Developing Metalogic to Formalize Ontological Disputes of the Systems in Metaphysics by Introducing the Notion of Functionally Isomorphic Quantifiers

A general meta-logical theory is developed by considering ontological disputes in the systems of metaphysics. The usefulness of this general meta-logical theory is demonstrated by considering the case of the ontological dispute between the metaphysical systems of Lewis’ Modal Realism and Terence Parsons’ Meinongianism. Using Quine’s criterion of ontological commitments and his views on ontological disagreement, three principles of metalogic is formulated. Based on the three principles of metalogic, the notions of independent variable and dependent variable are introduced. Then, the ontological dispute between Lewis’ Modal Realism and Terence Parsons’ Meinongianism are restated in the light of the principles of metalogic. After the restatement, Independent variable and dependent variables are fixed in both Lewis’ Modal Realism and Terence Parsons’ Meinongianism to resolve the dispute. Subsequently, a new variety of quantifiers are introduced which is known as functionally isomorphic quantifiers to provide a formal representation of the resolution of the dispute. The specific functionally isomorphic quantifier which is developed in this work is known as st-quantifier. It is indicated that how st-quantifier which is one of the functionally isomorphic quantifiers can function like existential quantifier. It is also shown that there is some kind of inconsistency which is unavoidable in stating the ontological disagreement and therefore, paraconsistent logic is a requirement in stating the ontological disputes.     

Classical dynamics,arrow of time,and genesis of the Heisenberg commutation relations

Based on the assumption that time evolves only in one direction and mechanical systems can be described by Lagrangeans, a dynamical C*-algebra is presented for non-relativistic particles at atomic scales. Without presupposing any quantization scheme, this algebra is inherently non-commutative and comprises a large set of dynamics. In contrast to other approaches, the generating elements of the algebra are not interpreted as observables, but as operations on the underlying system; they describe the impact of temporary perturbations caused by the surroundings. In accordance with the doctrine of Niels Bohr, the operations carry individual names of classical significance. Without stipulating from the outset their “quantization”, their concrete implementation in the quantum world emerges from the inherent structure of the algebra. In particular, the Heisenberg commutation relations for position and velocity measurements are derived from it. Interacting systems can be described within the algebraic setting by a rigorous version of the interaction picture. It is shown that Hilbert space representations of the algebra lead to the conventional formalism of quantum mechanics, where operations on states are described by time-ordered exponentials of interaction potentials. It is also discussed how the familiar statistical interpretation of quantum mechanics can be recovered from operations.     

Mind in a Humean World

The paper defends Humean approaches to autonomous mental causation against recent attacks in the literature. One important criticism launched at Humean approaches says that the truth-makers of the counterfactuals in question include laws of nature, and there are laws that support physical-to-physical counterfactuals, but no laws in the same sense that support mental-to-physical counterfactuals. This paper argues that special science causal laws and physical causal laws cannot be distinguished in terms of degrees of strictness. It follows that mental-to-physical counterfactuals are supported—or not supported—by laws in just the same way as are physical-to-physical counterfactuals.     

Non-Symmetrical Relations,O-Roles,and Modes

I examine and discuss in this paper Orilia’s theory of external, non-symmetrical relations, that is based on ontological roles (O-Roles). I explore several attempts to interpret O-Roles from an ontological viewpoint and I reject them because of two problems concerning the status of asymmetrical relations (to be distinguished from non-symmetrical relations simpliciter) and of exemplification as an external, non-symmetrical relation. Finally, following Heil’s and Lowe’s characterization of modes as particular properties that ontologically depend on their “bearers”, I introduce relational modes in order to define a new solution to the problems of the ontological status of both external, non-symmetrical relations and O-Roles. I also deal with five objections raised by Fraser MacBride against relational modes and O-Roles and I elaborate an analysis of the relations of being to the left of and being to the right of.     

Conditional Entropy and Information in Quantum Systems

The concepts of conditional entropy of a physical system given the state of another system and of information in a physical system about another one are generalized for quantum systems. The fundamental difference between the classical case and the quantum one is that the entropy and information in quantum systems depend on the choice of measurements performed over the systems. It is shown that some equalities of the classical information theory turn into inequalities for the generalized quantities. Specific quantum phenomena such as EPR pairs and superdense coding are described and explained in terms of the generalized conditional entropy and information.     

