演繹

• Reading: えんえき
• Romaji: eneki
• Kanji breakdown: 演 (en) — to perform, to unfold, to develop; 繹 (eki) — to unravel, to trace, to draw out
• Pronunciation: /e.neː.ki/

Meaning

Deduction; deductive reasoning. Drawing specific conclusions from general premises or principles.

A Sino-Japanese noun used in logic, philosophy, mathematics, and the sciences to describe the process of deriving specific conclusions from general rules or axioms. Contrasted with 帰納 (kino — induction), which moves from specific observations to general principles. 演繹的推論 (deductive reasoning) is a foundational concept in formal logic and mathematical proof. The verb form is 演繹する.

Examples

1. 数学における証明の多くは、公理から結論を導く演繹的手法に基づいている。 Many proofs in mathematics are based on deductive methods that derive conclusions from axioms.
2. 演繹と帰納はどちらも科学的推論において不可欠な思考方法だ。 Both deduction and induction are indispensable modes of reasoning in scientific inquiry.
3. 彼の論証は一見説得力があるが、前提が誤っていれば演繹の結論も無効になる。 His argument appears convincing at first glance, but if the premises are wrong, the deductive conclusion is also invalidated.

Usage Guide

Context: logic, philosophy, mathematics, scientific reasoning, academic writing

Tone: scholarly, technical

Origin & History

Meiji-era Sino-Japanese coinage: 演 (en) — to perform, to unfold + 繹 (eki) — to unravel, to trace, to draw out. Used to translate the Western logical term 'deduction'. The compound captures the idea of drawing out and developing logical consequences from premises.

Cultural Context

Era: Meiji-Modern

Generation: Adult

Social background: Educated