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逻辑Ⅱ24.242 Logic |
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| 课程网址: | http://ocw.mit.edu/courses/linguistics-and-philosophy/24-242-logi... |
| 主讲教师: | Prof. Vann McGee |
| 开课单位: | 麻省理工学院 |
| 开课时间: | 信息不详。欢迎您在右侧留言补充。 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | This course begins with an introduction to the theory of computability, then proceeds to a detailed study of its most illustrious result: Kurt Gödel's theorem that, for any system of true arithmetical statements we might propose as an axiomatic basis for proving truths of arithmetic, there will be some arithmetical statements that we can recognize as true even though they don't follow from the system of axioms. In my opinion, which is widely shared, this is the most important single result in the entire history of logic, important not only on its own right but for the many applications of the technique by which it's proved. We'll discuss some of these applications, among them: Church's theorem that there is no algorithm for deciding when a formula is valid in the predicate calculus; Tarski's theorem that the set of true sentence of a language isn't definable within that language; and Gödel's second incompleteness theorem, which says that no consistent system of axioms can prove its own consistency. |
| 关 键 词: | 逻辑; 可计算性; 系统; 算术; 公理基础; 证明真理的算法; 应用历史; 算法; 公式; 有效; 谓词演算 |
| 课程来源: | 麻省理工大学公开课 |
| 最后编审: | 2016-03-23：cmh |
| 阅读次数: | 63 |