Robert Bishop

Two approaches toward the arrow of time for scattering processes have been proposed in rigged Hilbert space quantum mechanics. One, due to Arno Bohm, involves preparations and registrations in laboratory operations and results in two semigroups oriented in the forward direction of time. The other, employed by the Brussels-Austin group, is more general, involving excitations and de-excitations of systems, and apparently results in two semigroups oriented in opposite directions of time. It turns out that these two time arrows can be related to each other via Wigner's extensions of the spacetime symmetry group. Furthermore, their are subtle differences in causality as well as the possibilities for the existence and creation of time-reversed states depending on which time arrow is chosen.

Determinism is a rich and varied concept. At an abstract level of analysis, Jordan Howard Sobel (1998) identifies at least ninety varieties of what determinism could be like. When it comes to thinking about what deterministic laws and theories in physical sciences might be like, the situation is much clearer. There is a criterion by which to judge whether a law–expressed as some form of equation–is deterministic. A theory would then be deterministic just in case all its laws taken as a whole were deterministic. In contrast, if a law fails this criterion, then it is indeterministic and any theory whose laws taken as a whole fail this criterion must also be indeterministic. Although it is widely believed that classical physics is deterministic and quantum mechanics is indeterministic, application of this criterion yields some surprises for these standard judgments.

The concept of contextual emergence is proposed as a non-reductive, yet welldefined relation between different levels of description of physical and other systems. It is illustrated for the transition from statistical mechanics to thermodynamical properties such as temperature. Stability conditions are crucial for a rigorous implementation of contingent contexts that are required to understand temperature as an emergent property. It is proposed that such stability conditions are meaningful for contextual emergence beyond physics as well.

This is the definitive companion to the study of the philosophy of the social sciences. It provides the student with an accessible, comprehensive and philosophically rigorous introduction to all the major philosophical concepts, issues and debates raised by the social sciences. Ideal for use in undergraduate courses, the structure and content of this textbook-the most thorough, clearly argued and up-to-date available-closely reflect the way the philosophy of the social sciences is studied and taught. The text examines key conceptual and methodological questions in the social sciences and illustrates how these shape the practice of research, the interpretation of findings and theory formulation in such disciplines as economics, political science and psychology. The book not only offers lucid and incisive coverage of the philosophy of the social sciences, but also extends the major debates and considers the latest directions in this growing area of philosophical interest. Robert C. Bishop's cogent and rigorous analysis is supplemented by useful pedagogical features, including key examples from philosophical writing; summaries of core debates; sample questions and exercises; and guides for further reading.

In cognitive neuroscience and in philosophy of mind, causation is a notion that is immensely important but usually not defined precisely enough to afford careful application. A widespread basic flaw is the confusion of causation with correlation. All empirical knowledge in the sciences is based on observing correlations; assigning causal relations to them or interpreting them causally always requires a theoretical background that is implicitly or (better) explicitly stated. This entails that differing theoretical approaches might lead to different interpretations of correlations. In this special volume we attempt to contribute to an improved understanding of causation, in general, and its relationship to consciousness studies, specifically.

Recent developments in nonlinear dynamics have found wide application in many areas of science from physics to neuroscience. Nonlinear phenomena such as feedback loops, inter-level relations, wholes constraining and modifying the behavior of their parts, and memory effects are interesting candidates for emergence and downward causation. Rayleigh–Bénard convection is an example of a nonlinear system that, I suggest, yields important insights for metaphysics and philosophy of science. In this paper I propose convection as a model for downward causation in classical mechanics, far more robust and less speculative than the examples typically provided in the philosophy of mind literature. Although the physics of Rayleigh–Bénard convection is quite complicated, this model provides a much more realistic and concrete example for examining various assumptions and arguments found in emergence and philosophy of mind debates. After reviewing some key concepts of nonlinear dynamics, complex systems and the basic physics of Rayleigh–Bénard convection, I begin that examination here by (1) assessing a recently proposed definition for emergence and downward causation, (2) discussing some typical objections to downward causation and (3) comparing this model with Sperry’s examples.

Kellert (In the Wake of Chars, University of Chicago press, Chicago, 1993) has argued that Laplacean determinism in classical physics is actually a layered concept, where various properties or layers composing this form of determinism can be peeled away. Here, I argue that a layered conception of determinism is inappropriate and that we should think in terms of different deterministic models applicable to different kinds of systems. The upshot of this analysis is that the notion of state is more closely tied to the kind of system being investigated than is usually considered in discussions of determinism. So when investigating determinism corresponding changes to the appropriate notion of state – and, perhaps, the state space itself – also need to be considered.

The fundamental problem on which Ilya Prigogine and the Brussels–Austin Group have focused can be stated briefly as follows. Our observations indicate that there is an arrow of time in our experience of the world (e.g., decay of unstable radioactive atoms like uranium, or the mixing of cream in coffee). Most of the fundamental equations of physics are time reversible, however, presenting an apparent conflict between our theoretical descriptions and experimental observations. Many have thought that the observed arrow of time was either an artifact of our observations or due to very special initial conditions. An alternative approach, followed by the Brussels–Austin Group, is to consider the observed direction of time to be a basic physical phenomenon due to the dynamics of physical systems. This essay focuses mainly on recent developments in the Brussels–Austin Group after the mid-1980s. The fundamental concerns are the same as in their earlier approaches (subdynamics, similarity transformations), but the contemporary approach utilizes rigged Hilbert space (whereas the older approaches used Hilbert space). While the emphasis on nonequilibrium statistical mechanics remains the same, their more recent approach addresses the physical features of large Poincare systems, nonlinear dynamics and the mathematical tools necessary to analyze them.

