Translation guide
An axiom is a statement accepted as true without proof, often as a foundation for reasoning. In everyday English, it can also mean a widely accepted principle or saying.
A statement or proposition that is regarded as being established, accepted, or self-evidently true, especially in logic, mathematics, or philosophy.
The standard term for 'axiom' in mathematics and logic. It refers to a fundamental proposition assumed to be true without proof.
A pithy statement that expresses a general truth or rule of conduct, often used in everyday language.
In English, 'axiom' is sometimes used loosely for any accepted truth. In Japanese, 公理 is strictly mathematical/logical. For everyday principles, use 原理 or 格言 depending on context.
Euclidean geometry is based on five axioms.
Often translated as 'principle', but can be used for a fundamental truth or axiom, especially in philosophical or scientific contexts.
この理論はいくつかの基本原理に依存している。
This theory relies on several basic axioms.
Literally 'self-evident truth'. Used for something so obvious it needs no proof, similar to an axiom in everyday language.
人間は皆死ぬというのは自明の理だ。
It is an axiom that all humans are mortal.
A postulate or axiom, often used in geometry or formal systems. More technical and less common than 公理.
平行線公準は非ユークリッド幾何学では成り立たない。
The parallel postulate does not hold in non-Euclidean geometry.
A proverb or maxim; a short, well-known saying that expresses a common truth or piece of advice.
「時は金なり」は有名な格言だ。
'Time is money' is a well-known axiom.
A wise saying or golden rule; often used for timeless advice.
祖母はよく古い金言を口にした。
My grandmother often quoted old axioms.
A maxim or aphorism; a concise statement of a principle. Somewhat literary.
彼の著作には多くの箴言が含まれている。
His writings contain many axioms.