Deduction, Induction and Abduction

Deduction, induction, and abduction

Deduction
allows deriving b as a consequence of a. 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. It is true by definition and is independent of sense experience. For example, if it is true (given) that the sum of the angles is 180° in all triangles, and if a certain triangle has angles of 90° and 30°, then it can be deduced that the third angle is 60°.

Induction
allows inferring a entails b from multiple instantiations of a and b at the same time. Induction is the process of inferring probable antecedents as a result of observing multiple consequents. An inductive statement requires empirical evidence for it to be true. For example, the statement 'it is snowing outside' is invalid until one looks or goes outside to see whether it is true or not. Induction requires sense experience.

Abduction
allows inferring a as an explanation of b. Because of this, abduction allows the precondition a to be inferred from the consequence b. Deduction and abduction thus differ in the direction in which a rule like “a entails b” 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 b.

Unlike deduction and in some sense induction, abduction can produce results that are incorrect within its formal system. Hence the conclusions of abduction can only be made valid by separately checking them with a different method, either by deduction or exhaustive induction. However, it can still be useful as a heuristic, especially when something is known about the likelihood of different causes for b.