When the conclusion of an argument follows from its premise/premises…

Concept: Arguments are classified by the kind of support the premises are meant to give the conclusion. One kind of support is demonstrative, or necessary: the premises, if true, make the falsity of the conclusion impossible, because the conclusion asserts nothing beyond what the premises already contain. The other kind is non-demonstrative, or probable: the premises only make the conclusion more likely, and the conclusion carries information that goes beyond them.

Application: The stem's qualifier "conclusively" names the first kind of support. It says that once the premises are granted, the conclusion is settled and no room is left for it to be false. An argument that claims exactly this necessity-preserving support is a deductive argument, and it is judged by validity (a valid argument cannot have all true premises together with a false conclusion) and, when the premises are also true, by soundness.

Cross-check: the remaining named argument types do not claim that kind of support.

• Inductive argument: the premises make the conclusion probable only. The conclusion generalises beyond the observed cases, so true premises can still be accompanied by a false conclusion.

• Analogical argument: a property observed in one case is transferred to a case that resembles it. The transfer is only as strong as the relevance of the resemblance, so the conclusion again remains probable.

• Circular argument: the claim to be established is already assumed among the premises (petitio principii). This names a defect in how the premises were chosen, not a degree of support the premises give.

Hence an argument whose conclusion follows from its premise or premises conclusively is a deductive argument.