Quantum MV algebras

We introduce the notion of quantum MV algebra (QMV algebra) as a generalization of MV algebras and we show that the class of all effects of any Hilbert space gives rise to an example of such a structure. We investigate some properties of QMV algebras and we prove that QMV algebras represent non-idempotent extensions of orthomodular lattices.I should like to thank Prof. M.L. Dalla Chiara and Dr. P. Minari for many interesting comments and remarks. Daniele Mundici     

MV-Algebras and Quantum Computation

We introduce a generalization of MV algebras motivated by the investigations into the structure of quantum logical gates. After laying down the foundations of the structure theory for such quasi-MV algebras, we show that every quasi-MV algebra is embeddable into the direct product of an MV algebra and a “flat” quasi-MV algebra, and prove a completeness result w.r.t. a standard quasi-MV algebra over the complex numbers. Presented by Heinrich Wansing     

Quantum Logic as a Fragment of Independence-Friendly Logic

The working assumption of this paper is that noncommuting variables are irreducibly interdependent. The logic of such dependence relations is the author's independence-friendly (IF) logic, extended by adding to it sentence-initial contradictory negation ¬ over and above the dual (strong) negation . Then in a Hilbert space turns out to express orthocomplementation. This can be extended to any logical space, which makes it possible to define the dimension of a logical space. The received Birkhoff and von Neumann quantum logic can be interpreted by taking their disjunction to be ¬(A & B). Their logic can thus be mapped into a Boolean structure to which an additional operator has been added.     

The Logic of Quantum Measurements in terms of Conditional Events

This paper shows that the non-Boolean logic of quantum measurementsis more naturally represented by a relatively new 4-operationsystem of Boolean fractions—conditional events—thanby the standard representation using Hilbert Space. After therequirements of quantum mechanics and the properties of conditionalevent algebra are introduced, the quantum concepts of orthogonality,completeness, simultaneous verifiability, logical operations,and deductions are expressed in terms of conditional eventsthereby demonstrating the adequacy and efficacy of this formulation.Since conditional event algebra is nearly Boolean and consistsmerely of ordered pairs of standard events or propositions,quantum events and the so-called "superpositions" of statesneed not be mysterious, and are here fully explicated. Conditionalevent algebra nicely explains these non-standard "superpositions"of quantum states as conjunctions or disjunctions of conditionalevents, Boolean fractions, but does not address the so-called"entanglement phenomena" of quantum mechanics, which remainphysically mysterious. Nevertheless, separating the latter phenomenafrom superposition issues adds clarity to the interpretationof quantum entanglement, the phenomenon of influence propagatedat faster than light speeds. With such treacherous possibilitiespresent in all quantum situations, an observer has every reasonto be completely explicit about the environmental–instrumentalconfiguration, the conditions present when attempting quantummeasurements. Conditional event algebra allows such explicationwithout the physical and algebraic remoteness of Hilbert space.     

Measurement and Indeterminacy in the Quantum Mechanics of Dirac

The quantum-measurement problem and the Heisenberg indeterminacy principle are presented in the language of the Dirac formulation of the quantum theory. Particularly the relationship between quantum state prior to measurement and the result of the measurement are discussed. The relation between the indeterminacy principle and the analog between quantum and classical systems is presented, showing that this principle may be discussed independently of the wave-particle duality. The importance of statistics in the treatment of many body systems is outlined and the approach to investigating God's interaction with human beings is discussed in this context. The treatment is nonmathematical.     

On Retaining Classical Truths and Classical Deducibility in Many-Valued and Fuzzy Logics

In this paper, I identify the source of the differences between classical logic and many-valued logics (including fuzzy logics) with respect to the set of valid formulas and the set of inferences sanctioned. In the course of doing so, we find the conditions that are individually necessary and jointly sufficient for any many-valued semantics (again including fuzzy logics) to validate exactly the classically valid formulas, while sanctioning exactly the same set of inferences as classical logic. This in turn shows, contrary to what has sometimes been claimed, that at least one class of infinite-valued semantics is axiomatizable.     

