The objective–subjective dichotomy and its use in describing probability

ABSTRACT

This article reviews the nature of the objective–subjective dichotomy, first from a general historical point of view, and then with regard to the use of these terms over time to describe theories of probability. The different (metaphysical and epistemological) meanings of ‘objective’ and ‘subjective’ are analysed, and then used to show that all probability theories can be divided into three broad classes. A formal definition of (epistemological) objectivity is given and used to clarify this division.

KEYWORDS:

• Probability
• objective
• subjective
• dichotomy
• objectivity
• subjectivity

Disclosure statement

No potential conflict of interest was reported by the author.

Notes on contributor

Arnold Baise is an independent scholar. Formerly a research chemist, he obtained a PhD in Physical Chemistry from the University of Wales before moving to the USA. There he worked for IBM, doing research on the materials used in making microelectronic components. After retiring, he became interested in studying probability and statistics, in particular the historical development of theories of probability.

Notes

1 The word ‘fictum’ was not translated by Spade. Words added in brackets are suggested replacements taken from alternative translations, see Ockham (1990, 41) and Karskens (1992, 214).

2 Adolph Friedrich Hoffmann (1707–1741) taught at the University of Leipzig and was a follower of the influential German philosopher Christian Thomasius (1655–1728). Their ideas are regarded as anticipating in some ways the philosophy of Kant. See Klemme and Kuehn (2010).

3 For details of Cournot’s analysis of probability, see Zabell (2011, 1154–1157).

4 Fisher (1956, 25) writes that Venn ‘was developing the concept of probability as an objective fact, verifiable by observations of frequency.’

5 An anonymous reviewer has supplied a relevant reference dealing with objective and subjective probability, in particular with regard to the British probabilists de Morgan, Mill, Boole, Ellis, and Venn (Verburgt 2015). Verburgt discusses in detail the difficulties involved in classifying their work from an objective or subjective point of view, which arise partly from their varying use of these terms. With regard to Venn, he argues that Venn was a frequentist but should not be regarded as advocating an objective probability.

6 The ‘hidden variables’ referred to by Jauch are variables that would allow one, in principle, to predict the future of a quantum system if only they could be accessed experimentally. In other words, a quantum system would then be regarded as deterministic and predictable, i.e. described by a metaphysically subjective probability.

7 This description of objective probability resembles Karl Popper’s propensity theory, which was intended, in part, to handle the interpretation of probability in quantum theory, see Gillies (2000, 113–136).