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The Natural-Range Conception of Probability

Rosenthal, Jacob (2009) The Natural-Range Conception of Probability. [Preprint]

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Objective interpretations of probability are usually discussed in two varieties: frequency and propensity accounts. But there is a third, neglected possibility, namely, probabilities as deriving from ranges in suitably structured initial state spaces. Roughly, the probability of an event is the proportion of initial states that lead to this event in the space of all possible initial states, provided that this proportion is approximately the same in any not too small interval of the initial state space. This idea can also be expressed by saying that in the types of situations that give rise to probabilistic phenomena we may expect to find an initial state space such that any "reasonable" density function over this space leads to the same probabilities for the possible outcomes. This "method of arbitrary functions" was introduced by Poincaré, studied and extended by Hopf and more recently by Eduardo Engel (mathematically), Jan von Plato and Michael Strevens (philosophically). The natural-range, or method-of-arbitrary-functions approach to probabilities is usually treated as an explanation for the occurrence of probabilistic patterns, whereas I examine its prospects for an objective interpretation of probability, in the sense of providing truth conditions for probability statements that do not depend on our state of mind or information. The main objection to such a proposal is that it is circular, i.e. presupposes the concept of probability, because a measure on the initial state has to be introduced, and density functions over the space are considered. I try to argue that this objection can be successfully met.

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Item Type: Preprint
Rosenthal, Jacob
Additional Information: Forthcoming in: Gerhard Ernst and Andreas Hüttemann (eds.): Time, Chance, and Reduction. Philosophical Aspects of Statistical Mechanics. Cambridge University Press 2009, p. 71-90.
Keywords: probability, chance, determinism
Subjects: Specific Sciences > Probability/Statistics
General Issues > Determinism/Indeterminism
Depositing User: Jacob Rosenthal
Date Deposited: 06 Nov 2009
Last Modified: 07 Oct 2010 15:18
Item ID: 4978
Subjects: Specific Sciences > Probability/Statistics
General Issues > Determinism/Indeterminism
Date: December 2009

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