Informally, two kinds of logical reasoning can be distinguished in addition to formal deduction: induction and abduction. Given a precondition or premise, a conclusion or logical consequence and a rule or material conditional that implies the conclusion given the precondition, one can explain that:
- Deductive reasoning determines whether the truth of a conclusion can be determined for that rule, based solely on the truth of the premises. Example: "When it rains, things outside get wet. The grass is outside, therefore: when it rains, the grass gets wet." Mathematical logic and philosophical logic are commonly associated with this style of reasoning.
- Inductive reasoning attempts to support a determination of the rule. It hypothesizes a rule after numerous examples are taken to be a conclusion that follows from a precondition in terms of such a rule. Example: "The grass got wet numerous times when it rained, therefore: the grass always gets wet when it rains." While they may be persuasive, these arguments are not deductively valid, see the problem of induction. Science is associated with this type of reasoning.
- Abductive reasoning selects a cogent set of preconditions. Given a true conclusion and a rule, it attempts to select some possible premises that, if true also, can support the conclusion, though not uniquely. Example: "When it rains, the grass gets wet. The grass is outside and nothing outside is dry, therefore: maybe it rained." Diagnosticians and detectives are commonly associated with this type of reasoning.
Famous quotes containing the words logical and/or reasoning:
“Nature’s law says that the strong must prevent the weak from living, but only in a newspaper article or textbook can this be packaged into a comprehensible thought. In the soup of everyday life, in the mixture of minutia from which human relations are woven, it is not a law. It is a logical incongruity when both strong and weak fall victim to their mutual relations, unconsciously subservient to some unknown guiding power that stands outside of life, irrelevant to man.”
—Anton Pavlovich Chekhov (1860–1904)
““Now what I want is, Facts. Teach these boys and girls nothing but Facts. Facts alone are wanted in life. Plant nothing else, and root out everything else. You can only form the minds of reasoning animals upon Facts: nothing else will ever be of service to them.””
—Charles Dickens (1812–1870)