It is well known that in quantum mechanics we cannot always define consistently properties that are context independent. Many approaches exist to describe contextual properties, such as Contextuality by Default (CbD), sheaf theory, topos theory, and non-standard or signed probabilities. In this paper, we propose a treatment of contextual properties that is specific to quantum mechanics, as it relies on the relationship between contextuality and indistinguishability. In particular, we propose that if we assume the ontological thesis that quantum (...) particles or properties can be indistinguishable yet different, no contradiction arising from a Kochen–Specker-type argument appears: when we repeat an experiment, we are in reality performing an experiment measuring a property that is indistinguishable from the first, but not the same. We will discuss how the consequences of this move may help us understand quantum contextuality. (shrink)

Realist interpretations of quantum mechanics presuppose the existence of elements of reality that are independent of the actions used to reveal them. Such a view is challenged by several no-go theorems that show quantum correlations cannot be explained by non-contextual ontological models, where physical properties are assumed to exist prior to and independently of the act of measurement. However, all such contextuality proofs assume a traditional notion of causal structure, where causal influence flows from past to future according to (...) ordinary dynamical laws. This leaves open the question of whether the apparent contextuality of quantum mechanics is simply the signature of some exotic causal structure, where the future might affect the past or distant systems might get correlated due to non-local constraints. Here we show that quantum predictions require a deeper form of contextuality: even allowing for arbitrary causal structure, no model can explain quantum correlations from non-contextual ontological properties of the world, be they initial states, dynamical laws, or global constraints. (shrink)

It is explained on a physical basis how absence of contextuality allows Bell inequalities to be violated, without bringing an implication on locality or realism. Hereto we connect first to the local realistic theory Stochastic Electrodynamics, and then put the argument more broadly. Thus even if Bell Inequality Violation is demonstrated beyond reasonable doubt, it will have no say on local realism, because absence of contextuality prevents the Bell inequalities to be derived from local realistic models.

Western imperialism and colonialism have tremendously affected the epistemological conception of Africa and Africans. In the same vein, early missionaries did not countenance the cosmologies and lived experiences of the Africans in their interpretation and application of the Bible. On the contrary, they imposed Western epistemologies and theological images on Africa. Although much work has been carried out in these areas, little attention has been devoted to how contextuality, interculturality and decolonisation are exercised in power struggles: the power to (...) define what counts for Africa and Africans as they daily deploy the resources of the Bible. The author argues that contextuality, interculturality and decolonisation are schemes of power relations on the one hand and of owning the Bible on the other, rather than mere methods of biblical hermeneutics in Africa. As schemes of power, they reject imperialist agenda of unequal barter of cultural exchange claimed as civilising the African. Presenting contextuality as a finished product is a violation of the rights of Africans to productively apply the Bible as a text seeking understanding in a different clime from the West; it is also a denial of the reality of interculturality, and thus it ignites the need for decolonisation. By utilising conceptual analysis as a framework, it is argued that these schemes are beyond hermeneutical methods but have the power to resist the suffusing influence of Western theological suffocation in Africa. Contribution: This study argues that contextuality, interculturality and decolonisation are not mere hermeneutical methods for studying the Bible in context; they are instruments of struggle to liberate it from Western epistemological stranglehold. (shrink)

Western imperialism and colonialism have tremendously affected the epistemological conception of Africa and Africans. In the same vein, early missionaries did not countenance the cosmologies and lived experiences of the Africans in their interpretation and application of the Bible. On the contrary, they imposed Western epistemologies and theological images on Africa. Although much work has been carried out in these areas, little attention has been devoted to how contextuality, interculturality and decolonisation are exercised in power struggles: the power to (...) define what counts for Africa and Africans as they daily deploy the resources of the Bible. The author argues that contextuality, interculturality and decolonisation are schemes of power relations on the one hand and of owning the Bible on the other, rather than mere methods of biblical hermeneutics in Africa. As schemes of power, they reject imperialist agenda of unequal barter of cultural exchange claimed as civilising the African. Presenting contextuality as a finished product is a violation of the rights of Africans to productively apply the Bible as a text seeking understanding in a different clime from the West; it is also a denial of the reality of interculturality, and thus it ignites the need for decolonisation. By utilising conceptual analysis as a framework, it is argued that these schemes are beyond hermeneutical methods but have the power to resist the suffusing influence of Western theological suffocation in Africa. CONTRIBUTION: This study argues that contextuality, interculturality and decolonisation are not mere hermeneutical methods for studying the Bible in context; they are instruments of struggle to liberate it from Western epistemological stranglehold. (shrink)

