Abstract

This general type of view may be characterized more fully by using the notion of an inductive method. All scientists use approximately the same inductive method, which we will call the standard inductive method. This method is based on the rule of induction by simple enumeration, which may be roughly stated as follows: if it is known only that a certain property Ψ has accompanied another property Φ in a number of instances, then the larger this number of instances the higher the probability that the next occurrence of Φ will be accompanied by Ψ. Though scientists actually reason inductively in accord with this rule, it is important that there are logically consistent inductive methods based on alternative rules. We will describe two of these briefly. The inverse inductive method assigns probabilities according to the rule that if it is known only that Ψ has accompanied Φ a number of times, then the larger the number of instances the lower the probability that the next occurrence of Φ will be accompanied by Ψ. The random predictive method assigns to the proposition that the next occurrence of Φ will be accompanied by Ψ a probability completely independent of the number of times that Ψ has accompanied Φ in the past..