形式科学简史

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注：机翻，未校。

形式科学（formal science）是与形式系统，如逻辑学、数学、理论计算机科学、信息理论、系统理论、判定理论、统计学和一些语义学等有关的知识的分支。和其他科学不同，形式科学不是和基于真实世界观察理论有效性联系的，而与定义和规律为基础的形式系统性质相联系，但形式科学的方法可以被用来建造和检验观察真实世界的科学模型（或通用手段）。

Formal science

Smartencyclopedia

October 30, 2021

Formal science is a branch of science studying formal language disciplines concerned with formal systems, such as logic, mathematics, statistics, theoretical computer science, artificial intelligence, information theory, game theory, systems theory, decision theory, and theoretical linguistics. Whereas the natural sciences and social sciences seek to characterize physical systems and social systems, respectively, using empirical methods, the formal sciences are language tools concerned with characterizing abstract structures described by symbolic systems. The formal sciences aid the natural science, social science, and actuarial science all through providing information about the structures used to describe the physical and the contemporary world, and what inferences may be made about them.
形式科学是研究与形式系统有关的形式语言学科的科学分支，例如逻辑、数学、统计学、理论计算机科学、人工智能、信息论、博弈论、系统论、决策论和理论语言学。自然科学和社会科学分别寻求使用实证方法描述物理系统和社会系统，而形式科学是涉及描述符号系统描述的抽象结构的语言工具。正规科学通过提供有关用于描述物理世界和当代世界的结构以及可以对它们做出哪些推断的信息来帮助自然科学、社会科学和精算学。

Etymology 词源

The modern usage of the term formal sciences, in English-language literature, occurs at least as early as 1860, in a posthumous publication of lectures on philosophy by Sir William Hamilton wherein logic and mathematics are listed as formal sciences. Going even further back to 1819, a German-language textbook on logic was published by Wilhelm Esser, elucidating the significance of the designation formal science (Formalwissenschaft) as applied to logic; an English-language translation of it is provided in William Hamilton’s lecture:
在英语文学中，形式科学一词的现代使用至少早在 1860 年就出现在威廉·汉密尔顿爵士 （Sir William Hamilton） 死后出版的哲学讲座中，其中逻辑和数学被列为形式科学。再往前追溯到 1819 年，Wilhelm Esser 出版了一本德语逻辑教科书，阐明了形式科学 （Formalwissenschaft） 这一名称应用于逻辑的重要性;威廉·汉密尔顿 （William Hamilton） 的演讲中提供了它的英文翻译：

Logic thus obtains, in common parlance, the appellation of a formal science, not indeed in the sense as if Logic had only a form and not an object, but simply because the form of human thought is the object of Logic; so that the title formal science is properly only an abbreviated expression.
因此，用通俗的话来说，逻辑获得了形式科学的称谓，这并不是说逻辑只有一个形式而没有对象，而仅仅是因为人类思想的形式是逻辑的对象;因此，形式科学这个标题只是一个缩写词。

History 历史

Branches 分支

Differences from other sciences 与其他科学的区别

— Albert Einstein

As opposed to empirical sciences (natural and social), the formal sciences do not involve empirical procedures. They also do not presuppose knowledge of contingent facts or describe the real world. In this sense, formal sciences are both logically and methodologically a priori, for their content and validity are independent of any empirical procedures.
与实证科学（自然科学和社会科学）相反，正式科学不涉及实证程序。它们也不以对或有事实的了解为前提，也不以描述现实世界为前提。从这个意义上说，形式科学在逻辑和方法论上都是先验的，因为它们的内容和有效性独立于任何实证程序。

References

• American Mathematical Society. “MSC2010 database”. mathscinet.ams.org. Retrieved 17 May 2019.
• Hamilton, William. Lectures on metaphysics and logic. 1860. Ed. Henry Longueville Mansel & John Veitch, pub. Gould and Lincoln. Vol. 4, pp. 64–65. “Formal truth will, therefore, be of two kinds,—Logical and Mathematical. […] The case is the same with the other formal science, the science of Quantity, or Mathematics.”
• Esser, Wilhelm. Logik, § 3, pp. 5–6. Cf. et seq. 2d edit. 1819.—Ed. Krug, Denklehre oder Logik, § 8, p. 17
• Hamilton, William. Lectures on metaphysics and logic. 1860. Ed. Henry Longueville Mansel & John Veitch, pub. Gould and Lincoln. Vol. 3, p. 17
• edited by Karine Chemla (2012). The History of Mathematical Proof in Ancient Traditions. Cambridge. ISBN 978-1-107-01221-9. OCLC .
• Albert Einstein (1923). “Geometry and Experience”. Sidelights on relativity. Courier Dover Publications. p. 27. Reprinted by Dover (2010), ISBN 978-0-486-24511-9.
• Carnap, Rudolf (1938). “Logical Foundations of the Unity of Science”. International Encyclopaedia of Unified Science. I. Chicago: University of Chicago Press.
• Bill, Thompson (2007), “2.4 Formal Science and Applied Mathematics”, The Nature of Statistical Evidence, Lecture Notes in Statistics, 189 (1st ed.), Springer, p. 15

Formal science – Smartencyclopedia

https://smartencyclopedia.org/content/formal-science/