A. W. Price explores the varying ways in which context is relevant to our reasoning about what to do.

The ontological model framework for an operational theory has generated much interest in recent years. The debate concerning reality of quantum states has been made more precise in this framework. With the introduction of generalized notion of contextuality in this framework, it has been shown that completely mixed state of a qubit is preparation contextual. Interestingly, this new idea of preparation contextuality has been used to demonstrate nonlocality of some \(\psi \) -epistemic models without any use of Bell’s (...) inequality. In particular, nonlocality of a non maximally \(\psi \) -epistemic model has been demonstrated from preparation contextuality of a maximally mixed qubit and Schrödinger’s steerability of the maximally entangled state of two qubits (Leifer and Maroney, Phys Rev Lett 110:120401, 2013). In this paper, we, show that any mixed state is preparation contextual. We, then, show that nonlocality of any bipartite pure entangled state, with Schmidt rank two, follows from preparation contextuality and steerability provided we impose certain condition on the epistemicity of the underlying ontological model. More interestingly, if the pure entangled state is of Schmidt rank greater than two, its nonlocality follows without any further condition on the epistemicity. Thus our result establishes a stronger connection between nonlocality and preparation contextuality by revealing nonlocality of any bipartite pure entangled states without any use of Bell-type inequality. (shrink)

Nieuwenhuizen argued that there exists some “contextuality loophole” in Bell’s theorem. This claim is unjustified. In Bell’s theorem non-contextuality is not presupposed but derived from Einstein causality using the EPR argument.

I will argue that Kochen-Specker arguments do not provide an algebraic proof for quantum contextuality since, for the argument to be effective, operators must be uniquely associated with measur...

Beginning with Barry Hoffmaster’s charge that we reclaim bioethics from the moral philosopher’s top-down theorizing, I discuss two moral philosophy contexts that offer resources for the kind of complex attention Hoffmaster demands: Iris Murdoch and Cora Diamond in moral philosophy and Margaret Urban Walker, Hilde Lindeman, and Marian Verkerk’s joint take on bioethics. My aim is: 1) to dispel a simplified notion of philosophy in bioethics; 2) to unite two strands of philosophy, which converge on important issues relevant to contemporary (...) bioethics; and 3) to explore these strands in terms of enabling, maieutic work on our ethical points of departure. (shrink)

Quantum theory is a probabilistic theory that embodies notoriously striking correlations, stronger than any that classical theories allow but not as strong as those of hypothetical ‘super-quantum’ theories. This raises the question ‘Why the quantum?’—whether there is a handful of principles that account for the character of quantum probability. We ask what quantum-logical notions correspond to this investigation. This project isn’t meant to compete with the many beautiful results that information-theoretic approaches have yielded but rather aims to complement that work.

This paper reviews and develops the concept of “contextuality” whose profound significance—or lack thereof—was clarified especially by Detlef Dürr and his collaborators. In particular, we explore, in the context of a simple toy model of a measurement procedure described using Bohmian mechanics, the dependence of measurement outcomes on the (continuously variable) strength of the coupling between the system and measuring apparatus. This provides a revealing illustration of the fact that the outcomes of experiments may, and in general do, depend (...) on details of the experiment other than simply the Hermitian operator which (as it is often misleadingly said) is “measured” in the experiment. (shrink)