Three Flawed Distinctions in the Philosophy of Time

The distinctions between A-series and B-series, between synchronic and diachronic identity and between perdurance and endurance are basic in the philosophy of time; yet they are flawed. McTaggart’s claim that the B-series is static and that a series has to be changing to be really temporal arises from a misunderstanding of temporal relations and of the task of ontological analysis. The dynamic appearance of the A-series results from the incompleteness of the analysis. “Synchronic identity” is synonymous with “strict identity”, which has nothing to do with simultaneity. “Diachronic Identity” is another designation for persistence of an ordinary thing through time and change. Now, strict self-identity holds independently of whether a thing has a short or a long duration. Hence, diachronic identity is synchronic identity. Lewis’ distinguishes two kinds of ontological analyses of persistence, the perdurance and the endurance analysis. This dichotomy is in several respects not exhaustive. Above all, his definition of “persist” is inadequate being based on the notion of multiple temporal localisation which is apt with interrupted but misplaced with persistent, i.e., temporally continuous objects.     

Energy-Time Uncertainty Principle and Lower Bounds on Sojourn Time

One manifestation of quantum resonances is a large sojourn time, or autocorrelation, for states which are initially localized. We elaborate on Lavine’s time-energy uncertainty principle and give an estimate on the sojourn time. For the case of perturbed embedded eigenstates the bound is explicit and involves Fermi’s Golden Rule. It is valid for a very general class of systems. We illustrate the theory by applications to resonances for time-dependent systems including the AC Stark effect as well as multistate systems.     

Coherent control of a qubit is trap-free

There is a strong interest in optimal manipulating of quantum systems by external controls. Traps are controls which are optimal only locally but not globally. If they exist, they can be serious obstacles to the search of globally optimal controls in numerical and laboratory experiments, and for this reason the analysis of traps attracts considerable attention. In this paper we prove that for a wide range of control problems for two-level quantum systems all locally optimal controls are also globally optimal. Hence we conclude that two-level systems in general are trap-free. In particular, manipulating qubits—two-level quantum systems forming a basic building block for quantum computation—is free of traps for fundamental problems such as the state preparation and gate generation.     

Consciousness as a state of matter

We examine the hypothesis that consciousness can be understood as a state of matter, “perceptronium”, with distinctive information processing abilities. We explore four basic principles that may distinguish conscious matter from other physical systems such as solids, liquids and gases: the information, integration, independence and dynamics principles. If such principles can identify conscious entities, then they can help solve the quantum factorization problem: why do conscious observers like us perceive the particular Hilbert space factorization corresponding to classical space (rather than Fourier space, say), and more generally, why do we perceive the world around us as a dynamic hierarchy of objects that are strongly integrated and relatively independent? Tensor factorization of matrices is found to play a central role, and our technical results include a theorem about Hamiltonian separability (defined using Hilbert–Schmidt superoperators) being maximized in the energy eigenbasis. Our approach generalizes Giulio Tononi’s integrated information framework for neural-network-based consciousness to arbitrary quantum systems, and we find interesting links to error-correcting codes, condensed matter criticality, and the Quantum Darwinism program, as well as an interesting connection between the emergence of consciousness and the emergence of time.     

The Truthmaker Account Is Not a Causal Theory

It is argued that the part-whole account of the relation between evidence and the larger state of affairs the evidence is evidence of—an account that was elucidated in the paper ‘Truthmaking, Evidence of, and Impossibility Proofs’ (this journal)—provides a better basis for epistemology than causal relations between events. I apply this to a well-known phenomenon in physics which suggests that causal connectedness is not necessary for knowledge.     

功率型变分原理和功能型拟变分原理及其应用

自从钱伟长建立了功率型变分原理以来,功率型变分原理和功能型变分原理在理论方面和应用方面有什么区别和联系,成为学术界关注的课题.应用变积方法,根据Jourdain原理和d’Alembert原理,建立了不可压缩黏性流体力学的功率型变分原理和功能型拟变分原理,推导了不可压缩黏性流体力学的功率型变分原理的驻值条件和功能型拟变分原理的拟驻值条件.研究了不可压缩黏性流体力学的功率型变分原理在有限元素法中的应用.研究表明,功率型变分原理与Jourdain原理相吻合,功能型变分原理与d’Alembert原理相吻合.功率型变分原理直接在状态空间中研究问题,不仅在建立变分原理的过程中可以省略在时域空间中的一些变换,而且给动力学问题有限元素法的数值建模带来方便.     

A Humean Argument for Personal Identity

Considering various arguments in Hume’s Treatise, I reconstruct a Humean argument against personal identity or unity. According to this argument, each distinct perception is separable from the bundle of perceptions to which it belongs and is thus transferable either to the external, material reality or to another psychical reality, another bundle of perceptions. Nevertheless, such transference (Hume’s word!) is entirely illegitimate, otherwise Hume’s argument against causal inference would have failed; furthermore, it violates private, psychical accessibility. I suggest a Humean thought experiment clearly demonstrating that, to the extent that anything within a psychical reality is concerned, no distinction leads to separation or transference and that private, psychical accessibility has to be allowed in the Humean argument for personal identity or unity. Private accessibility and psychical untransferability secure personal identity and unity. Referring to the phenomenon of multiple personality along the lines of the Humean argument for personal identity or unity, I illustrate both private accessibility and a possible notion of one and the same person distinct from his/her alters or psychical parts. Finally, I show why Parfit’s Humean argument against personal identity must fail.     

