Deduktive

Deduktive (deductive) reasoning is a mode of reasoning in which the conclusion follows necessarily from the premises. In a valid deductive argument, if the premises are true and the reasoning is structurally correct, the conclusion cannot be false. Deductive reasoning is contrasted with inductive reasoning, where conclusions generalize beyond the premises, and with abductive reasoning, which infers the best explanations.

Core concepts include validity and soundness. Validity concerns form: a deductive argument is valid if the conclusion follows from the premises regardless of their content. Soundness requires not only validity but also actually true premises. An example: All humans are mortal; Socrates is a human; therefore Socrates is mortal. In propositional form: If p then q; p; therefore q. Deductive methods include syllogistic reasoning (classical Aristotle), natural deduction, and formal proof systems used in mathematics and logic.

History and scope: Deductive reasoning underpins mathematical proofs and formal sciences, and is central to analytic philosophy and legal reasoning. It provides a framework for deriving conclusions with certainty given true premises, assuming proper rules of inference. Limitations include dependence on the truth of premises and on the correctness of the inference rules; a valid argument can be unsound if premises are false. Deduction does not by itself generate new empirical knowledge; it clarifies what follows logically from established axioms or facts.