This paper introduces an extension of the de Broglie-Bohm-Bell formulation of quantum mechanics, which includes intrinsic particle degrees of freedom, such as spin, as elements of reality. To evade constraints from the Kochen-Specker theorem the discrete spin values refer to a specific basis – i.e., a single spin vector orientation for each particle; these spin orientations are, however, not predetermined, but dynamic and guided by the wave function of the system, which is conditional on the realized location values of the (...) particles. In this way, the unavoidable contextuality of spin is provided by the wave function and its realized particle configuration, whereas spin is still expressed as a local property of the individual particles. This formulation, which furthermore features a rigorous discrete-time stochastic dynamics, allows for numerical simulations of particle systems with entangled spin, such as Bohm’s version of the EPR experiment. (shrink)

This paper proposes a view on epistemic relativism that arises from the problem of the criterion, keeping in consideration that the assessment of criterion standards always occurs in a certain context. The main idea is that the epistemic value of the assertion “S knows that p” depends not only on the criterion adopted within an epistemic framework and the relationship between said criterion and a meta-criterion, but also from the collaboration with other subjects who share the same standards. Thus, one (...) can choose between particularist and methodist criteria according to the context of assessment. This position has the advantage of presenting a new perspective concerning both the criterion problem and the problem of inter-contextuality in the evaluation of different epistemic frameworks. (shrink)

The focus of the article is the question of the nature of contextuality in quantum phenomena. What underlies it: normative procedures of description dictated by rules and language, or is reality itself structured procedurally? At the core of Igor Prisyazhnuk's contextual quantum realism lies the distinction between the ideal and the real. Quantum uncertainty is interpreted by him as a situation where the rule has not yet been applied to the object, and the measurement context merely creates conditions in (...) which the object can be identified. This allows for the avoidance of both subjectivism and flat objectivism, while maintaining the conception of a reality that objectively exists, yet is sensitive to context. Prisyazhnuk draws a line between sequential contextualism (the Bohr-Benoit line) and what he calls ontological correlationalism, classifying the latter under agency realism by Karen Barad. The methodology is based on a comparative analysis of two philosophical traditions concerning quantum contextuality. First, the foundations of each position and key concepts are reconstructed to reveal the divergence: Prisyazhnuk's categorical dualism versus Simondonian ontogenesis. Then this divergence is tested against the material of quantum uncertainty and entanglement. The goal is to understand which strategy more consistently explains the nature of quantum reality, avoiding relativism and anthropocentrism. The comparison is made along three parameters: the relationship between reality and its description, the status of the subject and norms, and the explanatory power of the conceptual apparatus in the context of experimental data. Viewing this through the lens of Simondon reveals a different ontological perspective. Quantum contextuality ceases to be a relation between norm and reality; it becomes a phase of individuation. The measurement situation appears not as the application of a rule, but as the resolution of a metastable state. In this state, the system and the instrument do not yet exist separately; they exist in an inseparable potential being, and only in the act of measurement do their outlines emerge. The comparison of the two approaches raises questions about ontological depth. Does Prisyazhnuk's normative structure provide the tools necessary to explain quantum entanglement and the emergence of the world, or does the Simondonian model, with its transduction, metastability, and associated environment, offer a more coherent description of the formation of a quantum event, avoiding anthropocentrism? (shrink)

This article proposes a synthesis of Gödel’s incompleteness theorems—landmark results in mathematical logic—with Relational Quantum Dynamics, an interpretation of quantum mechanics that emphasizes relational properties over absolute states. Gödel’s theorems establish that any sufficiently complex formal system cannot prove all true statements within itself (incompleteness) nor its own consistency. In parallel, quantum mechanics reveals limits through phenomena like contextuality (where measurement outcomes depend on the measurement context) and Bell’s theorem (which rules out local hidden variables). The article uses category (...) theory—a mathematical framework for abstract structures—to formalize these parallels, suggesting that both logic and quantum physics reflect inherent limitations in achieving a single, absolute description of reality. It further incorporates consciousness as a fundamental aspect of RQD, linking it to quantum interactions via information theory. (shrink)

