背理

• Reading: はいり
• Romaji: hairi
• Kanji breakdown: 背 (hai/se/somu) — back, go against, betray; 理 (ri/kotowari) — reason, logic, principle
• Pronunciation: /haiɾi/

Meaning

Absurdity; contradiction; irrationality. A conclusion or premise that contradicts reason, logic, or established truth.

A formal, philosophical term. Most often appears in 背理法 (proof by contradiction, reductio ad absurdum) — a logical method that assumes the opposite of what one wants to prove and derives a contradiction. Also used more broadly for irrational or self-defeating reasoning in general discourse.

Examples

1. 背理法を使えば、素数が無限に存在することを証明できる。 Using proof by contradiction, one can prove that there are infinitely many prime numbers.
2. 彼の主張には根本的な背理が含まれており、論理的に成立しない。 His argument contains a fundamental contradiction and does not hold up logically.
3. 自由を守るために自由を制限するという議論は、背理に陥りやすい。 The argument that freedom must be restricted in order to protect it easily falls into absurdity.

Usage Guide

Context: mathematics, philosophy, logic, argumentation

Tone: analytical

Origin & History

Compound of 背 (hai, to go against/turn one's back) and 理 (ri, reason/principle/logic). Together they convey the sense of turning against or contradicting the principles of reason.

Cultural Context

Era: Classical

Generation: Adults

Social background: Educated