In this paper we attempt to analyze the concept of quantum probability within quantum computation and quantum computational logic. While the subjectivist interpretation of quantum probability explains it as a reliable predictive tool for an agent in order to compute measurement outcomes, the objectivist interpretation understands quantum probability as providing reliable information of a real state of affairs. After discussing these different viewpoints we propose a particular objectivist interpretation grounded on the idea that the Born rule provides information about an (...) intensive realm of reality. We then turn our attention to the way in which the subjectivist interpretation of probability is presently applied within both quantum computation and quantum computational logic. Taking as a standpoint our proposed intensive account of quantum probability we discuss the possibilities and advantages it might open for the modeling and development of both quantum computation and quantum computational logic. (shrink)

In de Ronde and Massri it was argued against the orthodox definition of quantum entanglement in terms of pure and separable states. In this paper we attempt to discuss how the logos categorical approach to quantum mechanics is able to provide an objective formal account of the notion of entanglement—completely independent of both purity and separability—in terms of the potential coding of intensive relations and effective relations. We will show how our novel redefinition allows us to provide an anschaulich content (...) to the notion of entanglement, erasing in this way the “spookiness” still present within its orthodox understanding in terms of space-time separated collapse particles. (shrink)

According to de Ronde it was Bohr's interpretation of Quantum Mechanics which closed the possibility of understanding physical reality beyond the realm of the actual, so establishing the Orthodox Line of Research. In this sense, it is not the task of any physical theory to look beyond the language and metaphysics supposed by classical physics, in order to account for what QM describes. If one wishes to maintain a realist position regarding physical theories, one seems then to be trapped by (...) an array of concepts that do not allow to understand the main principles involved in the most successful physical theory thus far, mainly: the quantum postulate, the principle of indetermination and the superposition principle. If de Ronde is right in proposing QM can only be completed as a physical theory by the introduction of `new concepts' that admit as real a domain beyond actuality, then a new ontology that goes beyond Aristotelian and Newtonian actualism is needed. It was already in the early 20th century that misunderstood philosopher Alexius von Meinong proposed a Theory of Objects that admits a domain of being beyond existence-actuality. Member of the so called `School of Brentano', Meinong's concerns were oriented to provide an ontology of everything that can be thought of, and at the same time an intentionality theory of how objects are thought of. I wish to argue that in Meinong's theory of objects we find the rudiments of the ontology and the intentionality theory we need to account for QM's basic principles: mainly the possibility of predicating properties of non-entities, or in other words, the possibility of objectively describing a domain of what is, that is different from the domain of actual existence. (shrink)

In [7] the authors of this paper argued in favor of the possibility to consider a Paraconsistent Approach to Quantum Superpositions. We claimed that, even though most interpretations of quantum mechanics attempt to escape contradictions, there are many hints -coming from present technical and experimental developments in QM- that indicate it could be worth while to engage in a research of this kind. Recently, Arenhart and Krause have raised several arguments against the PAQS [1, 2, 3]. In [11, 12] it (...) was argued that their reasoning presupposes a metaphysical stance according to which the physical representation of reality must be exclusively considered in terms of the equation: Actuality = Reality. However, from a different metaphysical standpoint their problems disappear. It was also argued that, if we accept the idea that quantum superpositions exist in a potential realm, it makes perfect sense to develop QM in terms of a paraconsistent approach and claim that quantum superpositions are contradictory, contextual existents. Following these ideas, and taking as a standpoint an interpretation in terms of the physical notions of power and potentia put forward in [10, 12, 15], we present a paraconsistent formalization of quantum superpositions that attempts to capture the main features of QM. (shrink)

In this paper we intend to discuss the importance of providing a physical representation of quantum superpositions which goes beyond the mere reference to mathematical structures and measurement outcomes. This proposal goes in the opposite direction to the project present in orthodox contemporary philosophy of physics which attempts to “bridge the gap” between the quantum formalism and common sense “classical reality”—precluding, right from the start, the possibility of interpreting quantum superpositions through non-classical notions. We will argue that in order to (...) restate the problem of interpretation of quantum mechanics in truly ontological terms we require a radical revision of the problems and definitions addressed within the orthodox literature. On the one hand, we will discuss the need of providing a formal redefinition of superpositions which captures explicitly their contextual character. On the other hand, we will attempt to replace the focus on the measurement problem, which concentrates on the justification of measurement outcomes from “weird” superposed states, and introduce the superposition problem which focuses instead on the conceptual representation of superpositions themselves. In this respect, after presenting three necessary conditions for objective physical representation, we will provide arguments which show why the classical representation of physics faces severe difficulties to solve the superposition problem. Finally, we will also argue that, if we are willing to abandon the presupposition according to which ‘Actuality = Reality’, then there is plenty of room to construct a conceptual representation for quantum superpositions. (shrink)

