"我说谎"的挑战
语言,可以说是属于人类"熟知而非真知"的事物之一。
语言存在的问题之一,就是悖论的存在,如"我说慌",这句话使人无法辨认真假。比较经典的还有罗素发现的"最大集悖论"问题。一个最大的集,应该包括其他一切集。问题是,它是否应该包括自己?如果不包括,它就不是最大集。如果包括,就违反了"包括其他一切集"的规定。
通俗地说,罗素悖论也叫"理发师悖论"。一个理发师作广告说,"我只给全城不自己刮胡子的人刮胡子"。理发师,很明显,无法确定是否应该给自己刮胡子。因为,按照广告,如果自己不属于"自己刮胡子"的人,那么,自己就必须自己给自己刮胡子。而如果自己属于"给自己刮胡子的人",自己就不应该给自己刮胡子。
据说,当福雷格接到罗素的明信片时,立刻叫停了马上就要开印的几卷本的数学基础论著作,它一生努力的工作付之东流。
所以,究竟为什么语言会出现悖论?悖论仅仅是人类语言的错误吗?还是也存在于自然界?我们应该怎样来理解悖论?
等等这些问题,一个世纪以来,人类还在继续寻找答案......
Reference:
"Russell's Paradox
Russell's paradox is the most famous of the logical or set-theoretical paradoxes. The paradox arises within naive set theory by considering the set of all sets that are not members of themselves. Such a set appears to be a member of itself if and only if it is not a member of itself, hence the paradox.
Some sets, such as the set of all teacups, are not members of themselves. Other sets, such as the set of all non-teacups, are members of themselves. Call the set of all sets that are not members of themselves “R.” If R is a member of itself, then by definition it must not be a member of itself. Similarly, if R is not a member of itself, then by definition it must be a member of itself. Discovered by Bertrand Russell in 1901, the paradox has prompted much work in logic, set theory and the philosophy and foundations of mathematics."