Category theory as a rival

Category theory is a unifying theory of mathematics that was initially developed in the second half of the 20th century. In this respect it is an alternative and complement to set theory. A key theme from the “categorical” point of view is that mathematics requires not only certain kinds of objects (Lie groups, Banach spaces, etc.) but also mappings between them that preserve their structure.

In particular, this clarifies exactly what it means for mathematical objects to be considered to be the same.

— Wikipedia on Unifying theories in mathematics

2010.01.11 Thursday ACHK

The least of all evils 4

眾害取其輕 4

”眾害取其輕”(the least of all evils)這個表達式對我思考(intellectual mind)有很大啟發:有些時候,”邪惡”是必須的,唯有接受。但是 ”接受” 不代表 ”坐以待斃”。反而,我們應努力把邪惡減到最低,即是”眾害取最輕”。

但是,有一點要補充:evil在很多情況下都一定存在,但不是在任何情況下。有些時候,evil可以完全不存在。換句話說,有些時候,眾害中最輕的一個是零,即是無害。(Sometimes, the least of all evils is zero.)

有些人有一個錯誤而極端的看法:他們以為任何情況下,evil一定存在。

(安:你的重點是,雖然建議要眾害中取最輕(Choose the least of all evils),但是不能以此為作惡的借口,因為有些時候,evil毋須存在。)

留意,”evil有時可以不存在” 並不是 ”眾害取最輕” 的例外(exception case)。

反而,”evil有時可以不存在” 已包括在 ”眾害取最輕” 之中,是特例(special case)。

有時,”最輕之害” 不是零;

有時,”最輕之害” 是零。

— Me@2010.01.20

2010.01.20 Wednesday (c) All rights reserved by ACHK