Science does not exist in vacuum; it arises and works in context. Ground-breaking achievements transforming the scientific landscape often stem from philosophical thought, just as symbolic logic and computer science were born from the early analytic philosophy, and for the very reason they impact our global worldview as a coherent whole as well as local knowledge production in different specialised domains. Here we take first steps in elucidating rich philosophical contexts in which Samson Abramsky’s far-reaching work centring around categorical science (...) as a new kind of science may be placed, explicated, and articulated. We argue, inter alia, that Abramsky’s work, as a whole, may be construed as demonstrating the categorical unity of science, or rather the sciences, in a mathematically rigorous, down-to-earth manner, which has been a salient feature of his work. At the same time we trace his intellectual history, leading from duality, to intensionality, and to contextuality, and place it in a broader context of philosophy beyond the analytic-continental divide, namely towards the reintegration of them as in the post-analytic tradition. Besides, we address issues in philosophy of category theory, such as the foundational autonomy of category theory and the (presumably two) dogmas of set-theoretical foundationalism, which Abramsky actually touch upon in one of his few philosophically inclined works. As to philosophy of category theory, we also address categorical structuralism as higher-order structuralism, categorical epistemology as elucidating higher-order meta-laws, and categorical ontology as allowing for reduction of ontological commitment via structural realism, the structuralist resolution of Benaceraff’s dilemma, and the pluralistic multiverse view of science as opposed to the set-theoretical reductionist ‘universe’ view. We conclude by speculating about the existence of the Oxford School of (Pluralistic) Unified Science as opposed to the Vienna Circle of (Monistic) Unified Science and to the Stanford School of (Pluralistic) Disunified Science; Categorical Unified Science may potentially allow us to reconcile the two camps on the unity and disunity of science whilst doing justice to both of them. Categorical unity arguably allows for unification via epistemological and ontological networking, and via knowledge transfer thus enabled, rather than unification via the reduction of everything and every truth to a single foundationalist framework, whilst taking at face value disunity, plurality, and diversity, and their significance in science and in human civilisation as a whole. (shrink)

In this paper, we defend two claims. First, we argue that a notion of contextuality that has been formalized in physics and psychology is applicable to linguistic contexts. Second, we propose that this formal apparatus is philosophically significant for the epistemology of language because it imposes homogeneous rational constraints on speakers. We propose a Contextuality Principle that explains and articulates these two claims. This principle states that speakers update contextual information by significantly reducing the space of probabilities and (...) variables in a non-commutative way. Some contexts affect other contexts not merely in terms of the information they contain, but also on the basis of their sequential order. In particular, we argue that the Contextuality by Default (CBD) theory provides a formalism that helps explain the role of contextuality in rational linguistic exchanges. (shrink)

This article extends the combinatorial approach to support the determination of contextuality amidst causal influences. Contextuality is an active field of study in Quantum Cognition, in systems relating to mental phenomena, such as concepts in human memory. In the cognitive field of study, a contemporary challenge facing the determination of whether a phenomenon is contextual has been the identification and management of disturbances. Whether or not said disturbances are identified through the modeling approach, constitute causal influences, or are (...) disregardableas as noise is important, as contextuality cannot be adequately determined in the presence of causal influences. To address this challenge, we first provide a formalization of necessary elements of the combinatorial approach within the language of canonical causal models. Through this formalization, we extend the combinatorial approach to support a measurement and treatment of disturbance, and offer techniques to separately distinguish noise and causal influences. Thereafter, we develop a protocol through which these elements may be represented within a cognitive experiment. As human cognition seems rife with causal influences, cognitive modelers may apply the extended combinatorial approach to practically determine the contextuality of cognitive phenomena. (shrink)