Lewis’ Modal Realism and Absence Causation

A major criticism of David Lewis’ counterfactual theory of causation is that it allows too many things to count as causes, especially since Lewis allows, in addition to events, absences to be causes as well. Peter Menzies has advanced this concern under the title “the problem of profligate causation.” In this paper, I argue that the problem of profligate causation provides resources for exposing a tension between Lewis’ acceptance of absence causation and his modal realism. The result is a different problem of profligate causation—one that attacks the internal consistency of Lewisian metaphysics rather than employing common sense judgments or intuitions that conflict with Lewis’ extensive list of causes.     

p-Adic valued quantization

This review covers an important domain of p-adic mathematical physics — quantum mechanics with p-adic valued wave functions. We start with basic mathematical constructions of this quantum model: Hilbert spaces over quadratic extensions of the field of p-adic numbers ? _p , operators — symmetric, unitary, isometric, one-parameter groups of unitary isometric operators, the p-adic version of Schrödinger’s quantization, representation of canonical commutation relations in Heisenberg andWeyl forms, spectral properties of the operator of p-adic coordinate.We also present postulates of p-adic valued quantization. Here observables as well as probabilities take values in ? _p . A physical interpretation of p-adic quantities is provided through approximation by rational numbers.     

A “no causal rivalry” solution to the problem of mental causation

Stephen Yablo has recently argued for a novel solution to the mental causation problem: the mental is related to the physical as determinables are related to determinates; determinables are not causal rivals with their determinates; so the mental and the physical are not causal rivals. Despite its attractions the suggestion seems hard to accept. In this paper I develop the idea that mental properties and physical properties are not causal rivals. Start with property dualism, supervenience, multiple realizability, and the claim that no more than one supervenience base for a mental property can be had by a single instance of the mental property. Then a probabilistic account of causation will be unable to certify either mental properties or physical properties as causal factors for effect types. I suggest that this shows that we should not count mental properties as causal rivals with physical properties.     

Is quantum space-time infinite dimensional

The stringy uncertainty relations, and corrections thereof, were explicitly derived recently from the new relativity principle that treats all dimensions and signatures on the same footing and which is based on the postulate that the Planck scale is the minimal length in nature in the same vein that the speed of light was taken as the maximum velocity in Einstein's theory of Special Relativity. A simple numerical argument is presented which suggests that quantum space-time may very well be infinite dimensional. A discussion of the repercussions of this new paradigm in Physics is given. A truly remarkably simple and plausible solution of the cosmological constant problem results from the new relativity principle: The cosmological constant is not a constant, in the same vein that energy in Einstein's Special Relativity is observer dependent. Finally, following El Naschie, we argue why the observed D=4 world might just be an average dimension over the infinite possible values of the quantum space-time and why the compactification mechanisms from higher to four dimensions in string theory may not be actually the right way to look at the world at Planck scales.     

A note on the applicability of recurrence theorems

We investigate the applicability of Poincaré’s and the quantum recurrence theorems to the physical systems such as a container filled with a gas from a physical perspective. We discuss certain difficulties with regard to the definition of the Hamiltonian for such systems and the existence of one-to-one mappings as solutions to the equations of motion. We examine a typical proof of Poincaré’s recurrence theorem and notice that a key part of the proof appeals to the motion of a neighborhood of finite volume in a phase space and this neighborhood possesses infinite kinetic energy, raising another question concerning the applicability of the theorem to physical systems. The same situations also present themselves in the application of Liouville’s theorem.     

Immense Multiple Realization

In his latest book Physicalism, or Something near Enough, Jaegwon Kim argues that his version of functional reductionism is the most promising way for saving mental causation. I argue, on the other hand, that there is an internal tension in his position: Functional reductionism does not save mental causation if Kim’s own supervenience argument is sound. My line of reasoning has the following steps: (1) I discuss the supervenience argument and I explain how it motivates Kim’s functional reductionism; (2) I present what I call immense multiple realization, which says that macro-properties are immensely multiply realized in determinate micro-based properties; (3) on that background I argue that functional reductionism leads to a specified kind of irrealism for mental properties. Assuming that such irrealism is part of Kim’s view, which Kim himself seems to acknowledge, I argue that Kim’s position gets the counterfactual dependencies between macro-causal relata wrong. Consequently, his position does not give a conservative account of mental causation. I end the paper by discussing some alternative moves that Kim seems to find viable in his latest book. I argue on the assumption that the supervenience argument is sound, so the discussion provides further reasons to critically reevaluate that argument because it generalizes in deeply problematic ways.