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.