# Deductive reasoning

Sherlock Holmes (right) and Dr. Watson, by Sidney Paget
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Deductive reasoning, also deductive logic or logical deduction or, informally, "top-down" logic, is the process of reasoning from one or more general statements (premises) to reach a logically certain conclusion.

Deductive reasoning links premises with conclusions. If all premises are true, the terms are clear, and the rules of deductive logic are followed, then the conclusion reached is necessarily true.

Deductive reasoning (top-down logic) contrasts with inductive reasoning (bottom-up logic) in the following way: In deductive reasoning, a conclusion is reached reductively by applying general rules that hold over the entirety of a closed domain of discourse, narrowing the range under consideration until only the conclusion is left. In inductive reasoning, the conclusion is reached by generalizing or extrapolating from initial information. As a result, induction can be used even in an open domain, one where there is epistemic uncertainty. Note, however, that the inductive reasoning mentioned here is not the same as induction used in mathematical proofs – mathematical induction is actually a form of deductive reasoning.

## Deductive logic

Deductive reasoning is supported by deductive logic (which is not quite the same thing).

For example:

All apples are fruit.
All fruits grow on trees.
Therefore all apples grow on trees.

Or

All apples are fruit.
Some apples are red.
Therefore some fruit is red.

Intuitively, one might deny the major premise and hence the conclusion; yet anyone accepting the premises accepts the conclusion.