Abductive Reasoning - Deduction, Induction, and Abduction

Deduction, Induction, and Abduction

Deduction

allows deriving from only where is a formal consequence of . In other words, deduction is the process of deriving the consequences of what is assumed. Given the truth of the assumptions, a valid deduction guarantees the truth of the conclusion. For example, given that all bachelors are unmarried males, and given that this person is a bachelor, it can be deduced that this person is an unmarried male.

Induction

allows inferring from, where does not follow necessarily from . might give us very good reason to accept, but it does not ensure . For example, if all of the swans that we have observed so far are white, we may induce that the possibility that all swans are white is reasonable. We have good reason to believe the conclusion from the premise, but the truth of the conclusion is not guaranteed. (Indeed, it turns out that some swans are black.)

Abduction

allows inferring as an explanation of . Because of this, abduction allows the precondition to be abduced from the consequence . Deduction and abduction thus differ in the direction in which a rule like " entails " is used for inference. As such abduction is formally equivalent to the logical fallacy affirming the consequent or Post hoc ergo propter hoc, because there are multiple possible explanations for . For example, after glancing up and seeing the eight ball moving towards us we may abduce that it was struck by the cue ball. The cue ball's strike would account for the eight ball's movement. It serves as a hypothesis that explains our observation. There are in fact infinitely many possible explanations for the eight ball's movement, and so our abduction does not leave us certain that the cue ball did in fact strike the eight ball, but our abduction is still useful and can serve to orient us in our surroundings. This process of abduction is an instance of the scientific method. There are infinite possible explanations for any of the physical processes we observe, but we are inclined to abduce a single explanation (or a few explanations) for them in the hope that we can better orient ourselves in our surroundings and eliminate some of the possibilities.