The Problem of Induction

Abstract

The problem of induction is sometimes motivated via a comparison between rules of induction and rules of deduction. Valid deductive rules are necessarily truth preserving, while inductive rules are not. So, for example, one valid deductive rule might be this: (D) From premises of the form “All F are G” and “a is F ,” the corresponding conclusion of the form “a is G” follows. The rule (D) is illustrated in the following depressing argument: (DA) All people are mortal. I am a person. So, I am mortal. The rule here is “valid” in the sense that there is no possible way in which premises satisfying the rule can be true without the corresponding conclusion also being true. A possible inductive rule might be this: (I) From premises of the form “Many many F s are known to be G,” “There are no known cases of F s that are not G,” and “a is F ,” the corresponding conclusion can be inferred of the form “a is G.” The rule (I) might be illustrated in the following “inductive argument.” (IA) Many many people are known to have been moral. There are no known cases of people who are not mortal. I am a person. So, I am mortal.