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The problem of multiple-computations discovered by Hilary Putnam presents a deep difficulty for functionalism (of all sorts, computational and causal). We describe in outline why Putnam’s result, and likewise the more restricted result we call the Multiple-Computations Theorem, are in fact theorems of statistical mechanics. We show why the mere interaction of a computing system with its environment cannot single out a computation as the preferred one amongst the many computations implemented by the system. We explain why nonreductive approaches to solving the multiple-computations problem, and in particular why computational externalism, are dualistic in the sense that they imply that nonphysical facts in the environment of a computing system single out the computation. We discuss certain attempts to dissolve Putnam’s unrestricted result by appealing to systems with certain kinds of input and output states as a special case of computational externalism, and show why this approach is not workable without collapsing to behaviorism. We conclude with some remarks about the nonphysical nature of mainstream approaches to both statistical mechanics and the quantum theory of measurement with respect to the singling out of partitions and observables.

We give a general background describing how the notion of levels of reality comes about in contemporary nonreductive approaches to the special sciences, what the notion of levels means in these approaches, its role in our scientific outlook of the world, and why it is important.

Can the second law of thermodynamics explain our mental experience of the direction of time? According to an influential approach, the past hypothesis of universal low entropy (required to ...

It is commonly maintained that neuroplastic mechanisms in the brain provide empirical support for the hypothesis of multiple realizability. We show in various case studies that neuroplasticity stems from preexisting mechanisms and processes inherent in the neural (or biochemical) structure of the brain. We argue that not only does neuroplasticity fail to provide empirical evidence of multiple realization, its inability to do so strengthens the mind-body identity theory. Finally, we argue that a recently proposed identity theory called Flat Physicalism can be enlisted to explain the current state of the mind-body problem more adequately.

We show that the so-called Multiple-Computations Theorem in cognitive science and philosophy of mind challenges Landauer’s Principle in physics. Since the orthodox wisdom in statistical physics is that Landauer’s Principle is implied by, or is the mechanical equivalent of, the Second Law of thermodynamics, our argument shows that the Multiple-Computations Theorem challenges the universal validity of the Second Law of thermodynamics itself. We construct two examples of computations carried out by one and the same dynamical process with respect to which Landauer’s principle implies contradictory predictions concerning the entropy increase. Our two examples are based on a weak version of the Multiple-Computations Theorem, which is quite uncontroversial, and therefore they amount to a clear refutation of the universal validity of Landauer’s Principle. We consider some responses to this argument that do not attempt to single out one computation over the others, and we show that they do not work. We further consider ways out of the argument by externalist approaches supporting the computational theory of the mind who propose that the interaction of a computing system with the environment is enough to select a single computation over the others. We show on physical grounds that this approach fails too. We then reverse the direction of our challenge and formulate a dilemma for supporters of the computational theory of the mind: (i) they must reject (or amend somehow) the causal closure of physic; or else (ii) they must accept on a priori grounds that Landauer’s Principle and the Second Law of thermodynamics are not universally valid. Finally, we present our version of a type–type mind-brain identity theory called Flat Physicalism, which is based on the paradigm case of statistical mechanics, and we show that it circumvents the challenge from Landauer’s Principle and the Multiple-Computations Theorem and does not fall prey to our dilemma.

This paper makes a novel linkage between the multiple-computations theorem in philosophy of mind and Landauer's principle in physics. The multiple-computations theorem implies that certain physical systems implement simultaneously more than one computation. Landauer's principle implies that the physical implementation of “logically irreversible” functions is accompanied by minimal entropy increase. We show that the multiple-computations theorem is incompatible with, or at least challenges, the universal validity of Landauer's principle. To this end we provide accounts of both ideas in terms of low-level fundamental concepts in statistical mechanics, thus providing a deeper understanding of these ideas than their standard formulations given in the high-level terms of thermodynamics and cognitive science. Since Landauer's principle is pivotal in the attempts to derive the universal validity of the second law of thermodynamics in statistical mechanics, our result entails that the multiple-computations theorem has crucial implications with respect to the second law. Finally, our analysis contributes to the understanding of notions, such as “logical irreversibility,” “entropy increase,” “implementing a computation,” in terms of fundamental physics, and to resolving open questions in the literature of both fields, such as: what could it possibly mean that a certain physical process implements a certain computation.

