Quantum mechanics and violations of the sure-thing principle: The use of probability interference and other concepts

The use of quantum mechanical concepts in social science is a fairly new phenomenon. This paper uses one of quantum mechanics’ most basic concepts, probability interference, to explain the violation of an important decision theory principle (the ‘sure-thing principle’). We also attempt to introduce other quantum mechanical concepts in relation to the sure-thing principle violation.     

Quantum mechanics and Priority Monism

The paper address the question of whether quantum mechanics (QM) favors Priority Monism, the view according to which the Universe is the only fundamental object. It develops formal frameworks to frame rigorously the question of fundamental mereology and its answers, namely (Priority) Pluralism and Monism. It then reconstructs the quantum mechanical argument in favor of the latter and provides a detailed and thorough criticism of it that sheds furthermore new light on the relation between parthood, composition and fundamentality in QM.     

Objective probability theory theory

I argue that to the extent to which philosophical theories of objective probability have offered theoretically adequateconceptions of objective probability (in connection with such desiderata as causal and explanatory significance, applicability to single cases, etc.), they have failed to satisfy amethodological standard — roughly, a requirement to the effect that the conception offered be specified with the precision appropriate for a physical interpretation of an abstract formal calculus and be fully explicated in terms of concepts, objects or phenomena understood independently of the idea of physical probability. The significance of this, and of the suggested methodological standard, is then briefly discussed.     

The foundations of probability and quantum mechanics

Taking as starting point two familiar interpretations of probability, we develop these in a perhaps unfamiliar way to arrive ultimately at an improbable claim concerning the proper axiomatization of probability theory: the domain of definition of a point-valued probability distribution is an orthomodular partially ordered set. Similar claims have been made in the light of quantum mechanics but here the motivation is intrinsically probabilistic. This being so the main task is to investigate what light, if any, this sheds on quantum mechanics. In particular it is important to know under what conditions these point-valued distributions can be thought of as derived from distribution-pairs of upper and lower probabilities on boolean algebras. Generalising known results this investigation unsurprisingly proves unrewarding. In the light of this failure the next topic investigated is how these generalized probability distributions are to be interpreted.     

Reconciling probability theory and coherentism

Recent results in the literature appear to show that it is impossible for two independent testimonies to jointly raise the probability of a proposition if neither testimony individually has any impact on that probability. I show that these impossibility results do not apply when testimonies agree on incidental details.     

Quantum mechanics as subjectivity and projective stimulus

In this paper I attempt to show that subjectivity, as an input to the creative core of physics, is a misunderstood, but crucial factor. Utilizing Rapaport's fundamental paper, Principles Underlying Projective Techniques which identifies the determinants of the projective technique as: 1. lack of organization, 2. undifferentiation, 3. closeness to the core of the personality, and 4. the meaning of the stimulus being unknown to the subject, a link is suggested to quantum mechanics. It is further suggested the revolutionary nature of quantum mechanics satisfies the projective criterion of the material being unorganized or unfamiliar so that the function of organization can become predominant (Rapaport 1942, p. 93).     

Random dynamics and the research programme of classical mechanics

The modern mathematical theory of dynamical systems proposes a new model of mechanical motion. In this model the deterministic unstable systems can behave in a statistical manner. Both kinds of motion are inseparably connected, they depend on the point of view and researcher's approach to the system. This mathematical fact solves in a new way the old problem of statistical laws in the world which is essentially deterministic. The classical opposition: deterministic‐statistical, disappears in random dynamics. The main thesis of the paper is that the new theory of motion is a revolution in the research programme of classical mechanics. It is the revolution brought about by the development of mathematics.     

Quantum mechanics, interference, and the brain

In this paper we discuss the use of quantum mechanics to model psychological experiments, starting by sharply contrasting the need of these models to use quantum mechanical nonlocality instead of contextuality. We argue that contextuality, in the form of quantum interference, is the only relevant quantum feature used. Nonlocality does not play a role in those models. Since contextuality is also present in classical models, we propose that classical systems be used to reproduce the quantum models used. We also discuss how classical interference in the brain may lead to contextual processes, and what neural mechanisms may account for it.     

The theory of nomic probability

This article sketches a theory of objective probability focusing on nomic probability, which is supposed to be the kind of probability figuring in statistical laws of nature. The theory is based upon a strengthened probability calculus and some epistemological principles that formulate a precise version of the statistical syllogism. It is shown that from this rather minimal basis it is possible to derive theorems comprising (1) a theory of direct inference, and (2) a theory of induction. The theory of induction is not of the familiar Bayesian variety, but consists of a precise version of the traditional Nicod Principle and its statistical analogues.     

Quantum perichoresis: Quantum field theory and the Trinity

The main thesis of this article is that the Trinitarian theological doctrine of perichoresis can be metaphorically interpreted as a form of Divine phase entanglement with the world. Such entanglement would entail non-local, relational holism and superposition through which the immanent unity of the Trinity is economically present in creation. Christ kenoticly empties himself of the immanent perichoresis of the Trinity in order to enter the economic perichoresis of the creation. The Spirit is then the continuing perichoretic love of God sanctifying the creation toward life and fulfillment from within. It is the Trinity in ongoing perichoretic entanglement with the creation, affirming Divine ubiquity and panentheism.