Definition
Deductive reasoning is inference in which the conclusion follows from the premises with strict necessity: if the premises are true, the conclusion cannot be false. A successful deductive argument is valid, and its force is all-or-nothing — there are no degrees of deductive support.
This is the kind of reasoning that mathematical proof relies on, and it is the primary subject of formal logic. Deduction does not add new information to the world; it draws out what was already implicitly contained in the premises, making explicit what we were committed to all along.
Why it matters
How it works
A deductive argument succeeds by virtue of its logical form. Once the form guarantees that no counter-example is possible — no situation with true premises and a false conclusion — the inference is locked in regardless of subject matter. The certainty comes from structure, not from accumulated evidence.
Priest contrasts this sharply with inductive reasoning. Induction reaches beyond its premises and so can always be overturned by new data; deduction never reaches beyond them, which is exactly why it can be certain. The price of that certainty is that deduction tells us nothing genuinely new about the world — only about the consequences of what we already accept.