Anonymous

# 1. 原理 定律 定義 理論 學說 有什麼不同?

1. 原理 定律 定義 理論 學說 有什麼不同

2. What are the differences among definition, theorem, axiom, principle, and a law?

Rating

簡單的說 (comes from me, don't take too serious...)

定義 definition

給某項東西(事物)意義, 或對其性質完整周延的說明, 當然我們還要去檢驗是否良好定義 (well-defined)

定理 theorem

一條需被嚴謹邏輯方法證明的敘述

學說 theory

一些規則或規範集合而成為邏輯性的系統 可以去解釋一些社會及自然現象

公理 axiom

最基本和不證自明(或假定為不證自明)的真理

原理 principle

近似於某項事物的規則或規範

定律 law

物理學用得較多

經過多次實驗, 觀察所得出的結論

較嚴謹的...

The meanings and explanations of terms come from Wikipedia...

定義 (DEFNITION)

A definition may be a statement of the essential properties of a certain thing, or a statement of equivalence between a term and that term's meaning. The two are not mutually exclusive, nor are they equivalent.

定理 (THEOREM)

定理是經過受邏輯限制的證明為真的敘述。一般來說，在數學中，只有重要或有趣的陳述才叫定理。證明定理是數學的中心活動。

A theorem is a proposition that has been or is to be proved on the basis of explicit assumptions. Proving theorems is a central activity of mathematicians. Note that "theorem" is distinct from "theory".

學說 (THEORY)

In various sciences, a theory is a logically self-consistent model or framework describing the behavior of a certain natural or social phenomenon, thus either originating from observable facts or supported by them. Scientific theories are formulated, developed, and evaluated according to the scientific method.

In physics, the term theory is generally used for a mathematical framework derived from a small set of basic principles, capable of producing experimental predictions for a given category of physical systems. An example is "electromagnetic theory", which is usually taken to be synonymous with classical electromagnetism, the specific results of which can be derived from Maxwell's equations.

公理 (AXIOM) -- 源自希臘文axioma，原意是「有價值的思想」。

最基本和不證自明(或假定為不證自明)的真理，例如在數學及邏輯系統上，若對之否定便會想破壞系統的一致性。

推定任何其他命題的原始出發點，它本身不能由其他命題演繹而來。

故此，公理不像其他由之推導出來的命題一樣可以被證明，而其功能在於建構出一個協調並相容的系統。

In epistemology, an axiom is a self-evident truth upon which other knowledge must rest, from which other knowledge is built up. Not all epistemologists agree that any axioms, understood in that sense, exist.

In mathematics, an axiom is not necessarily a self-evident truth but rather, a formal logical expression used in a deduction to yield further results. Mathematics distinguishes two types of axioms: logical axioms and non-logical axioms.

原理 (PRINCIPLE)

A principle is something, usually a rule or norm, that is part of the basis for something else. For example, the ethics of someone may be seen as a set of principles that the individual obeys. These principles form the basis for their ethics.

Principles may also be introduced as pedagogy: laying down basics in a topic, in order later to proceed to more detailed developments.

Identifying or defining a rule as a principle says that, for the purpose at hand, the principle will not be questioned or further derived. This is a convenient way of reducing the complexity of an argumentation.

定律 (LAW)

作為物理學基本的概念，物理定律是描述物體運動或狀態的可測量量的數學表達，是在科學界公開發表和被廣泛驗證的理論。物理學定律通常被認為是正確的。

不象數學定理可以被證明為真，物理學定律永遠無法被證明，不能保證在所有可能的情況下100%有效。物理學定律會被實驗證明是錯的，通常這意味著物理學的突破。

A physical law or a law of nature is a scientific generalization based on empirical observations. Laws of nature are conclusions drawn from, or hypotheses confirmed by scientific experiments. The production of a summary description of nature in the form of such laws is the fundamental aim of science. Laws of nature are distinct from legal code and religious Law, and should not be confused with the concept of natural law.

http://www.wikipedia.org/

Source(s): wikipedia and me
• Anonymous

定義是固定的基本遊戲規模

理論是從定義發展出來的