首页数学
   首页哲学
0


悖论与无限

Paradox and Infinity
课程网址: https://openlearninglibrary.mit.edu/courses/course-v1:MITx+24.118...  
主讲教师: Agustín Rayo; David Balcarras; Cosmo Grant
开课单位: 麻省理工学院
开课时间: 2021-11-15
课程语种: 英语
中文简介:
在《悖论与无限》一书中,你将看到哲学与数学交叉的亮点。 本课程分为三个模块: 无穷大:了解一些无穷大是如何比其他无穷大的,并探索越来越大的无穷大令人难以置信的层次结构。 时间旅行和自由意志:了解时间旅行在逻辑上是否可行,以及它是否与自由意志兼容。 可计算性和哥德尔定理:了解一些数学函数是如何如此复杂,以至于任何计算机都无法计算它们。用这个结果来证明哥德尔著名的不完全性定理。 Paradox and Infinity是一门数学课,它的前提是你对大学水平的数学感到满意,并且你熟悉数学证明。 在课堂上表现出色的学员有资格获得MITx哲学奖。高中生有资格获得该奖项,此外还有MITx高中哲学奖。有关更多信息,请参见下面的常见问题部分。 注:在Paradox方面表现出色的学习者通常会至少参加几门大学水平的数学或计算机科学课程。另一方面,悖论并不以熟悉数学或计算机科学的任何特定分支为前提。你只需要在数学环境中感到舒适。
课程简介: In Paradox and Infinity, you will be introduced to highlights from the intersection of philosophy and mathematics. The class is divided into three modules: Paradox and Infinity is a math-heavy class, which presupposes that you feel comfortable with college-level mathematics and that you are familiar with mathematical proofs. Learners who display exceptional performance in the class are eligible to win the MITx Philosophy Award. High School students are eligible for that award and, in addition, the MITx High School Philosophy award. Please see the FAQ section below for additional information. Note: learners who do well in Paradox will have typically taken at least a couple of college-level classes in mathematics or computer science. On the other hand, Paradox does not presuppose familiarity with any particular branch of mathematics or computer science. You just need to feel comfortable in a mathematical setting. Infinity: Learn about how some infinities are bigger than others, and explore the mind-boggling hierarchy of bigger and bigger infinities. Time Travel and Free Will : Learn about whether time travel is logically possible, and whether it is compatible with free will.
关 键 词: 哥德尔定理; 无穷大; 数学与哲学
课程来源: 麻省理工学院公开课
数据采集: 2022-04-08:cyh
最后编审: 2022-04-08:cyh
阅读次数: 81