God's Action in the World: The Relevance of Quantum Mechanics

It has been suggested that God can act on the world by operating within the limits set by Heisenberg's uncertainty principle (HUP) without violating the laws of nature. This requires nature to be intrinsically indeterministic. However, according to the statistical interpretation the quantum mechanical wavefunction represents the average behavior of an ensemble of similar systems and not that of a single system. The HUP thus refers to a relation between the spreads of possible values of position and momentum and so is consistent with a fully deterministic world. This statistical interpretation of quantum mechanics is supported by reference to actual measurements, resolves the quantum paradoxes, and stimulates further research. If this interpretation is accepted, quantum mechanics is irrelevant to the question of God's action in the world.     

The RNA World and Divine Action in and Through Quantum Mechanics

ABSTRACT

Life emerged on Earth approximately 4.1 billion years ago. Current scholarship on the origin of life supports the RNA world scenario, although controversy still goes on. This article examines the origin issue in light of a divine action theory proposed by Robert J. Russell. Although the author himself has not much considered the issue in light of the divine action, the article is still fruitful in the sense that the origin of life issue is now incorporated into the dialogue with divine action, and also that Russell’s divine action theory can be reconsidered in a new context.     

Quantum Mechanics and "Song of Myself": Getting a Grip on Reality

Most recent writing linking science and literature has concerned itself with challenges to the epistemological status of scientific knowledge in an attempt to demonstrate its contingency, arguing in the more radical efforts that the structures of science are no more than useful fictions. This essay also includes an epistemological comparison between science and literature, but instead of making grand or meta–statements about the nature of knowing generally in the two fields, mine is a much narrower aim. My exploration entails two tasks. First, I provide a close–up look at a particular type of experiment, called the delayed–choice experiment, which clearly reveals the strangeness of the quantum world. In connection with this experiment, I discuss wave functions—mathematical expressions used by physicists to describe quantum behavior and predict the outcome of experiments involving quanta. Second, I look at Walt Whitman's “Song of Myself” focusing on the meaning of the “self” in the poem. My aim is to treat the object of study in each field as a “text” and to assert and demonstrate a parallel in the strategies of thought and response between physicists (“readers”) pondering the meaning and status of a wave function and poem readers pondering the meaning and status of the poem's self. In Whitman's “Song” we find an attempt to understand complex aspects of human experience that are said to transcend ordinary reality, an effort for which I believe there are parallels in the attempts of modern physicists to understand complex, nonintuitive aspects of the subatomic world. While not making the kind of broad claims eschewed above, I do suggest that this focused study has interesting implications since both the wave function and the poem's self force their respective sets of “readers” to confront questions of ultimacy—to consider, that is, epistemological and ontological issues of more than passing interest to students of science as well as those of metaphysics and theology.     

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.     

经典力学革命中的概念图式变化

经典力学革命中起核心作用的是运动概念的变化。亚里士多德力学把运动理解成位移,这种运动概念与因果解释图式一起,限定了力学解释的基本特征。为了解决抛体问题而引入的冲力理论是一个过渡,伽利略在用冲力理论解释自由落体运动时改变了思考问题的方向,转向新的运动概念——运动就是瞬时运动。这个概念结合力学解释的因果图式预告了惯性定律。     

A New Argument for the Nomological Interpretation of the Wave Function: The Galilean Group and the Classical Limit of Nonrelativistic Quantum Mechanics

In this article I investigate, within the framework of realistic interpretations of the wave function in nonrelativistic quantum mechanics, the mathematical and physical nature of the wave function. I argue against the view that mathematically the wave function is a two-component scalar field on configuration space. First, I review how this view makes quantum mechanics non-Galilei invariant and yields the wrong classical limit. Moreover, I argue that interpreting the wave function as a ray, in agreement with many physicists, ensures that Galilei invariance is preserved. In addition, I discuss how the wave function behaves more similarly to a gauge potential than to a field. Finally, I show how this favours a nomological rather than an ontological view of the wave function.     

Weakly higher order cylindric algebras and finite axiomatization of the representables

We show that the variety of n-dimensional weakly higher order cylindric algebras, introduced in Németi [9], [8], is finitely axiomatizable when n > 2. Our result implies that in certain non-well-founded set theories the finitization problem of algebraic logic admits a positive solution; and it shows that this variety is a good candidate for being the cylindric algebra theoretic counterpart of Tarski’s quasi-projective relation algebras. Supported by the Hungarian National Foundation for Scientific Research grant T73601.     

