A deductive argument is the presentation of statements that are assumed or known to be true as premises for a conclusion that necessarily follows from those statements. Deductive reasoning relies on what is assumed to be known to infer truths about similarly related conclusions.
In reality, few statements can be said to be true with 100 percent certainty. The classic deductive argument, for example, goes back to antiquity: All men are mortal, and Socrates is a man; therefore Socrates is mortal. However, although all men have historically been mortal (have died, that is), we cannot know if some man living now or in the future will live forever. Similarly, although it seems safe to assume that Socrates is a man, we cannot know for certain that he is not an extraterrestrial being or a phantom. Nevertheless, those premises are sufficiently strong to support the conclusion.
The provability of an argument through deductive reasoning relies on the truth of its assumed premises. The argument may be valid or invalid, independently of whether they are sound. The argument’s validity depends on whether the conclusion naturally follows from the premises. If the statements offered as premises are true, and the conclusion follows naturally from those premises, then a deductive argument is considered to be valid.
A deductive argument can be invalidated by a false assumption as a starting point. Before a deductively reasoned argument can be totally proven wrong, both its supporting premises and its conclusion must be proven false. Until all are disproven, it can be assumed one of the statements is false or falsely applied if the argument itself is proven false.
In contrast, an inductive argument is sampled from instances of supporting evidence that can't be fully proven true but can be considered to supply support for the conclusion. An inductive argument can be disproven by a single negative sample. Where deductive reasoning takes existing premises to infer an existing or past condition, inductive reasoning takes evidence from the past or present to support a conclusion of a future prediction.
See also: critical thinking