of nature, through a broadly perspectivist process, especially, with reference to quantum mechanics. In the present study, this is implemented by representing categorically the global structure of a quantum algebra of events in terms of structured interconnected families of local Boolean probing frames, realized as suitable perspectives or contexts for measuring physical quantities. The essential philosophical meaning of the proposed approach implies that the quantum world can be consistently approached and comprehended through a multilevel structure of locally variable perspectives, which interlock, in a category-theoretical environment, to form a coherent picture of the whole in a non-trivial way.

The category-theoretic representation of quantum event structures provides a canonical setting for confronting the fundamental problem of truth valuation in quantum mechanics as exemplified, in particular, by Kochen-Specker’s theorem. In the present study, this is realized by representing categorically the global structure of a quantum algebra of events in terms of sheaves of local Boolean frames forming Boolean localization functors. The category of sheaves is a topos providing the possibility of applying the powerful logical classification methodology of topos theory with reference to the quantum world. In particular, we show that the topos-theoretic representation scheme of quantum event algebras by means of Boolean localization functors incorporates an object of truth values, which constitutes the appropriate tool for the definition of quantum truth-value assignments to propositions describing the behavior of quantum systems. Effectively, this scheme induces a contextualist account of truth in the quantum domain of discourse. The philosophical implications of the resulting account are analyzed. Such an account essentially denies that there can be a universal context of reference or an Archimedean standpoint from which to state the totality of facts of nature.

The category-theoretic representation of quantum event structures provides a canonical setting for confronting the fundamental problem of truth valua- tion in quantum mechanics as exemplified, in particular, by Kochen-Specker’s theorem. In the present study, this is realized on the basis of the existence of a categorical adjunction between the category of sheaves of variable local Boolean frames, constituting a topos, and the category of quantum event al- gebras. We show explicitly that the latter category is equipped with an object of truth values, or classifying object, which constitutes the appropriate tool for assigning truth values to propositions describing the behavior of quantum systems. Effectively, this category-theoretic representation scheme circumvents consistently the semantic ambiguity with respect to truth valuation that is in- herent in conventional quantum mechanics by inducing an objective contextual account of truth in the quantum domain of discourse. The philosophical im- plications of the resulting account are analyzed. We argue that it subscribes neither to a pragmatic instrumental nor to a relative notion of truth. Such an account essentially denies that there can be a universal context of reference or an Archimedean standpoint from which to evaluate logically the totality of facts of nature. In this light, the transcendence condition of the usual concep- tion of correspondence truth is superseded by a reflective-like transcendental reasoning of the proposed account of truth that is suitable to the quantum domain of discourse.

La sémantique sous-jacente à la structure propositionnelle de la mécanique quantique des espaces de Hilbert implique une ambiguïté intrinsèque concernant l'impossibilité d'assigner des valeurs de vérité définies à toutes les propositions ayant trait à un système quantique sans générer de contradiction de type Kochen-Specker. Bien que ledit résultat de Kochen-Specker interdise une assignation globale et absolue des valeurs de vérité aux propositions de la mécanique quantique, il n'exclut pas les assignations contextuelles. À cet égard, le théorème d'unicité de Bub-Clifton est utilisé pour montrer que le caractère défini des valeurs de vérité est restauré de façon cohérente pour un sous-ensemble déterminé de propositions, défini par l'état du système quantique considéré et une observable préférée appropriée. Il est suggéré que le choix le plus naturel pour cette dernière, en particulier vis-à-vis du problème de l'assignation de valeurs de vérité en mécanique quantique, est que ce soit l'observable sur le point d'être mesurée qui ait une valeur déterminée. On fournit ainsi une conception de la vérité de la correspondance contextuelle qui est appropriée au domaine quantique du discours. La conception de la vérité qui en résulte est compatible avec une conception réaliste de la vérité, qui nie qu'il puisse exister un contexte de référence universel ou un point d'appui archimédien à partir duquel la totalité des faits de la nature puisse être évaluée logiquement.