We present a proof for a conjecture previously formulated by Dzhafarov et al.. The conjecture specifies a measure for the degree of contextuality and a criterion for contextuality in a broad class of quantum systems. This class includes Leggett–Garg, EPR/Bell, and Klyachko–Can–Binicioglu–Shumovsky type systems as special cases. In a system of this class certain physical properties \ are measured in pairs \ \); every property enters in precisely two such pairs; and each measurement outcome is a binary random (...) variable. Denoting the measurement outcomes for a property \ in the two pairs it enters by \ and \, the pair of measurement outcomes for \ \) is \ \). Contextuality is defined as follows: one computes the minimal possible value \ for the sum of \ ) that is allowed by the individual distributions of \ and \; one computes the minimal possible value \ for the sum of \ across all possible couplings of the entire set of random variables \ in the system; and the system is considered contextual if \ ). This definition has its justification in the general approach dubbed Contextuality-by-Default, and it allows for measurement errors and signaling among the measured properties. The conjecture proved in this paper specifies the value of \ in terms of the distributions of the measurement outcomes \ \). (shrink)

In this paper we give additional arguments in favor of the point of view that the violation of Bell, CHSH and CH inequalities is not due to a mysterious non locality of nature. We concentrate on an intimate relation between a protocol of a random experiment and a probabilistic model which is used to describe it. We discuss in a simple way differences between attributive joint probability distributions and generalized joint probability distributions of outcomes from distant experiments which depend on (...) how the pairing of these outcomes is defined. We analyze in detail experimental protocols implied by local realistic and stochastic hidden variable models and show that they are incompatible with the protocols used in spin polarization correlation experiments. We discuss also the meaning of “free will”, differences between quantum and classical filters, contextuality of Kolmogorov models, contextuality of quantum theory and show how this contextuality has to be taken into account in probabilistic models trying to explain in an intuitive way the predictions of QT. The long range imperfect correlations between the clicks of distant detectors can be explained by partially preserved correlations between the signals created by a source. These correlations can only be preserved if the clicks are produced in a local and deterministic way depending on intrinsic parameters describing signals and measuring devices in the moment of the measurement. If an act of a measurement was irreducibly random they would be destroyed. It seems to indicate that QT may be in fact emerging from some underlying more detailed theory of physical phenomena. If this was a case then there is a chance to find in time series of experimental data some fine structures not predicted by QT. This would be a major discovery because it would not only prove that QT does not provide a complete description of individual physical systems but it would prove that it is not predictably complete. (shrink)

Let random vectors \ represent joint measurements of certain subsets \ of properties\ in different contexts\. Such a system is traditionally called noncontextual if there exists a jointly distributed set \ of random variables such that \ has the same distribution as \ for all \ A trivial necessary condition for noncontextuality and a precondition for many measures of contextuality is that the system is consistently connected, i.e., all \ measuring the same property \ have the same distribution. The (...) contextuality-by-default approach allows defining more general measures of contextuality that apply to inconsistently connected systems as well, but at the price of a higher computational cost. In this paper we propose a novel measure of contextuality that shares the generality of the CbD approach and the computational benefits of the previously proposed negative probability approach. The present approach differs from CbD in that instead of considering all possible joints of the double-indexed random variables \, it considers all possible approximating single-indexed systems \. The degree of contextuality is defined based on the minimum possible probabilistic distance of the actual measurements \ from \. We show that this measure, called the optimal approximation measure, agrees with a certain measure of contextuality of the CbD approach for all systems where each property enters in exactly two contexts. The OA measure can be calculated far more efficiently than the CbD measure and even more efficiently than the NP measure for sufficiently large systems. We also define a variant, the OA-NP measure of contextuality that agrees with the NP measure for consistently connected systems while extending it to inconsistently connected systems. (shrink)

