Online research in philosophy

This article is an attempt at a systematic account of decision making under greater uncertainty than what traditional, mathematically oriented decision theory can cope with. Four components of great uncertainty are distinguished: (1) the identity of the options is not well determined (uncertainty of demarcation) ; (2) the consequences of at least some option are unknown (uncertainty of consequences); (3) it is not clear whether information obtained from others, such as experts, can be relied on (uncertainty of reliance); and (4) the values relevant for the decision are not determined with sufficient precision (uncertainty of values). Some possible strategy types are proposed for each of these components. Decisions related to environmental issues are used to illustrate the proposals.

Uncertainty is pervasive in ecology where the difficulties of dealing with sources of uncertainty are exacerbated by variation in the system itself. Attempts at classifying uncertainty in ecology have, for the most part, focused exclusively on epistemic uncertainty. In this paper we classify uncertainty into two main categories: epistemic uncertainty (uncertainty in determinate facts) and linguistic uncertainty (uncertainty in language). We provide a classification of sources of uncertainty under the two main categories and demonstrate how each impacts on applications in ecology and conservation biology. In particular, we demonstrate the importance of recognizing the effect of linguistic uncertainty, in addition to epistemic uncertainty, in ecological applications. The significance to ecology and conservation biology of developing a clear understanding of the various types of uncertainty, how they arise and how they might best be dealt with is highlighted. Finally, we discuss the various general strategies for dealing with each type of uncertainty and offer suggestions for treating compounding uncertainty from a range of sources.

The idea of complementarity already appears in William James’ (1890a, p. 206) Principles of Psychology in the chapter on “the relations of minds to other things”. Later, in 1927, Niels Bohr introduced complementarity as a fundamental concept in quantum mechanics. It refers to properties (observables) that a system cannot have simultaneously, and which cannot be simultaneously measured with arbitrarily high accuracy. Yet, in the context of classical physics they would both be needed for an exhaustive description of the system.

In information theory there is a fundamental principle, usually referred to as the informational “uncertainty principle”, which expresses a limitation of any information processing system (or agent) in terms of a relation between the system's response property and its inherent processing capacity. From this principle, it can be argued that a salutary strategy for dealing with conflicting information processing requirements is to adopt various complementary processes (or channels). Donald M. MacKay had attempted to relate the informational uncertainty principle to spatial and temporal response properties of neurons in the mammalian visual cortex, and suggested that the spatial and the temporal aspects of such neurons are complementary. I attempt to extend his efforts and to show that the informational uncertainty principle may indeed underlie many complementary relations exhibited in human perception and cognition, such as the relation between the two principal processing streams in vision and the relation between parallel and serial processes in cognition.

The concepts of complementarity and entanglement are considered with respect to their significance in and beyond physics. A formally generalized, weak version of quantum theory, more general than ordinary quantum theory of physical systems, is outlined and tentatively applied to two examples.

Updating the wave-particle duality María C. Boscá e-mail: bosca@ugr.es Departamento de Física Atómica, Molecular y Nuclear Universidad de Granada E-18071. Granada Spain The wave-particle-duality, the fundamental component of the new quantum formalism in Bohr’s opinion, must be reformulated by incorporating the results of some experiments accomplished in the last decades of twentieth century. The Bohr´s complementarity principle stated the mutual exclusiveness and joint full completeness of the two (classical) descriptions of quantum systems; after Einstein-Podolsky-Rosen’paper, the wave-particle duality, or wave-particle complementarity, could be expressed by stating that it is impossible to build up an experimental arrangement in which we observe at the same time both corpuscular and wave aspects. In a two-slit experiment, they would correspond, respectively, to the which-way knowledge and the observation of interference pattern. Bohr showed this mutual exclusivity in numerous examples , and linked it to the unavoidable disturbance inherent in any measurement event. In quantum mechanical formalism, the complementarity principle has a clear mathematical expression: two observables are complementary if precise knowledge of one of them implies that all possible outcomes of the other are equally probable; their extension to classical concepts (as wave and particle) is not concerned. In 1991 Scully et al published a variant of the two-slit experiment that incorporates two micromasers cavities and a laser beam to provide which-path information without net momentum transferred during the interaction ; the impossibility of know which slit an atom went through and still observe the interference fringes is preserved by the establishing of quantum correlations between the measuring apparatus and the system being observed. They claimed that complementarity, of which wave-particle duality would be to them a manifestation, is more fundamental than the uncertainty principle . In 1996 B-G. Englert, following an approach originally due to Wooters and Zurek , derived , without making use of Heisenberg’s uncertainty relation, an inequality that quantifies the mutual compatibility relation between fringe visibility and which-way information. The inequality, that they denominated as “interferometric duality”, has the expression D^2 + V^2 ≤ 1, where D stands for the distinguishability of the ways and V for the fringe visibility; both of them are mathematical expressions that can be measured to check experimentally the inequality . Today, it is clear that intermediate particle-wave behaviours exist and, in addition to that, there are single experiments in which both classical wave-like and particle-like behaviours are showed total and simultaneously on an individual system. For instance, in the Bose’s double-prism experiment , tunnelling and perfect anticoincidence were observed in single photon states. Consequently, the meaning of the wave-particle duality must incor

Boundary completion and surface filling-in are computationally complementary processes whose multiple processing stages form processing streams that realize a hierarchical resolution of uncertainty. Such complementarity and uncertainty principles provide a new foundation for philosophical discussions about visual perception, and lead to neural explanations of difficult perceptual data.

Quantum observables can be identified with vector fields on the sphere of normalized states. Consequently, the uncertainty relations for quantum observables become geometric statements. In the Letter the familiar uncertainty relation follows from the following stronger statement: Of all parallelograms with given sides the rectangle has the largest area.

Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a condition ensuring that mutually exclusive experimental options can be reconciled if an appropriate trade-off is accepted. The uncertainty principle is shown to appear in three manifestations, in the form of uncertainty relations: for the widths of the position and momentum distributions in any quantum state; for the inaccuracies of any joint measurement of these quantities; and for the inaccuracy of a measurement of one of the quantities and the ensuing disturbance in the distribution of the other quantity. Whilst conceptually distinct, these three kinds of uncertainty relations are shown to be closely related formally. Finally, we survey models and experimental implementations of joint measurements of position and momentum and comment briefly on the status of experimental tests of the uncertainty principle.

Uncertainty relations and complementarity of canonically conjugate position and momentum observables in quantum theory are discussed with respect to some general coupling properties of a function and its Fourier transform. The question of joint localization of a particle on bounded position and momentum value sets and the relevance of this question to the interpretation of position-momentum uncertainty relations is surveyed. In particular, it is argued that the Heisenberg interpretation of the uncertainty relations can consistently be carried through in a natural extension of the usual Hilbert space frame of the quantum theory.