Probability and Scientific Inference

Extract

This book would be very important indeed if Mr. Spencer Brown had substantiated his claims “that the concept of probability used in statistical science is meaningless in its own terms” (p. 66), and that confirming this is the only significance of experiments in psychical research. The six short (and not very relevant) introductory chapters need not be discussed here. It is in Chapters VII to IX that the author develops his thesis that the concept of randomness is self–contradictory, and the statistician's concept of probability consequently meaningless. I shall examine what I take to be the central argument leading to this conclusion. This is developed from a distinction between “primary chance or randomness” and “secondary chance or randomness” (“chance” and “randomness” are used interchangeably). The former concept is to be applicable only to individual events and is to depend upon their “unexpectedness or unpredictability”; the latter concept, applicable only to a series as such, is denned as “possessing no discernible pattern” (p. 46). The definition of “primary randomness” is amplified, but not clarified, on page 49: “An event is primarily random in so far as... one cannot be sure of its occurrence... The only relevant criterion is that we are able to guess”. (My italics. Notice that the former sentence implies unpredictability in the strong sense, i.e. not predictable with certainty, whereas the latter suggests unpredictability in a weak sense, i.e. not predictable as more or less likely. Spencer Brown oscillates between these different interpretations.) We are then told that primary randomness “admits of analysis in subjective terms”, since the same event may be predictable by one person but unpredictable by another; whereas secondary randomness is “a more objective concept”. (Is the author claiming that people vary less in their ability to discern patterns in a series than in their ability to predict its unobserved members? Or is he, as I suspect, arbitrarily interpreting “primary randomness” in terms of the speaker's ability to predict, and “secondary randomness” in terms of anyone's ability to discern?)