Friday, August 29, 2014

Gillies’ Philosophical Theories of Probability, Chapter 1

Donald Gillies’ Philosophical Theories of Probability (2000) is an excellent overview of probability theory.

The book is of great interest, because Gillies (2000: xiv) has knowledge of Post Keynesian work on probability and uncertainty, and also sees his “intersubjective” theory of probability as a compromise between the theories of Keynes and Ramsey.

Probability has both a mathematical and philosophical/epistemic aspect.

The earliest “Classical” interpretation of probability of Pierre-Simon Laplace (1749–1827), which was based on earlier work from the 1650 to 1800 period, is now of historical interest only, and has no supporters today (Gillies 2000: 3).

Gillies (2000: 1) identifies five major modern interpretations of probability, which are in turn divided into two broad categories, as follows:
(i) Epistemological/Epistemic probability theories
(1) the logical interpretation;
(2) the subjective interpretation (personalism, subjective Bayesianism);
(3) the intersubjective view.
(ii) Objective probability theories
(4) the frequency interpretation;
(5) the propensity interpretation.
The “intersubjective” interpretation of probability is developed by Gillies (2000: 2) himself.

The epistemological/epistemic group of probability theories take probability to be a degree of belief, whether rational or subjective (Gillies 2000: 2).

The objective probability theories take probabilities to be an objective aspect of certain things or processes in the external world (Gillies 2000: 2).

Gillies (2000: 2–3) argues that all the major theories of probability may be compatible, as long as they are limited to their appropriate domains: for example, objective probabilities are usually appropriate for the natural sciences and epistemological/epistemic probabilities for the social sciences.

Serious study of probability began with mathematical theories of probability, often inspired by interest in gambling games (Gillies 2000: 4, 10), and these mathematical theories emerged in the 17th and 18th centuries, and famously in the correspondence between Blaise Pascal (1623–1662) and Pierre de Fermat (1601/1607–1665) in 1654 (Gillies 2000: 3), Jacob Bernoulli’s (1655–1705) treatise Ars Conjectandi (1713), the work of Abraham de Moivre (1667–1754), and of Thomas Bayes (c. 1701–1761) (Gillies 2000: 4–8).

Gillies, D. A. 2000. Philosophical Theories of Probability. Routledge, London.

1 comment:

  1. Impressive quote!

    You might like to look at some of his papers if you get the chance:

    Gillies, D. A. 2004. “Can Mathematics be used successfully in Economics?,” in Edward Fullbrook (ed.), A Guide to What’s Wrong with Economics. Anthem Press, London. 187–197.

    Gillies, D. A. 2006. “Keynes and Probability,” in Roger E. Backhouse and Bradley W. Bateman (eds.), The Cambridge Companion to Keynes. Cambridge University Press, Cambridge, UK and New York. 199–216.

    Gillies, D. A. 2003. “Probability and Uncertainty in Keynes’s General Theory,” in J. Runde and S. Mizuhara (eds.), The Philosophy of Keynes’s Economics: Probability, Uncertainty and Convention. Routledge, London. 111–129.

    I've summarised Gillies (2003) here: