This is an attempt to axiomatise the natural laws. Note especially axiom 4, which is expressed in third order predicate logic, and which permits a solution to the problem of causation in nature without stating that “everything has a cause”. The undefined term “difference” constitutes the basic element and each difference is postulated to have an exact position and to have a discrete cause. The set of causes belonging to a natural set of dimensions is defined as a law. This (...) means that a natural law is determined by the discrete causes tied to a natural set of dimensions. A law is defined as “defined” in a point if a difference there has a cause. Given that there is a point for which the law is not defined it is shown that a difference is caused that connects two points in two separate sets of dimensions. (shrink)

Physics is not just mathematics. This seems trivial, but poses difficult and interesting questions. In this paper we analyse a particular discrepancy between non-relativistic quantum mechanics and ‘classical’ space and time. We also suggest, but not discuss, the case of the relativistic QM. In this work, we are more concerned with the notion of space and its mathematical representation. The mathematics entails that any two spatially separated objects are necessarily different, which implies that they are discernible —we say that the (...) space is T2, or “Hausdorff”, or yet “separable”. But when enters QM, sometimes the systems need to be taken as completely indistinguishable, so that there is no way to tell which system is which, and this holds even in the case of fermions. But in the NST setting, it seems that we can always give an identity to them by means of their individuation, which seems to be contra the quantum physical situation, where individuation does not entail identity. Here we discuss this topic by considering a case study and conclude that, taking into account the quantum case, that is, when physics enter the discussion, even NST cannot be used to say that the systems do have identity. This case study seems to be relevant for a more detailed discussion on the interplay between physical theories and their underlying mathematics, in a simple way apparently never realized before. (shrink)

The aim of this paper is to explore the ways in which Axiomatic Reconstructions of Quantum Theory in terms of Information-Theoretic principles can contribute to explaining and understanding quantum phenomena, as well as to study their explanatory limitations. This is achieved in part by offering an account of the kind of explanation that axiomatic reconstructions of Quantum Theory provide, and re-evaluating the epistemic status of the program in light of this explanation. As illustrative case studies, I take Clifton's, Bub's and (...) Halvorson's characterization theorem and Popescu's and Rohrlich's toy models, and their explanatory contribution with respect to quantum nonlocality. On the one hand, I argue that ARQITs can aspire to provide genuine explanations of quantum nonlocality. On the other hand, I argue that such explanations cannot rule out a mechanical quantum theory. (shrink)

According to the Gottesman–Knill theorem, quantum algorithms that utilize only the operations belonging to a certain restricted set are efficiently simulable classically. Since some of the operations in this set generate entangled states, it is commonly concluded that entanglement is insufficient to enable quantum computers to outperform classical computers. I argue in this article that this conclusion is misleading. First, the statement of the theorem is, on reflection, already evident when we consider Bell’s and related inequalities in the context of (...) a discussion of computational machines. This, in turn, helps us to understand that the appropriate conclusion to draw from the Gottesman–Knill theorem is not that entanglement is insufficient to enable a quantum performance advantage, but rather that if we limit ourselves to the operations referred to in the Gottesman–Knill theorem, we will not have used the resources provided by an entangled quantum system to their full potential. (shrink)

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 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 we will argue against the orthodox definition of quantum entanglement which has been implicitly grounded on several widespread presuppositions which have no relation whatsoever to the formalism of QM. We will show how these presuppositions have been introduced through a naive interpretation of the quantum mathematical structure which assumes dogmatically that the theory talks about "small particles" represented by pure states which suddenly "collapse" when a measurement takes place. In the second part of this paper we (...) will present a non-collapse approach to QM which makes no use whatsoever of particle metaphysics, escaping the need to make reference to space-time separability or the restriction to certain predictions of definite valued binary properties. Our paper ends up concluding the essential need to redefine the notion of quantum entanglement, at least in the cases of: i) non-collapse interpretations of QM; or, ii) any other interpretation which abandons the idea that QM makes reference to "small particles". (shrink)

In this essay I make use of the resources of ‘naturalized ontology’ in order to determine what quantum mechanics implies about answers to fundamental metaphysical questions. Naturalized ontology is a methodology for metaphysics influenced by the philosopher Willard Van Orman Quine which makes explicit reference to our best scientific theories in order to answer questions which have traditionally been reckoned to belong solely to the realm of philosophy such as ‘What is the nature of reality in the most general sense?’ (...) Quantum mechanics faces a unique interpretational problem known as the ‘measurement problem’ which makes determining the answer to such general metaphysical questions on this view especially problematic; nevertheless, naturalized ontology interprets and evaluates the various responses to this problem via measures of ‘theoretical virtue’, and ultimately concludes that the best interpretation of quantum mechanics—and thus reality—is absurd. (shrink)

Jaegwon Kim (1998a, 2005) claims that his exclusion problem follows a priori for the non-reductive physicalist given her commitment to five apparently inconsistent theses: mental causation, non-identity, supervenience, causal closure and non-overdetermination. For Kim, the combination of these theses entails that mental properties are a priori excluded as causes, forcing the non-reductive physicalist to accept either epiphenomenalism, or some form of reduction. In this thesis, I argue that Kim’s exclusion problem depends on a particular conception of causation, namely sufficient production, (...) and that when causation is understood in interventionist terms, the non-reductive physicalist can avoid the exclusion problem. I argue that Woodward’s (2003, 2008a, 2011a) version of interventionism not only provides an account of mental causation that avoids the exclusion problem, but argue that it also upholds all of the minimal commitments of non-reductive physicalism, thereby providing a successful non-reductive physicalist solution to the exclusion problem. In Chapter 2, I argue that all five theses are minimal commitments of non-reductive physicalism that cannot be rejected in order to avoid the exclusion problem. Chapter 3 identifies the assumptions that I take to underlie the exclusion problem. Chapter 4 introduces and outlines the central features of Woodward’s (2003) interventionism and Chapter 5 argues that Woodward’s interventionist account of mental causation provides a solution to the exclusion problem. I examine two alternative interventionist accounts of mental causation[1] that fail to provide satisfactory solutions to the exclusion problem and conclude that Woodward’s account therefore provides the only satisfactory account of mental causation and solution to the exclusion problem. Chapter 6 addresses some challenges proposed by Michael Baumgartner (2009, 2010) and argues that the interventionist is able to defend her position against these objections and uphold the interventionist solution to the exclusion problem outlined in this thesis. [1. Proposed by List and Menzies (2009) and Campbell (2007, 2008a, 2008b, 2010).]. (shrink)

Global yoga has become exceptionally popular. The emic description of this global yoga network is often called Yogaland. This paper maps out some of the key topographical features of this metaphysical, social imaginary –scape, and situates the physical body of the global yoga practitioner within a complex entanglement of intersecting social, political, economic and theological ‘worlds’. This paper first explores how the concept of spiritual bypass effects a particular averted gaze towards problematic issues within Yogaland. This leads to the second (...) part of the paper that discusses the fundamental nature of entanglement, which often involves being entangled in worlds the individual would not want, mean to be, or perhaps even be aware, exist. Therefore, this paper identifies ways in which global yoga participants are socialised through their neo-liberal subjectivities to unwittingly support, in an often banal way, a Hindu supremacist ideology; which, in turn, can lead to a type of ‘yoga fundamentalism’. (shrink)