Online research in philosophy

The dominant argument for the introduction of propensities or chances as an interpretation of probability depends on the difficulty of accounting for single case probabilities. We argue that in almost all cases, the "single case" application of probability can be accounted for otherwise. "Propensities" are needed only in theoretical contexts, and even there applications of probability need only depend on propensities indirectly.

These are the introduction chapters to the forthcoming collection of essays published by Springer (Synthese Library) and entitled Probabilities, Causes and Propensities in Physics.

Four interpretations of single-case conditional propensities are described and it is shown that for each a version of what has been called ‘Humphreys' Paradox’ remains, despite the clarifying work of Gillies, McCurdy and Miller. This entails that propensities cannot be a satisfactory interpretation of standard probability theory. Introduction The basic issue The formal paradox Values of conditional propensities Interpretations of propensities McCurdy's response Miller's response Other possibilities 8.1 Temporal evolution 8.2 Renormalization 8.3 Causal influence Propensities to generate frequencies Conclusion.

GRW Theory postulates a stochastic mechanism assuring that every so often the wave function of a quantum system is `hit', which leaves it in a localised state. How are we to interpret the probabilities built into this mechanism? GRW theory is a firmly realist proposal and it is therefore clear that these probabilities are objective probabilities (i.e. chances). A discussion of the major theories of chance leads us to the conclusion that GRW probabilities can be understood only as either single case propensities or Humean objective chances. Although single case propensities have some intuitive appeal in the context of GRW theory, on balance it seems that Humean objective chances are preferable on conceptual grounds because single case propensities suffer from various well know problems such as unlimited frequency tolerance and lack of a rationalisation of the principal principle.

Popper’s introduction of ‘‘propensity’’ was intended to provide a solid conceptual foundation for objective single-case probabilities. By considering the partly opposed contributions of Humphreys and Miller and Salmon, it is argued that when properly understood, propensities can in fact be understood as objective single-case causal probabilities of transitions between concrete events. The chief claim is that propensities are well-explicated by describing how they fit into the existing formal theory of branching space-times, which is simultaneously indeterministic and causal. Several problematic examples, some commonsense and some quantum-mechanical, are used to make clear the advantages of invoking branching space-times theory in coming to understand propensities. r 2007 Elsevier Ltd. All rights reserved.