Axiomatic Quantum Theory

The basis of a rigorous formal axiomatization of quantum mechanics is constructed, built upon Dirac's bra–ket notation. The system is three-sorted, with separate variables for scalars, vectors and operators. First-order quantification over all three types of variable is permitted. Economy in the axioms is effected by, e.g., assigning a single logical function * to transform (i) a scalar into its complex conjugate, (ii) a ket vector into a bra and a bra into a ket, (iii) an operator into its adjoint. The system is accompanied by a formal semantics. Further papers will deal with vector subspaces and projection operators, operators with continuous spectra, tensor products, observables, and quantum mechanical probabilities.     

Divine Action and Quantum Theory

Recent articles by Nicholas Saunders, Carl Helrich, and Jeffrey Koperski raise important questions about attempts to make use of quantum mechanics in giving an account of particular divine action in the world. In response, I make two principal points. First, some of the most pointed theological criticisms lose their force if we attend with sufficient care to the limited aims of proposals about divine action at points of quantum indetermination. Second, given the current state of knowledge, it remains an open option to make theological use of an indeterministic interpretation of quantum mechanics. Any such proposal, however, will be an exploratory hypothesis offered in the face of deep uncertainties regarding the measurement problem and the presence in natural systems of amplifiers for quantum effects.     

Modality and Contextuality in Topos Quantum Theory

Topos quantum theory (TQT) 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.     

Quantum Theory and the Resurrection of Jesus

Abstract :  Ever since the time of Hume it has been a truism that the worldview of empirical science, and Christian assertion of the resurrection of Jesus, are antithetical to each other. Yet post‐Newtonian science, and especially quantum theory, suggests the need for a reappraisal of this truism. This reappraisal will first examine the implications of the indeterminism of the quantum world, to consider the physical possibility of Jesus' resurrection. Second, an appraisal of the historical evidence will suggest the likelihood of Jesus' resurrection. Finally, I will consider some implications of all this for contemporary Christian thought.     

Proof Theory of Paraconsistent Quantum Logic

Paraconsistent quantum logic, a hybrid of minimal quantum logic and paraconsistent four-valued logic, is introduced as Gentzen-type sequent calculi, and the cut-elimination theorems for these calculi are proved. This logic is shown to be decidable through the use of these calculi. A first-order extension of this logic is also shown to be decidable. The relationship between minimal quantum logic and paraconsistent four-valued logic is clarified, and a survey of existing Gentzen-type sequent calculi for these logics and their close relatives is addressed.     

Generalized Quantum Theory: Overview and Latest Developments

The main formal structures of generalized quantum theory are summarized. Recent progress has sharpened some of the concepts, in particular the notion of an observable, the action of an observable on states (putting more emphasis on the role of proposition observables), and the concept of generalized entanglement. Furthermore, the active role of the observer in the structure of observables and the partitioning of systems is emphasized.     

Quantum Theory Beyond the Physical: Information in Context

Measures and theories of information abound, but there are few formalised methods for treating the contextuality that can manifest in different information systems. Quantum theory provides one possible formalism for treating information in context. This paper introduces a quantum inspired model of the human mental lexicon. This model is currently being experimentally investigated and we present a preliminary set of pilot data suggesting that concept combinations can indeed behave non-separably.     

The Structural Metaphysics of Quantum Theory and General Relativity

The paper compares ontic structural realism in quantum physics with ontic structural realism about space–time. We contend that both quantum theory and general relativity theory support a common, contentful metaphysics of ontic structural realism. After recalling the main claim of ontic structural realism and its physical support, we point out that both in the domain of quantum theory and in the domain of general relativity theory, there are objects whose essential ways of being are certain relations so that these objects do not possess an intrinsic identity. Nonetheless, the qualitative, physical nature of these relations is in the quantum case (entanglement) fundamentally different from the classical, metrical relations treated in general relativity theory.     

Decompositional Equivalence: A Fundamental Symmetry Underlying Quantum Theory

Decompositional equivalence is the principle that there is no preferred decomposition of the universe into subsystems. It is shown here, by using a simple thought experiment, that quantum theory follows from decompositional equivalence together with Landauer’s principle. This demonstration raises within physics a question previously left to psychology: how do human—or any—observers identify or agree about what constitutes a “system of interest”?     