According to influential views the probabilities in classical statistical mechanics and other special sciences are objective chances, although the underlying mechanical theory is deterministic, since the deterministic low level is inadmissible or unavailable from the high level. Here two intuitions pull in opposite directions: One intuition is that if the world is deterministic, probability can only express subjective ignorance. The other intuition is that probability of high-level phenomena, especially thermodynamic ones, is dictated by the state of affairs in the world. We argue in support of this second intuition and we show that in fact there are two different ways in which high-level probability describes matters of fact, even if the underlying microscopic reality is deterministic. Our analysis is novel, but supports approaches by, e.g., Loewer, Albert, Frigg and Hoefer, List and Pivato. In particular, the reductive view we propose here can be seen as a naturalization of the above approaches. We consider consequences of our result for nonreductive physicalist approaches, such as functionalism, that admit multiple realization of the kinds that appear in the special sciences by physical kinds. We show that nonreductive physicalism implies the existence of nonphysical matters of fact.

We examine two quite different threads in Pitowsky’s approach to the measurement problem that are sometimes associated with his writings. One thread is an attempt to understand quantum mechanics as a probability theory of physical reality. This thread appears in almost all of Pitowsky’s papers (see for example 2003, 2007). We focus here on the ideas he developed jointly with Jeffrey Bub in their paper ‘Two Dogmas About Quantum Mechanics’ (2010) (See also: Bub (1977, 2007, 2016, 2020); Pitowsky (2003, 2007)). In this paper they propose an interpretation in which the quantum probabilities are objective chances determined by the physics of a genuinely indeterministic universe. The other thread is sometimes associated with Pitowsky’s earlier writings on quantum mechanics as a Bayesian theory of quantum probability (Pitowsky 2003) in which the quantum state seems to be a credence function tracking the experience of agents betting on the outcomes of measurements. An extreme form of this thread is the so-called Bayesian approach to quantum mechanics. We argue that in both threads the measurement problem is solved by implicitly adding structure to Hilbert space. In the Bub-Pitowsky approach we show that the claim that decoherence gives rise to an effective Boolean probability space requires adding structure to Hilbert space. With respect to the Bayesian approach to quantum mechanics, we show that it too requires adding structure to Hilbert space, and (moreover) it leads to an extreme form of idealism.

We present the framework of Empirical Models and Hidden Variables Models in the foundations of Quantum Mechanics and its relation to Special Relativity. In this framework we discuss the definitions of properties such as non-signaling, strong and weak determinism, locality and, especially contextuality and show that (under mild assumptions) contextuality is equivalent to non-locality and to weak determinism, and non-contextuality is equivalent to locality and strong determinism. The central derivation of this paper is that a contextual Empirical Model cannot be accounted for by a Lorentz invariant (in the broad sense; see Sect. 19.1) and deterministic (strong or weak) theory. Hence, a relativistic theory which yields the empirical predictions of quantum mechanics must be genuinely stochastic (i.e., cannot be deterministic at its fundamental level). Finally, we discuss certain debates about the existence of relativistic versions of Bohm’s and the GRW interpretations of quantum mechanics.

In this paper we analyze the relation between the notion of typicality and the notion of probability and the related question of how the choice of measure in deterministic theories in physics may be justified. Recently it has been argued that although the notion of typicality is not a probabilistic notion, it plays a crucial role in underwriting probabilistic statements in classical statistical mechanics and in Bohm’s theory. We argue that even in theories with deterministic dynamics, like classical statistical mechanics and Bohm’s theory, the notion of probability can be understood as fundamentally objective, and that it is the notion of probability rather than typicality that may (sometimes) have an explanatory value.

"Maxwell's Demon", the famous thought experiment of James Clerk Maxwell, has been devised in 1867 as a counter example for the Second Law of thermodynamics. During the 140 years since the Demon was first suggested, numerous attempts have been made to counter Maxwell's argument. The attempts have been to show that Maxwell was wrong, since his Demon cannot work for one reason or another (see Leff and Rex 2003 for details and references). In this paper we show (following an argument by Albert 2000, Ch. 5.) that Maxwell was basically right, in the sense that his thought experiment is compatible with the laws of mechanics as well as with central principles of statistical mechanics. We then derive some (weak) restrictions on the Demon's efficiency. Finally, we prove that the Demon's cycle of operation can be completed (in particular, the Demon's memory can be erased) without increasing the total entropy of the universe. We draw some conclusions about the way to understand the meaning and role of probability in classical statistical mechanics

We argue that if everything there is in the world is physical, then time has an objective direction. If the fundamental equations of motion are time reversal invariant we show that the direction of time cannot be explained by anything else in physics (e.g. the direction of processes in time) and therefore must be added to physics. We further argue that the direction of time gives rise to both the thermodynamic and the psychological arrows of time (whenever they exist), and that it is necessary in order to construct a meaningful Past Hypothesis in statistical mechanics.

