Definition
Deduction is the mode of reasoning in which the conclusion is taken to follow with logical necessity from the premises. If a deductive argument is valid in form and its premises are true, the conclusion must be true — there is no possible state of affairs in which the premises hold and the conclusion fails. This necessity-relation distinguishes deduction from induction, where the premises only make the conclusion more probable, never certain.
The canonical example is the syllogism: "All humans are mortal; Socrates is human; therefore Socrates is mortal." The form of the argument guarantees the inference regardless of the content. Substitute any terms preserving the pattern and the same logical guarantee holds.
Why it matters
How it works
A deductive system rests on a set of axioms (statements taken as true without proof) and a set of inference rules (patterns by which new statements can be derived from those already accepted). Starting from the axioms and applying the inference rules in sequence produces a proof — a chain of statements each of which is either an axiom or the consequence of earlier statements under a valid rule. Every theorem in a deductive system is the endpoint of such a chain.
Validity in deduction is checked by examining the form, not the content. A common diagnostic is to substitute different terms with the same structure and ask whether the conclusion still seems to follow. If the same form can yield true premises and a false conclusion under any substitution, the original argument was invalid; the apparent persuasiveness depended on the content rather than the structure. This separation of form from content is what makes deductive logic mechanical enough to be performed by computers.