In this paper we consider the notion of quantum entanglement from the perspective of the logos categorical approach [26, 27]. Firstly, we will argue that the widespread distinctions, on the one hand, between pure states and mixed states, and on the other, between separable states and entangled states, are completely superfluous when considering the orthodox mathematical formalism of QM. We will then argue that the introduction of these distinctions within the theory of quanta is due to another two completely unjustified (...) metaphysical presuppositions, namely, the idea that there is a “collapse” of quantum states when being measured and the idea that QM talks about “elementary particles”. At distance from these distinctions and taking the logos approach as a standpoint, we will propose an objective formal account of the notion of entanglement in terms of potential coding which introduces the necessary distinction between intensive relations and effective relations. We will also discuss how this new definition of entanglement provides an anschaulich content to this —supposedly “spooky”— quantum relational feature. (shrink)

In this paper we attempt to consider quantum superpositions from the perspective of the logos categorical approach presented in [26]. We will argue that our approach allows us not only to better visualize the structural features of quantum superpositions providing an anschaulich content to all terms, but also to restore —through the intensive valuation of graphs and the notion of immanent power— an objective representation of what QM is really talking about. In particular, we will discuss how superpositions relate to (...) some of the main features of the theory of quanta, namely, contextuality, paraconsistency, probability and measurement. (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)

In this paper we provide a general account of the causal models which attempt to provide a solution to the famous measurement problem of Quantum Mechanics. We will argue that—leaving aside instrumentalism which restricts the physical meaning of QM to the algorithmic prediction of measurement outcomes—the many interpretations which can be found in the literature can be distinguished through the way they model the measurement process, either in terms of the efficient cause or in terms of the final cause. We (...) will discuss and analyze why both, ‘final cause’ and ‘efficient cause’ models, face severe difficulties to solve the measurement problem. In contradistinction to these schemes we will present a new model based on the immanent cause which, we will argue, provides an intuitive understanding of the measurement process in QM. (shrink)

In this paper we investigate the history of relationalism and its present use in some interpretations of quantum mechanics. In the first part of this article we will provide a conceptual analysis of the relation between substantivalism, relationalism and relativism in the history of both physics and philosophy. In the second part, we will address some relational interpretations of quantum mechanics, namely, Bohr’s relational approach, the modal interpretation by Kochen, the perspectival modal version by Bene and Dieks and the relational (...) interpretation by Rovelli. We will argue that all these interpretations ground their understanding of relations in epistemological terms. By taking into account the analysis on the first part of our work, we intend to highlight the fact that there is a different possibility for understanding quantum mechanics in relational terms which has not been yet considered within the foundational literature. This possibility is to consider relations in ontological terms. We will argue that such an understanding might be capable of providing a novel approach to the problem of representing what quantum mechanics is really talking about. (shrink)

We discuss the hypothesis that the debate about the interpretation of the orthodox formalism of quantum mechanics might have been misguided right from the start by a biased metaphysical interpretation of the formalism and its inner mathematical relations. In particular, we focus on the orthodox interpretation of the congruence relation, '=', which relates equivalent classes of different mathematical representations of a vector in Hilbert space, in terms of metaphysical identity. We will argue that this seemingly "common sense" interpretation, at the (...) semantic level, has severe difficulties when considering the syntactic level of the theory. (shrink)

Starting with the claim that Quantum Mechanics is in need of a new interpretation that would allow us to understand the phenomena of this realm, I wish to analyse in this paper de Ronde's theory of power and potentia from a phenomenological perspective. De Ronde's claim is that the reason for the lack of success in the foundations of QM is due to the reluctance of both physicists and philosophers to explore the possibility of finding a new ontology, new concepts (...) for the physical theory. De Ronde proposes such new ontology and the question I wish to address here, is whether his ontology is conceptually plausible. I will, for this purpose, recur to Edmund Husserl's phenomenology. After presenting some of the basic concepts and methodological tools of this theory, I shall apply them to de Ronde's ontology to determine the viability of his theory. (shrink)

In this paper we address a deeply interesting debate that took place at the end of the last millennia between David Mermin, Adan Cabello and Michiel Seevinck, regarding the meaning of relationalism within quantum theory. In a series of papers, Mermin proposed an interpretation in which quantum correlations were considered as elements of physical reality. Unfortunately, the very young relational proposal by Mermin was too soon tackled by specially suited no-go theorems designed by Cabello and Seevinck. In this work we (...) attempt to reconsider Mermin's program from the viewpoint of the Logos Categorical Approach to QM. Following Mermin's original proposal, we will provide a redefinition of quantum relation which not only can be understood as a preexistent element of physical reality but is also capable to escape Cabello’s and Seevinck's no-go-theorems. In order to show explicitly that our notion of ontological quantum relation is safe from no-go theorems we will derive a non-contextuality theorem. We end the paper with a discussion regarding the physical meaning of quantum relationalism. (shrink)