The arrow of time is a familiar phenomenon we all know from our experience: we remember the past but not the future and control the future but not the past. However, it takes an effort to keep records of the past, and to affect the future. For example, it would take an immense effort to unmix coffee and milk, although we easily mix them. Such time directed phenomena are subsumed under the Second Law of Thermodynamics. This law characterizes our experience of the arrow of time in terms of an increase of a theoretical magnitude called entropy. Statistical mechanics tries to explain the Second Law as an effect of the behavior of the microscopic particles that make up the universe. Since our senses are too coarse to see this microstructure, statistical mechanics describes our experience in terms of probability, or in terms of the partial information we have about the particles. In this paper we explain the workings of statistical mechanics; how it accounts for probability as an objective feature of the world based on the underlying dynamics; how it accounts for our memories of the past; how the statistical mechanical probability underwrites the Second Law; and how, at the same time, it leads to a violation of the Second Law by the so-called Maxwell’s Demon.

In a previous article, we have demonstrated by a general phase space argument that a Maxwellian Demon is compatible with statistical mechanics. In this article, we show how this idea can be put to work in the prevalent model of the Demon, namely, a particle-in-a-box, used, for example, by Szilard and Bennett. In the literature, this model is used in order to show that a Demon is incompatible with statistical mechanics, either classical or quantum. However, we show that a detailed phase space analysis of this model illustrates that a Maxwellian Demon is compatible with statistical mechanics.

We discuss the meaning of probabilities in the many worlds interpretation of quantum mechanics. We start by presenting very briefly the many worlds theory, how the problem of probability arises, and some unsuccessful attempts to solve it in the past. Then we criticize a recent attempt by Deutsch to derive the quantum mechanical probabilities from the non-probabilistic parts of quantum mechanics and classical decision theory. We further argue that the Born probability does not make sense even as an additional probability rule in the many worlds theory. Our conclusion is that the many worlds theory fails to account for the probabilistic statements of standard (collapse) quantum mechanics.

A remarkable theorem by Clifton, Bub and Halvorson (2003)(CBH) characterizes quantum theory in terms of information--theoretic principles. According to Bub (2004, 2005) the philosophical significance of the theorem is that quantum theory should be regarded as a ``principle'' theory about (quantum) information rather than a ``constructive'' theory about the dynamics of quantum systems. Here we criticize Bub's principle approach arguing that if the mathematical formalism of quantum mechanics remains intact then there is no escape route from solving the measurement problem by constructive theories. We further propose a (Wigner--type) thought experiment that we argue demonstrates that quantum mechanics on the information--theoretic approach is incomplete., Comment: 34 Pages

Von Neumann argued by means of a thought experiment involving measurements of spin observables that the quantum mechanical quantity \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape $S_{VN}=-k\mathrm{Tr}\,( \rho \mathrm{log}\,\rho ) $ \end{document} is conceptually equivalent to thermodynamic entropy. We analyze Von Neumann’s thought experiment and show that his argument fails.

Modal interpretations are hidden-variable, no-collapse interpretations of quantum mechanics that were designed to solve the measurement problem and reconcile this theory with relativity. Yet, as no-go theorems by Dickson and Clifton (1998), Arntzenius (1998) and Myrvold (2002) demonstrate, current modal interpretations are incompatible with relativity. In the mainstream modal interpretations, properties of composite systems are generally unrelated to the properties of their subsystems. We propose holistic and relational interpretations of properties to explain this failure of property composition. Based on these interpretations, we consider strategies for circumventing Myrvold's theorem, which are also effective against the other two theorems.

In a previous paper (Hemmo and Shenker 2003) we discussed a recent proposal by Albert (2000, Ch. 7) to recover thermodynamics on a purely dynamical basis, using the quantum theory of the collapse of the quantum state of Ghirardi, Rimini and Weber (1986). We proposed an alternative way to explain thermodynamics within no collapse interpretations of quantum mechanics. In this paper some difficulties faced by both approaches are discussed and solved: the spin echo experiments, and the problem of extremely light gases. In these contexts, we point out several ways in which the above quantum mechanical approaches as well as some other classical approaches to the foundations of statistical mechanics may be distinguished experimentally.