Similarity and Alignment in Choice

Research in decision making often assumes that corresponding dimensions or features of choices are compared. At the same time, recent models of similarity comparison stress the importance of structural alignment and associated inference processes. The present studies integrate these perspectives by examining feature listings and choices for pairs of video games varying in their comparability. In the first study, one group of participants simply compared pairs of games and listed commonalities and differences. Another group made selections between games and provided justifications for their decisions. We observed close correspondences between justifications and feature listings across wide variation in comparability. In addition, the justifications systematically favored comparable over noncomparable properties. Features also seemed to be created or inferred to promote alignability. The second study manipulated the comparability of individual properties. Here, justifications were more likely to include a property when it was comparable than when it was noncomparable. These observations suggest a constructive alignment process common to similarity and choice.     

Arrovian Aggregation of Generalised Expected-Utility Preferences: (Im)possibility Results by Means of Model Theory

Cerreia-Vioglio et al. (Econ Theory 48(2–3):341–375, 2011) have proposed a very general axiomatisation of preferences in the presence of ambiguity, viz. Monotonic Bernoullian Archimedean preference orderings. This paper investigates the problem of Arrovian aggregation of such preferences—and proves dictatorial impossibility results for both finite and infinite populations. Applications for the special case of aggregating expected-utility preferences are given. A novel proof methodology for special aggregation problems, based on model theory (in the sense of mathematical logic), is employed.     

Constitution and Similarity

Whenever an object constitutes, makes up orcomposes another object, the objects inquestion share a striking number of properties. This paper is addressed to the question of whatmight account for the intimate relation andstriking similarity between constitutionallyrelated objects. According to my account, thesimilarities between constitutionally relatedobjects are captured at least in part by meansof a principle akin to that of strongsupervenience. My paper addresses two mainissues. First, I propose independentlyplausible principles by means of which todelineate, in a non-ad-hoc, non-stipulative andnon-circular fashion, those properties whichcan be expected to be shared amongconstitutionally related objects in virtue oftheir being so related from those which ingeneral cannot be expected to be shared, orwhich are shared for other reasons. Secondly,I spell out in detail the nature of thesupervenience-principle at work in thiscontext. My account thus aims at isolating, ina methodologically responsible fashion, theparticular sort of restricted indiscernibilityprinciple which is a component of theconstitution-relation.     

Similarity and cotenability

In this paper I present some difficulties for Lewis’s and similar theories of counterfactuals, and suggest that the problem lies in the notion of absolute similarity. In order to explain the problem, I discuss the relation between Lewis’s and Goodman’s theory, and show that the two theories are not related in the way Lewis thought they were.     

Sir Francis Galton, Epigenetic Rules, Genetic Similarity Theory, and Human Life-History Analysis

ABSTRACT In this article, an evolutionary perspective is applied to individual differences Among the issues discussed are ( a ) the seminal contributions of Francis Galton and the subsequent ideological reaction, ( b ) the distalproximal continuum for understanding levels of explanation in social behavior, ( c ) consistent patterns of group differences in behavior (age, sex, social class, and race), ( d ) the heritability of personality and the role epigenetic rules play in guiding development in one direction over alternatives, ( e ) the genetic similarity theory perspective on friendship and mate choice, and ( f ) the view that personality is part of an r-K reproductive strategy involving a compensatory exchange between the production of gametes and parental care It is suggested in conclusion that personality traits be considered aspects of a coordinated life cycle deeply embedded in evolutionary history     

Newtonian Gravity,Quantum Discontinuity and the Determination of Theory by Evidence

A closer examination of scientific practice has cast doubt recently on the thesis that observation necessarily fails to determine theory. In some cases scientists derive fundamental hypotheses from phenomena and general background knowledge by means of demonstrative induction. This note argues that it is wrong to interpret such an argument as providing inductive support for the conclusion, e.g. by eliminating rival hypotheses. The examination of the deduction of the inverse square law of gravitation due to J. Bertrand, and R. Fowler's deduction of the quantization of the linear harmonic oscillator's energy spectrum from Planck's radiation law illustrates this point. It is suggested that demonstrative induction is a computational step in fitting a theoretical model and a set of phenomena, with little direct confirmational impact. The thesis of underdetermination, whatever one may think of it, is not threatened by demonstrative induction.