This paper examines the problem of founding irreversibility on reversible equations of motion from the point of view of the Brussels school's recent developments in the foundations of quantum statistical mechanics. A detailed critique of both their 'subdynamics' and 'transformation' theory is given. It is argued that the subdynamics approach involves a generalized form of 'coarse-graining' description, whereas, transformation theory cannot lead to truly irreversible processes pointing to a preferred direction of time. It is concluded that the Brussels school's conception of microscopic temporal irreversibility, as such, is tacitly assumed at the macroscopic level. Finally a logical argument is provided which shows, independently of the mathematical formalism of the theory concerned, that statistical reasoning alone is not sufficient to explain the arrow of time

Standard quantum mechanics undeniably violates the notion of separability that classical physics accustomed us to consider as valid. By relating the phenomenon of quantum nonseparability to the all-important concept of potentiality, we effectively provide a coherent picture of the puzzling entangled correlations among spatially separated systems. We further argue that the generalized phenomenon of quantum nonseparability implies contextuality for the production of well-defined events in the quantum domain, whereas contextuality entails in turn a structural-relational conception of quantal objects, viewed as carriers of dispositional properties. It is finally suggested that contextuality, if considered as a conditionalization preparation procedure of the object to be measured, naturally leads to a separable concept of reality whose elements are experienced as distinct, well-localized objects having determinate properties. In this connection, we find it necessary to distinguish the meaning of the term reality from the criterion of reality for us. The implications of the latter considerations for the notion of objectivity in quantum mechanics are also discussed.

It is shown that Lewis’ ontological doctrine of Humean supervenience incorporates at its foundation the so-called separability principle of classical physics. In view of the systematic violation of the latter within quantum mechanics, the claim that contemporary physical science may posit non-supervenient relations beyond the spatiotemporal ones is reinforced on a foundational basis concerning constraints on the state representation of physical systems. Depending on the mode of assignment of states to quantum systems — unit state vectors versus statistical density operators — we distinguish between strongly and weakly non-Humean, non-supervenient relations. It is demonstrated that in either case, the relations of quantum entanglement constitute prototypical examples of irreducible physical relations that do not supervene upon a spatiotemporal arrangement of Humean qualities, weakening, thereby, the thesis of Humean supervenience. In this respect, the status of Lewis’ recombination principle is examined, whereas his conception of lawhood is critically investigated. It is concluded that the assumption of ontological reductionism, as expressed in Lewis’ Humean doctrine, cannot be regarded as a reliable code of the nature of the physical world and its contents. It is proposed instead that due to the undeniable existence of non-supervenient relations, a metaphysic of relations of a moderate kind ought to be acknowledged as an indispensable part of our understanding of the natural world at a fundamental level

The conceptual structure of orthodox quantum mechanics has not provided a fully satisfactory and coherent description of natural phenomena. With particular attention to the measurement problem, we review and investigate two unorthodox formulations. First, there is the model advanced by GRWP, a stochastic modification of the standard Schrödinger dynamics admitting statevector reduction as a real physical process. Second, there is the ontological interpretation of Bohm, a causal reformulation of the usual theory admitting no collapse of the statevector. Within these two seemingly quite different approaches, we discuss in a comparative manner, several points: The meaning of the state vector, the status of quantum probability, the legitimacy of attributing macro objective properties to physical systems, and the possibility of retrieving the classical limit. Finally, we consider aspects of non-locality and relevant difficulties with formulating a relativistic generalization of the two approaches.

Standard quantum mechanics unquestionably violates the separability principle that classical physics (be it point-like analytic, statistical, or field-theoretic) accustomed us to consider as valid. In this paper, quantum nonseparability is viewed as a consequence of the Hilbert-space quantum mechanical formalism, avoiding thus any direct recourse to the ramifications of Kochen-Specker’s argument or Bell’s inequality. Depending on the mode of assignment of states to physical systems – unit state vectors versus non-idempotent density operators – we distinguish between strong/relational and weak/deconstructional forms of quantum nonseparability. The origin of the latter is traced down and discussed at length, whereas its relation to the all important concept of potentiality in forming a coherent picture of the puzzling entangled interconnections among spatially separated systems is also considered. Finally, certain philosophical consequences of quantum non-separability concerning the nature of quantum objects, the question of realism in quantum mechanics, and possible limitations in revealing the actual character of physical reality in its entirety are explored.

