deduced

Deduced is the past participle of deduce and is used as an adjective to describe a conclusion that has been reached by reasoning from evidence. In logic and mathematics, deduction is the rigorous process by which a conclusion follows necessarily from given premises, assuming the reasoning is valid and the premises are true.

Etymology: from Latin deducere “to lead away, derive,” via Old French and English. The term emphasizes derivation from facts or premises rather than discovery by accident or guesswork.

Distinctions: Deduction, induction, and abduction are common modes of reasoning. Deduction yields conclusions that are logically entailed by the premises (assuming the premises are true and the reasoning valid). Induction generalizes from observed instances to broader generalizations; abduction infers the best explanation for the available evidence. In everyday language, “deduced” is often used loosely to mean inferred.

Usage: In science and mathematics, results may be described as deduced from axioms or proven. In law and philosophy, careful deduction is essential to derive conclusions from established rules or premises. Example: If all humans are mortal and Socrates is a human, one can deduce that Socrates is mortal.