The Finite Model Property for the Implicational Fragment of IPC Without Exchange and Contraction

The aim of this paper is to show that the implicational fragment BKof the intuitionistic propositional calculus (IPC) without the rules of exchange and contraction has the finite model property with respect to the quasivariety of left residuation algebras (its equivalent algebraic semantics). It follows that the variety generated by all left residuation algebras is generated by the finite left residuation algebras. We also establish that BKhas the finite model property with respect to a class of structures that constitute a Kripke-style relational semantics for it. The results settle a question of Ono and Komori [OK85]. This revised version was published online in June 2006 with corrections to the Cover Date.     

Measurement and the Justification of the Statistical Postulate in Bohm's Causal Interpretation of Quantum Mechanics

I briefly sketch Bohm's causal interpretation (BCI) and its solution to the measurement problem. Crucial to BCI's no-collapse account of both ideal and non-ideal measurement is the existence of particles in addition to wavefunctions. The particles in their role as the producers of the observable experimental outcomes render practical considerations, such as what observables can be reasonably measured or how to get rid of interference terms in non-ideal measurements, secondary to BCI's account of measurement. I then explain why it is not easy for BCI to justify its statistical postulate. To successfully justify the postulate would be to solve the distribution problem. Two proposed deterministic solutions to this problem are only briefly set out and not discussed in detail. BCI can solve the measurement problem whether or not the distribution problem is solved. However, if the distribution problem is not solved, BCI cannot be shown to be empirically adequate. This revised version was published online in June 2006 with corrections to the Cover Date.     

On the uses of language in working and idealized logic

The interpretation of discourse covers a continuum with two extremes: on the one hand, a text considered as an ideal, distant object, and on the other hand, a conversation regarded as a real, present event. On the basis of a distinction between relatively context-invariant propositions and relatively context-dependent statements, it is argued that statements in conversational discourse are easier to interpret than statements in texts, whereas only propositions in symbolic logic can be interpreted with exactitude. In the same way, the interpretation of dialogical arguments proceeds more easily than the interpretation of arguments in texts. While dialogical argumentation requires a dialectical approach, textual argumentation necessitates an imaginative reconstruction of the argument. From this it can be concluded that for different sorts of argumentative discourse diverse sorts of interpretative activities have to be used.     

Discrete Process Model for Quantum Systems of Matter and Mind

Attempts to create a coherent scientific picture of the world as a whole on the basis of quantum physics has sped up at the turn of the millennium. There particularly seem to be expectations that the development of a new kind of quantum mechanics could make it possible to describe both matter and consciousness in one frame of reference (“dual aspect approach”). These ideas are often results of brilliant intuitive visions but as yet not able to produce testable hypotheses. Maybe “wave mechanics” is not very suitable in the study of consciousness from the quantum mechanical point of view. The aim of this article is to show how both the matter and the mind systems can be described with one coherent mathematical model if we assume both space and time to be discrete.     

中国逻辑史视野下的先秦易学与名辩学

19世纪以来的中国逻辑史研究,比照西方逻辑,仅仅将先秦的名辩学看成是中国逻辑史的主要部分。其间虽有对《周易》的涉及,但也是浅尝辄止。本文从《周易》经、传产生的年代,特别是《周易》经、传所蕴涵的逻辑内容与先秦名辩逻辑的代表人物孔子、惠施、邓析等人的思想对比,说明先秦易学逻辑对名辩逻辑产生了深刻的影响。得出《周易》的经、传发轫了中国古代逻辑中的推类理论,而名辩学尤其是墨家辩学的推类理论则是对自《周易》以来的推类逻辑传统的总结和提高的结论。     

脑的逻辑功能的核磁共振成像及其哲学意义

国际上关于逻辑对应的脑物理特征的功能核磁共振成像（fMRI）研究的主要成就在于：建立了高级精神活动和低级神经活动的关联关系的试验方法;提出了高级精神活动的（判断和推理）神经计算模型建立方法。这些研究的实验结果表明,逻辑与神经活动具有确定性的对应关系,它证明了强人工智能的观点：导致意识的可验证的实体（或者称为“意识关联物”）就是意识本身。意识的运行方式是可计算的,思维的本质可以还原为机械性的操作步骤,人工智能和人的天然智能在本质上并无二致。