"Apart from this older generation, there is scarcely a modern mathematician who still adheres without reservation to the classical theory of probability. The majority have more or less accepted the frequency definition."

“If the concept of probability and the formulae of the theory of probability are used without a clear understanding of the collectives involved, one may arrive at entirely misleading results.”

“I am prepared to concede without further argument that all the theoretical constructions, including geometry, which are used in the various branches of physics are only imperfect instruments to enable the world of empirical fact to be reconstructed in our minds.”

“Mass phenomena to which the theory of probability does not apply are, of course, of common occurrence.”

“We can only hope that statisticians will return to the use of the simple, lucid reasoning of Bayes's conceptions, and accord to the likelihood theory its proper role.”

“I do not want to defend the occult sciences; I am, however, convinced that further unbiased investigation of these phenomena by collection and evaluation of old and new evidence, in the usual scientific manner, will lead us sooner or later to the discovery of new and important relations of which we have as yet no knowledge, but which are natural phenomena in the usual sense.”

“The mean and variance are unambiguously determined by the distribution, but a distribution is, of course, not determined by its mean and variance: A number of different distributions have the same mean and the same variance.”