The Annotated Gödel: A Reader's Guide to his Classic Paper on Logic and Incompleteness
暫譯: 註解版哥德爾:讀者指南其經典邏輯與不完全性論文
Prince, Hal
- 出版商: Homebred Press
- 出版日期: 2022-08-21
- 售價: $880
- 貴賓價: 9.5 折 $836
- 語言: 英文
- 頁數: 184
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 9798986414218
- ISBN-13: 9798986414218
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相關分類:
數學
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商品描述
The Annotated Gödel offers a guided tour of Kurt Gödel's 1931 article on incompleteness, which demonstrated unexpected limits to the power of many logical systems. Today we call these results Gödel's First and Second Incompleteness Theorems. The book includes the complete article in a new English translation, interleaved with commentary that guides the reader through Gödel's work, step by step.
The commentary concentrates on Gödel's exposition. It describes what he is doing at each point, and how it relates to other parts of the article. It elaborates on his proofs by outlining them, for example, or by making a table of his variables and their uses, or by filling in gaps in his arguments.
The translation uses modern mathematical notation and terminology. It replaces Gödel's function and relation names, based on German word fragments, with English equivalents. Its language is less formal than that of the earlier translations, which date from the 1960s.
The book assumes some familiarity with mathematical definitions and proofs, at the level of an undergraduate abstract math course, as well as some knowledge of formal logic, from an introductory course or the equivalent.
商品描述(中文翻譯)
《註解版哥德爾》提供了對庫爾特·哥德爾(Kurt Gödel)1931年有關不完全性的文章的導覽,該文章展示了許多邏輯系統的能力所面臨的意外限制。今天我們稱這些結果為哥德爾的第一和第二不完全性定理。這本書包含了該文章的完整內容,並提供了新的英文翻譯,並穿插了逐步引導讀者理解哥德爾工作的註解。
註解集中於哥德爾的闡述。它描述了他在每個階段所做的事情,以及這些與文章其他部分的關聯。它通過概述他的證明、製作變數及其用法的表格,或填補他論證中的空白來詳細說明。
翻譯使用現代數學符號和術語。它將哥德爾基於德語詞根的函數和關係名稱替換為英文對應詞。其語言比1960年代早期翻譯的語言更不正式。
本書假設讀者對數學定義和證明有一定的熟悉程度,至少達到本科抽象數學課程的水平,以及對形式邏輯有一定的了解,來自入門課程或相當的知識。