deductively

Deductively is an adverb derived from deductive, describing the manner in which reasoning or argumentation proceeds. In logic and philosophy, a deductive argument is one in which the conclusion follows necessarily from the premises, provided the argument is valid and the premises are true. Thus, to argue deductively is to show that the conclusion is a logical consequence of the stated assumptions, rather than merely probable.

In practice, deductive reasoning moves from general rules or axioms to specific conclusions. For example: All humans are mortal; Socrates is a human; therefore Socrates is mortal. In mathematics, proofs are typically presented deductively: the truth of a theorem is established by a chain of deductive steps from axioms and previously proven results. In science and everyday discourse, the term may be used more loosely to describe arguments that are strongly reasoned, though the truth of the premises remains crucial for the overall force of the conclusion.

Deductively is contrasted with inductively and abductively; inductive arguments aim at high probability rather than necessity, and abductive reasoning seeks the best explanation. The precise status of a deductive argument depends on its logical form (validity) and, for real-world arguments, the truth of its premises (soundness). The adverb is commonly used in academic writing to describe the mode of reasoning, proofs, and demonstrations that rely on deduction rather than empirical generalization.