The context of a linguisticexpression is defined as everything outside theexpression itself that is necessary forunambiguous interpretation of the expression.As meaning can be conveyed either by theimplicit, shared context or by the explicitform of the expression, the degree ofcontext-dependence or ``contextuality'' ofcommunication will vary, depending on thesituation and preferences of the languageproducer. An empirical measure of thisvariation is proposed, the ``formality'' or``F-score'', based on the frequencies ofdifferent word classes. Nouns, adjectives,articles and prepositions are more frequent inlow-context or ``formal'' types (...) of expression;pronouns, adverbs, verbs and interjections aremore frequent in high-context styles. Thismeasure adequately distinguishes differentgenres of language production using data forDutch, French, Italian, and English. Factoranalyses applied to data in 7 differentlanguages produce a similar factor as the mostimportant one. Both the data and thetheoretical model suggest that contextualitydecreases when unambiguous understandingbecomes more important or more difficult toachieve, when the separation in space, time orbackground between the interlocutors increases,and when the speaker is male, introvertedand/or academically educated. (shrink)

This paper discusses the question of stable facts in relational quantum mechanics (RQM). I examine how the approach to quantum logic in the consistent histories formalism can be used to clarify what infomation about a system can be shared between different observers. I suggest that the mathematical framework for Consistent Histories can and should be incorporated into RQM, whilst being clear on the interpretational differences between the two approaches. Finally I briefly discuss two related issues: the similarities and differences between (...) special relativity and RQM and the recent Cross-Perspectival Links modification to RQM. (shrink)

This study examines the multi-contextual dynamics of refugee entrepreneurship through the lens of embeddedness. It attempts to explain the interplay of inclusion and exclusion within a host society. For this purpose, the study qualitatively analyses the narratives of 39 Syrian refugee entrepreneurs and four critical informants in Türkiye. Our findings reveal a diverse set of refugee entrepreneurs, categorized into survival, ethnic-targeting, and integrating entrepreneurs, based on their motivations and level of embeddedness. Interestingly, as refugee entrepreneurs become more embedded in the (...) host country, they experience increased exclusion due to various societal factors. To navigate these challenges, entrepreneurs continually negotiate their societal position using innovative strategies to combat exclusion. Our study incorporates social, political, institutional, and spatial contexts across host, home, and third countries. Thus, it extends the embeddedness literature by highlighting refugee entrepreneurs' multi-layered and multi-locational embeddedness. Our findings also emphasise the significant role of political embeddedness, which Research often overlooks. Differentially excluding refugee entrepreneurs from society and their counter-strategies are closely tied to their limited political embeddedness. Finally, we discuss the ethical and policy implications of promoting the inclusion of refugee entrepreneurs and contributing to the United Nations' Sustainable Development Goals. We argue that clear integration policies, removal of institutional barriers, and international cooperation are necessary. (shrink)

Hardy and Unruh constructed a family of non-maximally entangled states of pairs of particles giving rise to correlations that cannot be accounted for with a local hidden-variable theory. Rather than pointing to violations of some Bell inequality, however, they pointed to apparent clashes with the basic rules of logic. Specifically, they constructed these states and the associated measurement settings in such a way that the outcomes satisfy some conditionals but not an additional one entailed by them. Quantum mechanics avoids the (...) broken ‘if …then …’ arrows in such Hardy–Unruh chains, as we call them, because it cannot simultaneously assign truth values to all conditionals involved. Measurements to determine the truth value of some preclude measurements to determine the truth value of others. Hardy–Unruh chains thus nicely illustrate quantum contextuality: which variables do and do not obtain definite values depends on what measurements we decide to perform. Using a framework inspired by Bub and Pitowsky and developed in our book Understanding Quantum Raffles (co-authored with Michael E. Cuffaro), we construct and analyze Hardy–Unruh chains in terms of fictitious bananas mimicking the behavior of spin-1/2 particles. (shrink)

In this paper we attempt to analyze the physical and philosophical meaning of quantum contextuality. We will argue that there exists a general confusion within the foundational literature arising from the improper “scrambling” of two different meanings of quantum contextuality. While the first one, introduced by Bohr, is related to an epistemic interpretation of contextuality which stresses the incompatibility of measurement situations described in classical terms; the second meaning of contextuality is related to a purely formal (...) understanding of contextuality as exposed by the Kochen–Specker theorem which focuses instead on the constraints of the orthodox quantum formalism in order to interpret projection operators as preexistent or actual properties. We will show how these two notions have been scrambled together creating an “omelette of contextuality” which has been fully widespread through a popularized “epistemic explanation” of the KS theorem according to which: The measurement outcome of the observableAwhen measured together withBor together withCwill necessarily differ in case\, and\. We will show why this statement is not only improperly scrambling epistemic and formal perspectives, but is also physically and philosophically meaningless. Finally, we analyze the consequences of such widespread epistemic reading of KS theorem as related to statistical statements of measurement outcomes. (shrink)