The big news about chaos is supposed to be that the smallest of changes in a system can result in very large differences in that system's behavior. The so-called butterfly effect has become one of the most popular images of chaos. The idea is that the flapping of a butterfly's wings in Argentina could cause a tornado in Texas three weeks later. By contrast, in an identical copy of the world sans the Argentinian butterfly, no such storm would have arisen in Texas. The mathematical version of this property is known as sensitive dependence. However, it turns out that sensitive dependence is somewhat old news, so some of the implications flowing from it are perhaps not such “big news” after all. Still, chaos studies have highlighted these implications in fresh ways and led to thinking about other implications as well. In addition to exhibiting sensitive dependence, chaotic systems possess two other properties: they are deterministic and nonlinear (Smith 2007). This entry discusses systems exhibiting these three properties and what their philosophical implications might be for theories and theoretical understanding, confirmation, explanation, realism, determinism, free will and consciousness, and human and divine action.

In cognitive neuroscience and in philosophy of mind, causation is a notion that is immensely important but usually not defined precisely enough to afford careful application. A widespread basic flaw is the confusion of causation with correlation. All empirical knowledge in the sciences is based on observing correlations; assigning causal relations to them or interpreting them causally always requires a theoretical background that is implicitly or (better) explicitly stated. This entails that differing theoretical approaches might lead to different interpretations of correlations. In this special volume we attempt to contribute to an improved understanding of causation, in general, and its relationship to consciousness studies, specifically.

Arno Bohm and Ilya Prigogine's Brussels-Austin Group have been working on the quantum mechanical arrow of time and irreversibility in rigged Hilbert space quantum mechanics. A crucial notion in Bohm's approach is the so-called preparation/registration arrow. An analysis of this arrow and its role in Bohm's theory of scattering is given. Similarly, the Brussels-Austin Group uses an excitation/de-excitation arrow for ordering events, which is also analyzed. The relationship between the two approaches is discussed focusing on their semi-group operators and time arrows. Finally a possible realist interpretation of the rigged Hilbert space formulation of quantum mechanics is considered.

A much discussed argument in the philosophy of mind against non-reductive physicalism leads to the conclusion that all genuine causes involved in mental phenomena must be reductive physical causes. The latter ostensibly exclude any other causes from having genuine effects in human thought and behaviour. Jaegwon Kim has been the chief exponent of this line of argument, calling it variously the causal exclusion argument or the supervenience argument against non-reductive physicalism. I will analyse this argument and show that some of its key assumptions are unwarranted. Two assumptions on which I will particularly focus are the causal closure of the physical and the prohibition against causal overdetermination when multiple sufficient causes are involved in some effect. The upshot will be that rather than lower-level physical causes always excluding or pre-empting possible mental causes, context plays a key role in determining what kinds of causation are at work in human behaviour and how those causes cooperate.

The fundamental problem on which Ilya Prigogine and the Brussels-Austin Group have focused can be stated briefly as follows. Our observations indicate that there is an arrow of time in our experience of the world (e.g., decay of unstable radioactive atoms like Uranium, or the mixing of cream in coffee). Most of the fundamental equations of physics are time reversible, however, presenting an apparent conflict between our theoretical descriptions and experimental observations. Many have thought that the observed arrow of time was either an artifact of our observations or due to very special initial conditions. An alternative approach, followed by the Brussels-Austin Group, is to consider the observed direction of time to be a basic physical phenomenon and to develop a mathematical formalism that can describe this direction as being due to the dynamics of physical systems. In part I of this essay, I review and assess an attempt to carry out an approach that received much of their attention from the early 1970s to the mid 1980s. In part II, I will discuss their more recent approach using rigged Hilbert spaces.

Along with exploring some of the necessary conditions for the chemistry of our world given what we know about quantum mechanics, I will also discuss a different reductionist challenge than is usually considered in debates on the relationship of chemistry to physics. Contrary to popular belief, classical physics does not have a reductive relationship to quantum mechanics and some of the reasons why reduction fails between classical and quantum physics are the same as for why reduction fails between chemistry and quantum physics. However, a neoreductionist can accept that classical physics has some amount of autonomy from quantum mechanics, but still try to maintain that classical+quantum physics taken as a whole reduces chemistry to physics. I will explore some of the obstacles lying in the neoreductionist’s path with respect to quantum chemistry and thereby hope to shed more light on the conditions necessary for the chemistry of our world.

The "usual story" regarding molecular chemistry is that it is roughly an application of quantum mechanics. That is to say, quantum mechanics supplies everything necessary and sufficient, both ontologically and epistemologically, to reduce molecular chemistry to quantum mechanics. This is a reductive story, to be sure, but a key explanatory element of molecular chemistry, namely molecular structure, is absent from the quantum realm. On the other hand, typical characterizations of emergence, such as the unpredictability or inexplicability of molecular structure based on quantum mechanics, do not characterize the relationship between molecular chemistry and quantum mechanics well either. A different scheme for characterizing reduction and emergence is proposed that accommodates the relationship between quantum mechanics and molecular chemistry and some initial objections to the scheme are considered.

The role of contingent contexts in formulating relations between properties of systems at different descriptive levels is addressed. Based on the distinction between necessary and sufficient conditions for interlevel relations, a comprehensive classification of such relations is proposed, providing a transparent conceptual framework for discussing particular versions of reduction, emergence, and supervenience. One of these versions, contextual emergence, is demonstrated using two physical examples: molecular structure and chirality, and thermal equilibrium and temperature. The concept of stability is emphasized as a basic guiding principle of contextual property emergence.