The present study attempts to provide a consistent and coherent account of what the world could be like, given the conceptual framework and results of contemporary quantum theory. It is suggested that standard quantum mechanics can, and indeed should, be understood as a realist theory within its domain of application. It is pointed out, however, that a viable realist interpretation of quantum theory requires the abandonment or radical revision of the classical conception of physical reality and its traditional philosophical presuppositions. It is argued, in this direction, that the conceptualization of the nature of reality, as arising out of our most basic physical theory, calls for a kind of contextual realism. Within the domain of quantum mechanics, knowledge of 'reality in itself', 'the real such as it truly is' independent of the way it is contextualized, is impossible in principle. In this connection, the meaning of objectivity in quantum mechanics is analyzed, whilst the important question concerning the nature of quantum objects is explored

The overwhelming majority of the attempts in exploring the problems related to quantum logical structures and their interpretation have been based on an underlying set-theoretic syntactic language. We propose a transition in the involved syntactic language to tackle these problems from the set-theoretic to the category-theoretic mode, together with a study of the consequent semantic transition in the logical interpretation of quantum event structures. In the present work, this is realized by representing categorically the global structure of a quantum algebra of events (or propositions) in terms of sheaves of local Boolean frames forming Boolean localization functors. The category of sheaves is a topos providing the possibility of applying the powerful logical classification methodology of topos theory with reference to the quantum world. In particular, we show that the topos-theoretic representation scheme of quantum event algebras by means of Boolean localization functors incorporates an object of truth values, which constitutes the appropriate tool for the definition of quantum truth-value assignments to propositions describing the behavior of quantum systems. Effectively, this scheme induces a revised realist account of truth in the quantum domain of discourse. We also include an Appendix, where we compare our topos-theoretic representation scheme of quantum event algebras with other categorial and topos-theoretic approaches

The logic of a physical theory reflects the structure of the propositions referring to the behaviour of a physical system in the domain of the relevant theory. It is argued in relation to classical mechanics that the propositional structure of the theory allows truth-value assignment in conformity with the traditional conception of a correspondence theory of truth. Every proposition in classical mechanics is assigned a definite truth value, either ‘true’ or ‘false’, describing what is actually the case at a certain moment of time. Truth-value assignment in quantum mechanics, however, differs; it is known, by means of a variety of ‘no go’ theorems, that it is not possible to assign definite truth values to all propositions pertaining to a quantum system without generating a Kochen–Specker contradiction. In this respect, the Bub–Clifton ‘uniqueness theorem’ is utilized for arguing that truth-value definiteness is consistently restored with respect to a determinate sublattice of propositions defined by the state of the quantum system concerned and a particular observable to be measured. An account of truth of contextual correspondence is thereby provided that is appropriate to the quantum domain of discourse. The conceptual implications of the resulting account are traced down and analyzed at length. In this light, the traditional conception of correspondence truth may be viewed as a species or as a limit case of the more generic proposed scheme of contextual correspondence when the non-explicit specification of a context of discourse poses no further consequences

The category-theoretic representation of quantum event structures provides a canonical setting for confronting the fundamental problem of truth valuation in quantum mechanics as exemplified, in particular, by Kochen–Specker’s theorem. In the present study, this is realized on the basis of the existence of a categorical adjunction between the category of sheaves of variable local Boolean frames, constituting a topos, and the category of quantum event algebras. We show explicitly that the latter category is equipped with an object of truth values, or classifying object, which constitutes the appropriate tool for assigning truth values to propositions describing the behavior of quantum systems. Effectively, this category-theoretic representation scheme circumvents consistently the semantic ambiguity with respect to truth valuation that is inherent in conventional quantum mechanics by inducing an objective contextual account of truth in the quantum domain of discourse. The philosophical implications of the resulting account are analyzed. We argue that it subscribes neither to a pragmatic instrumental nor to a relative notion of truth. Such an account essentially denies that there can be a universal context of reference or an Archimedean standpoint from which to evaluate logically the totality of facts of nature.