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On Probabilities in Biology and Physics

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Abstract

This volume focuses on various questions concerning the interpretation of probability and probabilistic reasoning in biology and physics. It is inspired by the idea that philosophers of biology and philosophers of physics who work on the foundations of their disciplines encounter similar questions and problems concerning the role and application of probability, and that interaction between the two communities will be both interesting and fruitful. In this introduction we present the background to the main questions that the volume focuses on and summarize the highlights of the individual contributions.

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Notes

  1. http://conectahistoria.blogspot.ca/2010/02/barcelona-conference-on-causality-and.html.

  2. http://www.msha.fr/msha/actu/colloque/pages/presentation_time_of_nature.pdf.

  3. For more detailed reviews of interpretations of probability, see Gillies (2000a), Galavotti (2005) and Hájek (2012).

  4. In the literature, it is often assumed that by coherence de Finetti means consistency (Howson 2008; Dickey et al. 2009; Vineberg 2011), but Berkovitz (2014) argues that this assumption is unjustified.

  5. The conflation of the ontological status of theoretical terms with the way they are to be evaluated and their values as instruments is not particular to the interpretation of de Finetti's theory (Berkovitz 2014). In discussions of instrumentalism it is common to associate the instrumental value of theoretical postulates with their ontological status. Thus, for example, it is argued that under instrumentalism, theories are capable (at best) of accommodating known observable phenomena, and incapable of making novel predictions. Psillos (1999, p. 29) interprets Duhem as arguing along these lines. “Duhem’s point is that the fact that some theories generate novel predictions cannot be accounted for on a purely instrumentalist understanding of scientific theories. For how can one expect that an arbitrary (artificial) classification of a set of known experimental laws—i.e. a classification based only on considerations of convenience—will possibly be able to reveal unforeseen phenomena in the world?” The presupposition is that the ontological status of theoretical terms determines their capacity to generate novel predictions. But this presupposition begs the question against instrumentalism in general and de Finetti’s instrumentalism in particular (Berkovitz 2014).

  6. For the sake of brevity, in what follows by ‘frequency’ we will mean relative frequency.

  7. For a discussion of this tenet in the context of long-run propensity theories, see Berkovitz (2015, Sect. 3.5).

  8. However, his theory cannot be considered as an interpretation of the probability calculus since it violates it.

  9. For a detailed discussion of propensity theories, see Berkovitz (2015).

  10. Lewis (1986, p. 87) formulates the principal principle as follows: “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 \( C(A/XE) = x \).” C is a non-negative, normalized, finitely additive measure defined on all propositions (sets of worlds), and E is admissible at time t if it contains only information whose impact on the credence of A comes entirely by way of credence about the chance of A.

  11. Unlike Strevens and Rosenthal, Abrams intends his interpretation to apply to both deterministic and indeterministic processes.

  12. The standard conditional probability of A given B is defined as the ratio of the unconditional probability of A&B to the unconditional probability of B: \( {{P(A\& B)} \mathord{\left/ {\vphantom {{P(A\& B)} {P(B)}}} \right. \kern-0pt} {P(B)}} \).

  13. For a discussion of these arguments, see Berkovitz 2015, Sects. 5.2–5.3 and references therein.

  14. For a critical discussion of this resolution, see Bub (1975) and Bub and Pitowsky (1985).

  15. For examples of subjective interpretations of QM probabilities, see Caves et al. (2002a, b, 2007), Pitowsky (2003) and Berkovitz (2012).

  16. FTNS states that “the rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time” (Fisher 1930, p. 35). That is, a population’s rate of change in mean fitness due to natural selection is equal to the additive genetic variance. It is important to emphasize here the fact that the variation rate of mean fitness necessarily increases, so the principle singles out a trend in nature, like the Second Law in TD.

  17. In the classical view, this process happens primarily at the level of alleles.

  18. A concept that is explicitly analogous, ‘ecological drift’, has been forged in community ecology by Hubbell (2001).

  19. “[N]atural selection, acting on the heritable variation provided by the mutations and recombination of a Mendelian genetic constitution, is the main agency of biological evolution.” The letter from Huxley to Mayr was intended to explain the general orientation of the book Evolution as a process, to which Mayr contributed (see Huxley et al. 1954).

  20. As Landsman (2009, p. 60) notes, the pragmatic attitude taken by most physicists is that the probabilities in Born’s rule are to be interpreted as long-run frequencies.

  21. Roughly, an effective wavefunction of a system exists when ‘enough’ decoherence has occurred between the system and its environment (see Dürr et al. 1992; Callender 2007).

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Acknowledgments

For comments on earlier versions of this paper, we are grateful to Noah Stemeroff and Marshal Abrams.

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  1. IHPST, University of Toronto, Victoria College, 91 Charles St. West, Toronto, ON, M5S 1K7, Canada

    Joseph Berkovitz

  2. Institut d’Histoire et de Philosophie des Sciences et des Techniques, CNRS/Université Paris I Sorbonne, Paris, France

    Philippe Huneman

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Berkovitz, J., Huneman, P. On Probabilities in Biology and Physics. Erkenn 80 (Suppl 3), 433–456 (2015). https://doi.org/10.1007/s10670-015-9780-8

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