Abstract

Mr. E. J. Nelson, in “The Inductive Argument for an External World,” treats of fundamental topics with erudition and urbanity, but his essay remains inconclusive, I believe, with respect to its purpose of discrediting the argument. He agrees with Mr. Savery, Mr. Pratt, and me, as against the positivists, that the question of the existence of an external world is meaningful and indeed of paramount importance for both metaphysics and logic. But he argues against us that it cannot be inductively established by its supposed power of “saving the appearances.” He is not sure that any induction is valid; but even if other inductions are valid, he thinks this one can not be, for the following reasons. By the multiplicative axiom of probability-theory, evidence for a hypothesis can only multiply its antecedent probability, and can increase the probability only when the latter is finite, while the hypothesis of an external world has and can have no finite antecedent probability. By the same axiom, even granted an antecedent probability for the hypothesis itself, no experience can act as evidence to increase the probability of a hypothesis except in so far as the hypothesis implies, makes probable, or “explains” the evidence, and this the hypothesis of an external world cannot do.