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The classical model of scientific inquiry derives from Aristotle, [3] who distinguished the forms of approximate and exact reasoning, set out the threefold scheme of abductive, deductive, and inductive inference, and also treated the compound forms such as reasoning by analogy. [citation needed]
Inductive reasoning refers to a variety of methods of reasoning in which broad generalizations or principles are derived from a set of observations. [1] [2] Unlike deductive reasoning (such as mathematical induction), where the conclusion is certain, given the premises are correct, inductive reasoning produces conclusions that are at best probable, given the evidence provided.
Deductive reasoning is the building of knowledge based on what has been shown to be true before. It requires the assumption of fact established prior, and, given the truth of the assumptions, a valid deduction guarantees the truth of the conclusion. Inductive reasoning builds knowledge not from established truth, but from a body of observations.
This article is concerned only with this historical use. The syllogism was at the core of historical deductive reasoning, whereby facts are determined by combining existing statements, in contrast to inductive reasoning, in which facts are predicted by repeated observations.
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Non-deductive reasoning is an important form of logical reasoning besides deductive reasoning. It happens in the form of inferences drawn from premises to reach and support a conclusion, just like its deductive counterpart. The hallmark of non-deductive reasoning is that this support is fallible.
Deductive reasoning – Form of reasoning – from meaning postulate, axiom, or contingent assertion: if p then q (i.e., q or not-p) Inductive reasoning – Method of logical reasoning – theory formation; from data, coherence, simplicity, and confirmation: (inducibly) "if p then q"; hence, if p then (deducibly-but-revisably) q
Bacon's method is an example of the application of inductive reasoning. However, Bacon's method of induction is much more complex than the essential inductive process of making generalisations from observations.