INCOMPLETENESS THEOREM AND A SYSTEM WITHIN WHICH THE CONSTRUCTION OF A NAME OF A SENTENCE IS POSSIBLE

不完备性定理和可以构建句子名称的系统

• 批准号: 06801001
• 负责人: WARAGAI Toshiharu
• 金额: $ 0.64万
• 依托单位: TOKYO INSTITUTE OF TECHNOLOGY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1994
• 资助国家: 日本
• 起止时间: 1994 至 1995
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-06801001/
• 关键词: Incompleteness; Set theory; Definition; Event; Name of Events; General sentence; Knowledge Representation; Ontology; 命題の名前; ライプンッツの法則; 「もの」と「こと」; 命題における個別と普遍; Incomoleteness Theorems; Undefinability; Truth Predicate; Godel; Tarski; Genera

The main results of the present reserach are following :1 We constructed a logical system within which we can construct a name of a sentence by a proper extention of the standard logical system. We thus enriched the expressive power of the logical system.2 A remarkable feature if the system is that it contains as a theorem a formula that expresses the principle of comprehension. This fact implies that the notions considered to be peculiar to set theory belong to this enriched system. This suggests the inadequacy of the standard logical system the representative means of natural language.3 In the system thus obtained, we can develop a method by means of which we can distinguish singular sentences from general ones. This method leads us to a solution of [the problem of the unique correspondence between the form and the content of a sentence].

本研究的主要结果如下：1.我们构造了一个逻辑系统，在这个系统中，我们可以通过对标准逻辑系统的适当扩展来构造一个句子的名称。这样，我们就丰富了逻辑系统的表达能力。逻辑系统的一个显著特点是，它包含一个定理，这个定理是一个表达理解原理的公式。这一事实意味着被认为是集合论特有的概念属于这个丰富的系统。这表明标准的逻辑系统的不足之处自然语言的代表手段。3在这样获得的系统中，我们可以开发出一种方法，通过这种方法，我们可以区分一般的句子。这种方法使我们解决了[句子的形式和内容之间唯一对应的问题]。

项目成果

WARAGAI,Toshiharu: "On the Equivalence between the Leibnizian Law and the Singular Syllogism" in the Proceeding of the Centenary International Conference of Lvov-Warsaw School,Reidel. to appear.

WARAGAI，Toshiharu：“论莱布尼茨定律与奇异三段论之间的等价性”，利沃夫-华沙学派百年国际会议论文集，Reidel。

WARAGAI,Toshiharu: "IS-A Relation,the Principle of Comprehension and the Doctrine of Limitation of Size" Annals for Japan Association for Philosophy of Science. Vol 9 No.1. 23-34 (1996)

WARAGAI，Toshiharu：“IS-A关系，理解原理和大小限制学说”日本科学哲学协会年鉴。

WARAGAI,Toshiharu: "On Understanding the Axiom of Lesniewski's Ontology" Humanities Review. 21. 13-19 (1996)

WARAGAI、Toshiharu：《论理解列斯涅夫斯基本体论的公理》人文评论。

WARAGAI,Toshiharu: "On Understanding the Axiom of Lesniewski's Ontology" Humanities Review. No.21. 13-19 (1996)

WARAGAI、Toshiharu：《论理解列斯涅夫斯基本体论的公理》人文评论。

WARAGAI,Toshiharu: "A Natural Extension of Predicate Caluclus IS-A Relation is Expressible" 学位論文(博士(理学))(東京工業大学). (1994)

WARAGAI, Toshiharu：“谓词演算 IS-A 关系的自然扩展是可表达的”论文（理学博士）（东京工业大学）（1994 年）。