In this paper we present a new categorical approach which attempts to provide an original understanding of QM. Our logos categorical approach attempts to consider the main features of the quantum formalism as the standpoint to develop a conceptual representation that explains what the theory is really talking about —rather than as problems that need to be bypassed in order to allow a restoration of a classical “common sense” understanding of what there is. In particular, we discuss a solution to (...) Kochen-Specker contextuality through the generalization of the meaning of global valuation. This idea has been already addressed by the so called topos approach to QM —originally proposed by Isham, Butterfiled and D ̈oring— in terms of sieve-valued valuations. The logos approach to QM presents a different solution in terms of the notion of intensive valuation. This new solution stresses an ontological reading of the quantum formalism and the need to restore an objective conceptual representation and understanding of quantum physical reality. (shrink)

This paper responds to Stroud's important The Significance of Philosophical Scepticism. The author defends a view in which statements in a natural language have truth-evaluable content only in concrete contexts. It is argued that just what counts as a concrete possibility that must be defeated before one can say that one knows something is a highly context-sensitive matter, and that Stroud's alternative to this context-sensitive account of the way the verb "know" functions seems to be either a semantics in which (...) knowledge claims (about the "external world") are trivially logically false or no intelligible semantics at all. (shrink)

Topos quantum theory represents a whole new approach to the formalization of non-relativistic quantum theory. It is well known that TQT replaces the orthomodular quantum logic of the traditional Hilbert space formalism with a new intuitionistic logic that arises naturally from the topos theoretic structure of the theory. However, it is less well known that TQT also has a dual logical structure that is paraconsistent. In this paper, we investigate the relationship between these two logical structures and study the implications (...) of this relationship for the definition of modal operators in TQT. (shrink)

A discussion of Nieuwenhuizen’s description for the hidden variables of the detectors in the derivation of Bell’s theorem is presented. This description prevents Bell’s inequalities from being effected. However it will be argued, on mathematical and physical bases, that the flaws attributed by Nieuwenhuizen to Bell’s probability distribution function are unjustified.

Multi-agent scenarios, like Wigner’s friend and Frauchiger–Renner scenarios, can show contradictory results when a non-classical formalism must deal with the knowledge between agents. Such paradoxes are described with multi-modal logic as violations of the structure in classical logic. Even if knowledge is treated in a relational way with the concept of trust, contradictory results can still be found in multi-agent scenarios. Contextuality deals with global inconsistencies in empirical models defined on measurement scenarios even when there is local consistency. In (...) the present work, we take a step further to treat the scenarios in full relational language by using knowledge operators, thus showing that trust is equivalent to the Truth Axiom in these cases. A translation of measurement scenarios into multi-agent scenarios by using the topological semantics of multi-modal logic is constructed, demonstrating that logical contextuality can be understood as the violation of soundness by supposing mutual knowledge. To address the contradictions, assuming distributed knowledge is considered, which eliminates such violations but at the cost of lambda-dependence. We conclude by translating the main examples of multi-agent scenarios to their empirical model representation, contextuality is identified as the cause of their contradictory results. (shrink)

In this work, we discuss a formal way of dealing with the properties of contextual systems. Our approach is to assume that properties describing the same physical quantity, but belonging to different measurement contexts, are indistinguishable in a strong sense. To construct the formal theoretical structure, we develop a description using quasi-set theory, which is a set-theoretical framework built to describe collections of elements that violate Leibnitz's principle of identity of indiscernibles. This framework allows us to consider a new ontology (...) in order to study the properties of quantum systems. (shrink)