Two of the main interpretative problems in quantum mechanics are the so-called measurement problem and the question of the compatibility of quantum mechanics with relativity theory. Modal interpretations of quantum mechanics were designed to solve both of these problems. They are no-collapse (typically) indeterministic interpretations of quantum mechanics that supplement the orthodox state description of physical systems by a set of possessed properties that is supposed to be rich enough to account for the classical-like behavior of macroscopic systems, but sufficiently restricted so as to avoid the no-hidden-variables theorems. But, as recent no-go theorems suggest, current modal interpretations are incompatible with relativity. In this paper, we suggest a strategy for circumventing these theorems. We then show how this strategy could naturally be integrated in a relational version of the modal interpretation, where quantum-mechanical states assign relational rather than intrinsic properties.

I argue that in the many worlds interpretation of quantum mechanics time has no fundamental direction. I further discuss a way to recover thermodynamics in this interpretation using decoherence theory (Zurek and Paz 1994). Albert's proposal to recover thermodynamics from the collapse theory of Ghirardi et al. (1986) is also considered.

Can we explain the laws of thermodynamics, in particular the irreversible increase of entropy, from the underlying quantum mechanical dynamics? Attempts based on classical dynamics have all failed. Albert (1994a,b; 2000) proposed a way to recover thermodynamics on a purely dynamical basis, using the quantum theory of the collapse of the wavefunction of Ghirardi, Rimini and Weber (1986). In this paper we propose an alternative way to explain thermodynamics within no-collapse interpretations of quantum mechanics. Our approach relies on the standard quantum mechanical models of environmental decoherence of open systems, e.g. Joos and Zeh (1985) and Zurek and Paz (1994).

We address Albert and Loewer's criticism of non-ideal measurements in the modal interpretation, by examining the implications of the theory of decoherence for the modal interpretation. In the models originally considered by Albert and Loewer, the inclusion of decoherence provides an answer to their criticism. New problems seem to arise in different models and in situations more general than measurements.

An outline for a modal interpretation in terms of possible worlds is presented. The so-called Schmidt histories are taken to correspond to the physically possible worlds. The decoherence function defined in the histories formulation of quantum theory is taken to prescribe a non-classical probability measure over the set of the possible worlds. This is shown to yield dynamics in the form of transition probabilities for occurrent events in each world. The role of the consistency condition is discussed.

Time asymmetric phenomena are successfully predicted by statistical mechanics. Yet the foundations of this theory are surprisingly shaky. Its explanation for the ease of mixing milk with coffee is incomplete, and even implies that un-mixing them should be just as easy. In this book the authors develop a new conceptual foundation for statistical mechanics that addresses this difficulty. Explaining the notions of macrostates, probability, measurement, memory, and the arrow of time in statistical mechanics, they reach the startling conclusion that Maxwell's Demon, the famous perpetuum mobile, is consistent with the fundamental physical laws. Mathematical treatments are avoided where possible, and instead the authors use novel diagrams to illustrate the text. This is a fascinating book for graduate students and researchers interested in the foundations and philosophy of physics.

Introduction.- Physics and Chance.- Typicality and the Role of the Lebesgue Measure in Statistical Mechanics.- Typicality and Notions of Probability in Physics.- Deterministic Laws and Epistemic Chances.- Measures over Initial Conditions.- A New Approach to the Approach to Equilibrium.- Revising Statistical Mechanics - Probability, Typicality and Closure Time.- How Many Maxwell's Demons and Where?.- Locality and Determinism: the Odd Couple.- Why the Tsirelson Bound?.- Three Attempts at Two Axioms for Quantum Mechanics.- Generalized Probability Measures and the Framework of Effects.- Infinitely Challenging: Pitowsky's Subjective Interpretation and the Physics of Infinite Systems.- Bayesian Conditioning, the Reflection Principle, and Quantum Decoherence.- The World According to de Finetti.- Four and a Half Axioms for Finite-Dimensional Quantum Probability.- Probability in the Many-Worlds Interpretation of Quantum Mechanics.

One of the main goals of no-collapse interpretations of quantum mechanics is to show how results of measurements are objectified, or, in a more poignant terminology, how in a measurement situation facts arise. One needs to show how in their dynamical evolution the measured system and, perhaps more importantly, the measuring apparatus acquire, or at least appear to acquire, the definite properties that are otherwise explained by the collapse of the state. This can be seen as a special case of the problem whether quantum mechanics alone can account for the classical behaviour of macroscopic systems; in particular, the permanent definiteness of at least those properties of macroscopic systems that are directly observable, such as the position of the pointer of a measuring apparatus. In other words, whether quantum mechanics can account for macrofacts of the familiar kind.

This paper concerns the meaning of the idea of typicality in classical statistical mechanics and how typicality is related to the notion of probability.