axiomatics

简明释义

英[ˌæksɪˈɒmætɪks]美[ˌæksɪˈɒmætɪks]

n. 公理系统；公理学

英英释义

单词用法

同义词

反义词

例句

1.We conclude the paper with a brief statement of the theoretical application of axiomatics in medical philosophy and human body medicine.

最后，简明论述了公理学在医学哲学和人体医学理论上的应用。

2.We conclude the paper with a brief statement of the theoretical application of axiomatics in medical philosophy and human body medicine.

最后，简明论述了公理学在医学哲学和人体医学理论上的应用。

3.The concept of the grey utility function is proposed and the axiomatics for the existence of grey utility function are given.

提出了灰效用函数的概念，给出了灰效用函数存在的公理体系。

4.In the field of mathematics, axiomatics is essential for establishing foundational truths.

在数学领域，公理学 对于建立基础真理至关重要。

5.The axiomatics of a theory often dictate its applicability in real-world scenarios.

一个理论的公理学 通常决定了它在现实世界场景中的适用性。

6.Understanding the axiomatics behind logical reasoning can enhance critical thinking skills.

理解逻辑推理背后的公理学 可以提高批判性思维能力。

7.The philosopher's work focused on the axiomatics of ethical principles.

这位哲学家的工作集中在伦理原则的公理学 上。

8.In computer science, the axiomatics of algorithms helps in designing efficient solutions.

在计算机科学中，算法的公理学 有助于设计高效的解决方案。

作文

In the realm of philosophy and mathematics, the concept of axiomatics plays a crucial role in establishing the foundational principles upon which various theories are built. 公理学, as it is known in Chinese, refers to the study of axioms and their implications in logical reasoning and mathematical frameworks. An axiom is a statement or proposition that is regarded as being self-evidently true, serving as a starting point for further reasoning and arguments. The significance of axiomatics lies in its ability to provide a clear structure and framework for understanding complex ideas. One of the most well-known examples of axiomatics can be found in Euclidean geometry, where a set of axioms, such as 'through any two points, there is exactly one straight line,' serves as the foundation for deriving various geometric properties and theorems. By adhering to these axioms, mathematicians are able to construct a coherent system that allows for the exploration of geometric relationships and theorems. This systematic approach not only enhances clarity but also helps in identifying inconsistencies within a theory. The application of axiomatics extends beyond mathematics into fields such as logic, computer science, and even economics. In logic, for instance, the development of propositional calculus is heavily reliant on a set of axioms that govern the manipulation of logical statements. Similarly, in computer science, axiomatics is employed in formal verification processes to ensure that software systems adhere to specified properties and behave as intended. Moreover, the philosophical implications of axiomatics cannot be overlooked. Philosophers like David Hilbert have emphasized the importance of a rigorous foundation for mathematics through the use of axioms. Hilbert's program sought to formalize mathematics by demonstrating that all mathematical truths could be derived from a finite set of axioms through logical deduction. This endeavor highlights the interplay between axiomatics and the pursuit of certainty and rigor in mathematical thought. However, the reliance on axiomatics has also led to debates regarding the nature of truth and knowledge. Some philosophers argue that the choice of axioms is inherently subjective, and different sets of axioms can lead to divergent conclusions. For instance, non-Euclidean geometries emerged when mathematicians began to explore alternative axioms, leading to the realization that multiple geometrical systems could coexist, each valid within its own framework. This revelation challenges the notion of absolute truth in mathematics and encourages a broader perspective on the nature of knowledge. In conclusion, axiomatics serves as a fundamental pillar in various disciplines, providing a structured approach to reasoning and understanding. Its implications reach far beyond mathematics, influencing logic, computer science, and philosophy. As we continue to explore the boundaries of knowledge and truth, the study of axiomatics remains an essential area of inquiry, prompting us to question the foundations upon which our understanding is built. By engaging with axiomatics, we not only enhance our comprehension of mathematical concepts but also cultivate a deeper appreciation for the intricate web of ideas that shape our intellectual landscape.

在哲学和数学领域，公理学的概念在建立各种理论的基础原则方面发挥着至关重要的作用。公理学指的是对公理及其在逻辑推理和数学框架中影响的研究。公理是一种被视为自明真实的陈述或命题，作为进一步推理和论证的起点。公理学的重要性在于它能够提供一个清晰的结构和框架，以理解复杂的思想。 最著名的公理学例子之一可以在欧几里得几何中找到，其中一组公理，例如“通过任意两点，有且仅有一条直线”，作为推导各种几何属性和定理的基础。通过遵循这些公理，数学家们能够构建一个连贯的系统，使他们能够探索几何关系和定理。这种系统化的方法不仅增强了清晰度，还有助于识别理论中的不一致性。 公理学的应用超越了数学，扩展到逻辑、计算机科学甚至经济学等领域。例如，在逻辑学中，命题演算的发展在很大程度上依赖于一组支配逻辑陈述操作的公理。同样，在计算机科学中，公理学被用于形式验证过程，以确保软件系统遵循指定的属性并按预期行为。 此外，公理学的哲学意义也不可忽视。像大卫·希尔伯特这样的哲学家强调，通过使用公理为数学提供严格基础的重要性。希尔伯特的计划试图通过证明所有数学真理都可以通过逻辑推导从有限的公理集中得出，从而使数学形式化。这项工作突显了公理学与追求数学思想中的确定性和严谨性之间的相互作用。 然而，依赖于公理学也引发了关于真理和知识本质的辩论。一些哲学家认为，公理的选择本质上是主观的，不同的公理集可以导致不同的结论。例如，当数学家们开始探索替代公理时，非欧几里得几何出现了，导致人们意识到多种几何系统可以共存，每种在其自身框架内都是有效的。这一发现挑战了数学中绝对真理的概念，并鼓励我们对知识的本质采取更广阔的视角。 总之，公理学作为各个学科的基本支柱，为推理和理解提供了结构化的方法。它的影响远远超出了数学，影响着逻辑、计算机科学和哲学。随着我们继续探索知识和真理的边界，公理学的研究仍然是一个重要的探讨领域，促使我们质疑构成我们理解基础的根基。通过参与公理学，我们不仅增强了对数学概念的理解，还培养了对塑造我们智力景观的复杂思想网络的更深刻欣赏。