Michael Dickson

Economist Frank Knight drew a distinction between decisions under risk and decisions under uncertainty. Despite the significance of this distinction for decision theory, we argue that there has been inadequate attention to the difficulties involved in classifying decision situations into these categories. Using the risk assessment of carbon nanotubes as an example, we show that it is often unclear whether there is adequate information to classify a decision situation as being under risk as opposed to uncertainty. We conclude by providing two suggestions for responding to these difficulties: treating decisions as real-world experiments; and promoting broadly based deliberation about quantitative information.

The main goal of this essay is to propose and make plausible a framework for developing a philosophical account of musical notation. The proposed framework countenances four elements of notation: symbols (abstract objects that collectively constitute the backbone of a ‘system’ of notation), their characteristic ‘forms’ (for example, shapes, understood abstractly), the concrete instances, or ‘engravings’, of those forms, and the meanings of the symbols. It is argued that these elements are distinct. Along the way, several preliminary arguments are given for how one ought to understand them—for example, it is suggested that engravings represent symbols rather than instantiate forms, although they are characteristically seen to represent a symbol by being seen to instantiate an associated form. Having proposed this framework, the essay explores the nature of musical instructions, as the meanings of symbols, and offers an argument in favor of the commonly held (but recently challenged) view that those meanings are imperative. Specifically, composites of musical notation (paradigmatically, musical scores) primarily express instructional meaning, and denote something like ‘sonic structures’ only secondarily, in virtue of their primary, imperative, meaning.

This chapter reflects on transhumanism from a Christian perspective, specifically with reference to the Biblical teaching that human beings are made in the “image” and “likeness” of God. It considers a version of that teaching that is seemingly as permissive as could be about “transhumanist technologies,” and concludes that even that version places significant limits on the pursuit and adoption of such technologies. Those limits are far more restrictive than the limits acknowledged by prominent transhumanists, particularly those with a specific focus on proposals aimed at substantially lengthening the average human lifespan.

‘Seeing is believing’ perhaps means that some visual experience provides good evidence for some claims that go beyond the content of the experience. Intuition—intellectual ‘seeming’—does not provide similarly good evidence, at least not for metaphysical claims, or so I shall argue. In §2, I sketch the conception of ‘metaphysics’ that is in use here, a conception that leads naturally to a problem about what counts as evidence in metaphysics. Some have suggested that intuition counts. In §3 I raise some doubts (but not radical skeptical doubts) about intuition. These doubts are directed specifically at Bealer’s (1998) account of philosophical intuition. In §4 I will consider an argument in favor of the appeal to rational intuition as evidence in philosophy, and suggest that the argument is circular. I conclude §4 with some additional doubts about intuition, focused on whether intuitions could ever be ‘calibrated’.

It has been argued, partly from the lack of any widely accepted solution to the measurement problem, and partly from recent results from quantum information theory, that measurement in quantum theory is best treated as a black box. However, there is a crucial difference between ‘having no account of measurement' and ‘having no solution to the measurement problem'. We know a lot about measurements. Taking into account this knowledge sheds light on quantum theory as a theory of information and computation. In particular, the scheme of ‘one-way quantnum computation' takes on a new character in light of the role that reference frames play in actually carrying out any one-way quantum comptuation. ‡Thanks to audiences at the PSA and the Centre for Time, University of Sydney, for helpful comments and questions. †To contact the author, please write to: Department of Philosophy, University of South Carolina, Columbia, SC 29208; e-mail: [email protected].

I review the modal interpretation of quantum mechanics, some versions of which rely on the biorthonormal decomposition of a statevector to determine which properties are physically possessed. Some have suggested that these versions fail in the case of inaccurate measurements, i.e., when one takes tails of the wavefunction into account. I show that these versions of the modal interpretation are satisfactory in such cases. I further suggest that a more general result is possible, namely, that these versions of the modal interpretation never encounter the sort of trouble that has been claimed to arise in the case of inaccurate measurement.

I consider the fact that there are a number of interesting ways to ‘reconstruct’ quantum theory, and suggest that, very broadly speaking, a form of ‘instrumentalism’ makes good sense of the situation. This view runs against some common wisdom, which dismisses instrumentalism as ‘cheap’. In contrast, I consider how an instrumentalist might think about the reconstruction theorems, and, having made a distinction between ‘reconstructing’ quantum theory and ‘reinventing’ quantum theory, I suggest that there is an adequate instrumentalist approach to the theory that invokes both.

Is the quantum-logic interpretation dead? Its near total absence from current discussions about the interpretation of quantum theory suggests so. While mathematical work on quantum logic continues largely unabated, interest in the quantum-logic interpretation seems to be almost nil, at least in Anglo-American philosophy of physics. This paper has the immodest purpose of changing that fact. I shall argue that while the quantum-logic interpretation faces challenges, it remains a live option. The usual objections either miss the mark, or admit a reasonable answer, or fail to decide the issue conclusively.

An outstanding problem in so-called modal interpretations of quantum mechanics has been the specification of a dynamics for the properties introduced in such interpretations. We develop a general framework (in the context of the theory of stochastic processes) for specifying a dynamics for interpretations in this class, focusing on the modal interpretation by Vermaas and Dieks. This framework admits many empirically equivalent dynamics. We give some examples, and discuss some of the properties of one of them. This approach is applicable to a wider class of theories, in particular, those using (discrete) strict effective—as in decoherence theory—superselection rules.

The conceptual structure of orthodox quantum mechanics has not provided a fully satisfactory and coherent description of natural phenomena. With particular attention to the measurement problem, we review and investigate two unorthodox formulations. First, there is the model advanced by GRWP, a stochastic modification of the standard Schrödinger dynamics admitting statevector reduction as a real physical process. Second, there is the ontological interpretation of Bohm, a causal reformulation of the usual theory admitting no collapse of the statevector. Within these two seemingly quite different approaches, we discuss in a comparative manner, several points: The meaning of the state vector, the status of quantum probability, the legitimacy of attributing macro objective properties to physical systems, and the possibility of retrieving the classical limit. Finally, we consider aspects of non-locality and relevant difficulties with formulating a relativistic generalization of the two approaches.

This chapter elucidates quantum probabilities in the formal apparatus of quantum mechanics, while not taking sides about interpretive issues. A central contention is that the notion of a probability measure should not be captured in the usual classical framework, but instead in the more general framework of effect algebras. Two formulations of quantum mechanics in this framework are provided: one using projection-valued measures, another using positive-operator-valued measures. The chapter presents several versions of the Born Rule and critically examines justifications that have been proposed for the Born Rule. The chapter concludes with laying down the perennial puzzles about probability in quantum mechanics such as quantum correlations.