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268:. For Popper then, a deterministic experiment would have propensity 0 or 1 for each outcome, since those generating conditions would have the same outcome on each trial. In other words, non-trivial propensities (those that differ from 0 and 1) imply something less than determinism and yet still causal dependence on the generating conditions.
204:, however. Popper noted that the outcome of a physical experiment is produced by a certain set of "generating conditions". When we repeat an experiment, as the saying goes, we really perform another experiment with a (more or less) similar set of generating conditions. To say that a set of generating conditions
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The
Principal Principle. Let C be any reasonable initial credence function. Let t be any time. Let x be any real number in the unit interval. Let X be the proposition that the chance, at time t, of A's holding equals x. Let E be any proposition compatible with X that is admissible at time t. Then
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cannot be explicitly defined either, in terms of more basic things, but only in terms of what they do (such as attracting and repelling other electrical charges). In a similar way, propensity is whatever fills the various roles that physical probability plays in science.
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Thus, for example, suppose you are certain that a particular biased coin has propensity 0.32 to land heads every time it is tossed. What is then the correct credence? According to the
Principal Principle, the correct credence is .32.
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are unable to take this approach, since relative frequencies do not exist for single tosses of a coin, but only for large ensembles or collectives. These single-case probabilities are known as propensities or chances.
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What roles does physical probability play in science? What are its properties? One central property of chance is that, when known, it constrains rational belief to take the same numerical value.
294:) do not explicitly define propensities at all, but rather see propensity as defined by the theoretical role it plays in science. They argue, for example, that physical magnitudes such as
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In addition to explaining the emergence of stable relative frequencies, the idea of propensity is motivated by the desire to make sense of single-case probability attributions in
284:, have proposed propensity theories somewhat similar to Popper's, in that propensities are defined in terms of either long-run or infinitely long-run relative frequencies.
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repeating a certain kind of experiment will generate a given outcome type at a persistent rate. Stable long-run frequencies are a manifestation of invariant
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Volumes 7 and 8, Harvard
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814:(1957). "The Propensity Interpretation of the Calculus of Probability and of the Quantum Theory". In Korner; Price (eds.).
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is thought of as a physical propensity, disposition, or tendency of a given type of situation to yield an
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means that those exact conditions, if repeated indefinitely, would produce an outcome sequence in which
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317:. They show that the causal nature of the condition in propensity conflicts with an axiom needed for
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Giere, R. N. (1973). "Objective Single-Case
Probabilities and the Foundations of Statistics". In
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Ballentine developed an axiomatic propensity theory building on the work of
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Chance, Cause and Reason: An
Inquiry into the Nature of Scientific Evidence
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Chance, Cause and Reason: An
Inquiry into the Nature of Scientific Evidence
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of the observed stable relative frequencies. Propensities are invoked to
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Lewis, David (1980). "A Subjectivist's Guide to
Objective Chance". In
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Miller, Richard W. (1975). "Propensity: Popper or Peirce?".
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Propensities are not relative frequencies, but purported
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A later propensity theory was proposed by philosopher
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531:The British Journal for the Philosophy of Science
184:A propensity theory of probability was given by
848:Logic, Methodology and Philosophy of Science IV
527:"The Propensity Interpretation of Probability"
664:"Propensity, Probability, and Quantum Theory"
402:British Journal for the Philosophy of Science
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762:Studies in Inductive Logic and Probability
711:"Why Propensities Cannot be Probabilities"
508:Collected Papers of Charles Sanders Peirce
276:A number of other philosophers, including
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137:of a certain kind, or to yield a long-run
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478:. University of Chicago Press. pp.
515:, reprinted in 1998 Thoemmes Continuum.
436:Proceedings of the Aristotelian Society
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505:and Burks, Arthur W., ed. (1958), the
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662:Ballentine, Leslie E. (August 2016).
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302:Other theories have been offered by
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382:Stanford Encyclopedia of Philosophy
579:. Vol. 73. pp. 467–483.
380:'Interpretations of Probability',
325:Principal principle of David Lewis
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818:. Buttersworth. pp. 65–70.
796:. University of Chicago Press.
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641:. Cambridge University Press.
638:Logic of Statistical Inference
614:. Cambridge University Press.
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386:. Retrieved 23 December 2006.
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