On The Frequency Theory of Probability

Abstract

In his impressive critique of frequency theories,¹ Professor Williams accomplishes one-half of a worthwhile task: he discredits the claim that frequency is the sole meaning of probability. This is indeed a service to humanity, for it is true that frequentists have been strutting about proclaiming their gospel dogmatically, and with an unwholesome indifference to other points of view. For this reason, if for no other, Williams’ attack is likely to afford the objective reader a decent measure of retaliative satisfaction; but it is to be questioned whether it satisfies completely his intellectual appetites. Having deflated the frequentist, the author might have gone on to dispel the ghosts from other haunts, to survey and examine the field of his study with the equanimity and detachement which normally settle upon the critic when his destructive deed is done. Unfortunately, however, this second synthetic part of his task remains unfinished. We are offered, as a substitute for the frequency theory, the hoary formula of Laplace. To use a simple metaphor, a modern edifice has been torn down because of a few cracks in its facade, and it has been replaced by a cave dwelling.