axiomatize

简明释义

英[ˌæksɪəˈmaɪtaɪz]美[ˌæksɪəˈmaɪtaɪz]

v. （使）理论公理化

第 三 人 称 单 数 a x i o m a t i z e s

现 在 分 词 a x i o m a t i z i n g

过 去 式 a x i o m a t i z e d

过 去 分 词 a x i o m a t i z e d

英英释义

单词用法

同义词

反义词

例句

1.In mathematics, we often need to axiomatize 公理化 our theories to ensure they are based on solid foundations.

在数学中，我们经常需要对我们的理论进行公理化，以确保它们基于坚实的基础。

2.The philosopher aimed to axiomatize 公理化 ethical principles to create a universal moral framework.

这位哲学家旨在公理化伦理原则，以创建一个普遍的道德框架。

3.To develop a robust software system, we must axiomatize 公理化 the requirements clearly.

为了开发一个稳健的软件系统，我们必须清晰地公理化需求。

4.The scientist proposed to axiomatize 公理化 the laws of physics for better understanding and application.

科学家提议公理化物理定律，以便更好地理解和应用。

5.In computer science, it is essential to axiomatize 公理化 algorithms to validate their correctness.

在计算机科学中，对算法进行公理化以验证其正确性是至关重要的。

作文

In the realm of mathematics and logic, the process of establishing a set of principles or rules that serve as a foundation for further reasoning is known as axiomatize. This concept plays a crucial role in various fields, including philosophy, computer science, and even social sciences. To axiomatize means to formulate a system based on accepted truths or axioms, which are self-evident propositions that do not require proof. For instance, in Euclidean geometry, one might axiomatize the relationship between points, lines, and planes by starting with a few basic axioms, such as "through any two points, there exists exactly one straight line." The significance of axiomatize in mathematics cannot be overstated. By creating a structured framework, mathematicians can derive complex theorems from simple, foundational statements. This method not only enhances clarity but also ensures consistency within mathematical theories. When a system is well-axiomatized, it allows mathematicians to explore new territories of thought while remaining grounded in established knowledge. Moreover, the process of axiomatize extends beyond pure mathematics. In computer science, for instance, algorithms can be axiomatized to ensure that they operate under certain predefined conditions. By establishing clear rules, developers can create software that behaves predictably, which is essential for debugging and optimization. Similarly, in social sciences, researchers often axiomatize their theories to create models that can explain human behavior. By identifying core assumptions, they can build upon these foundations to analyze complex social phenomena. Philosophically, the act of axiomatize raises interesting questions about the nature of knowledge and belief. What constitutes an axiom, and how do we determine its validity? These inquiries lead to deeper discussions about the foundations of our understanding of the world. The ability to axiomatize a theory implies a level of confidence in the underlying assumptions, which can be both empowering and limiting. While it provides a sense of security in reasoning, it may also constrain creativity by binding thinkers to established norms. In conclusion, the term axiomatize encapsulates a fundamental process in various disciplines, serving as a bridge between basic truths and complex ideas. Whether in mathematics, computer science, or philosophy, axiomatize enables us to structure our understanding and explore new concepts systematically. As we continue to advance in these fields, the importance of clearly defining our axioms will remain paramount, ensuring that our reasoning remains sound and our conclusions valid. Ultimately, the ability to axiomatize empowers us to navigate the complexities of knowledge while fostering innovation and discovery.

在数学和逻辑的领域中，建立一套原则或规则，以作为进一步推理基础的过程被称为公理化。这一概念在哲学、计算机科学甚至社会科学等多个领域中都扮演着至关重要的角色。公理化意味着基于公认的真理或公理来制定一个系统，而公理是自明的命题，不需要证明。例如，在欧几里得几何中，人们可能会通过从一些基本公理开始，如“通过任意两点，恰好存在一条直线”，来公理化点、线和平面之间的关系。 在数学中，公理化的重要性不容小觑。通过创建一个结构化的框架，数学家可以从简单的基础语句推导出复杂的定理。这种方法不仅增强了清晰度，还确保了数学理论的一致性。当一个系统被良好地公理化时，它允许数学家在保持扎根于已建立知识的同时探索新的思维领域。 此外，公理化的过程超越了纯数学。在计算机科学中，例如，算法可以被公理化以确保它们在某些预定义条件下运行。通过建立明确的规则，开发人员可以创建行为可预测的软件，这对于调试和优化至关重要。同样，在社会科学中，研究人员经常公理化他们的理论，以创建能够解释人类行为的模型。通过识别核心假设，他们可以在这些基础上构建，以分析复杂的社会现象。 在哲学上，公理化的行为引发了关于知识和信仰本质的有趣问题。什么构成公理，我们如何确定其有效性？这些探讨引发了关于我们理解世界基础的更深层次讨论。能够公理化一个理论意味着对基础假设有一定程度的信心，这既可以是赋予力量，也可能是限制。虽然它提供了一种在推理中安全感，但也可能通过将思考者束缚于既定规范而限制创造力。 总之，术语公理化概括了多个学科中的一个基本过程，作为基本真理与复杂思想之间的桥梁。无论是在数学、计算机科学还是哲学中，公理化使我们能够结构化我们的理解并系统地探索新概念。随着我们在这些领域的不断进步，清晰定义我们的公理的重要性将始终是首要任务，确保我们的推理保持合理，我们的结论有效。最终，能够公理化使我们能够在知识的复杂性中导航，同时促进创新和发现。