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 type 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.
You could say that inductive reasoning moves from the specific to the general. Much scientific research is carried out by the inductive method: gathering evidence, seeking patterns, and forming a hypothesis or theory to explain what is seen.
Conclusions reached by the inductive method are not logical necessities; no amount of inductive evidence guarantees the conclusion. This is because there is no way to know that all the possible evidence has been gathered, and that there exists no further bit of unobserved evidence that might invalidate my hypothesis.
- Abductive reasoning, aka inference to the best explanation, 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 wet. Therefore, it might have rained." This kind of reasoning can be used to develop a hypothesis, which in turn can be tested by additional reasoning or data. Diagnosticians, detectives, and scientists often use this type of reasoning.
- Inductive-creative reasoning; this term has been coined by D. Iosif[non sequitur] to combine the specificity of the observation set from the inductive arena and the creativity (and intuition) element from the abductive arena therefore providing a cogent view of the future. This methodology will result in grounded creative thinking and can be used in strategy planning to generate future as-yet unobserved phenomena. One example would be: " we observed a large number of white swans on all continents and hypothesize that we need to protect by law all swans that are white but also black (in existence but unobserved) and red (possibly to be re-engineered in a distant future)". While inductive reasoning cannot yield an absolutely certain conclusion, it can actually increase human knowledge (it is ampliative).
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- Menzies, T. Applications of Abduction: Knowledge-Level Modeling. November 1996
- Thagard, Paul and Cameron Shelley. "Abductive reasoning: Logic, visual thinking, and coherence". Waterloo, Ontario: Philosophy Department, Univerisity of Waterloo, 1997. June 2, 2005.
- Verfaillie, Catherine. "Adult Bone Marrow Stem Cells Can Become Blood Vessels". News release from the University of Minnesota. Jan. 30, 2002. June 1, 2005.[relevant? ]