> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/300-logic/terms/inductive-reasoning.md). # Inductive Reasoning **Inductive reasoning** is a method of reasoning in which the premises are viewed as supplying some evidence, but not full assurance, of the truth of the conclusion. It is also described as a method where one's experiences and observations, including what are learned from others, are synthesized to come up with a general truth. Many dictionaries define inductive reasoning as the derivation of general principles from specific observations (arguing from specific to general), although there are many inductive arguments that do not have that form. Inductive reasoning is distinct from *deductive reasoning*. While, if the premises are correct, the conclusion of a deductive argument is certain, the *truth of the conclusion of an inductive argument is probable*, based upon the evidence given. ## Deductive vs inductive reasoning Deductive reasoning ("top-down logic") contrasts with *inductive reasoning* ("bottom-up logic"): * In deductive reasoning, a conclusion is reached *by reduction* by applying general rules which hold over the entirety of a closed domain of discourse, narrowing the range under consideration until only the conclusion remains. In deductive reasoning there is no *epistemic uncertainty*. * In inductive reasoning, the conclusion is reached *by generalizing* or extrapolating from specific cases to general rules resulting in a conclusion that has epistemic uncertainty. > The inductive reasoning is not the same as induction used in mathematical proofs - **mathematical induction is actually a form of deductive reasoning**. ## Deductive vs abductive reasoning Deductive reasoning differs from *abductive reasoning* by the direction of the reasoning relative to the conditionals. Deductive reasoning goes in the same direction as that of the conditionals, whereas abductive reasoning goes in the opposite direction to that of the conditionals.