| 关于悖论的统一模式——纪念罗素悖论发现100周年 |
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| 引用本文： | 蒋星耀.关于悖论的统一模式——纪念罗素悖论发现100周年[J].北京工业大学学报,2002,28(1):87-90. |
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| 作者姓名： | 蒋星耀 |
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| 作者单位： | 上海大学,计算机系,上海,200072 |
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| 摘 要： | 用数学的语言给出了一个抽象的悖论. 令F是从集合A到集合B的双射,记M＝{a∈A|aF(a)},如果在某个理论中M∈B是合法的(或看起来是合理的),则问题m∈M-将是该理论中的一个悖论. 该抽象悖论也可看成悖论的统一模式,只要适当选择双射F和集合A、B就可以将所有己知悖论包含在该模式中. 由于找到所有悖论的统一模式,也找到了产生悖论的唯一的本质的原因,为圆满解决悖论问题创造条件.
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| 关 键 词： | 悖论 罗素 反对角线集合 统一模式定理 准反对角线集合 加强的统一模式定理 抽象悖论 |
| 文章编号： | 0254-0037(2002)01-0087-04 |
| 修稿时间： | 2001年11月1日 |
On the Unified Schema of Paradoxes |
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| JIANG Xing-yao.On the Unified Schema of Paradoxes[J].Journal of Beijing Polytechnic University,2002,28(1):87-90. |
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| Authors: | JIANG Xing-yao |
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| Abstract: | We give an abstract paradox in mathematical language. Let F be a bijection from set A to set B. Denote M= {a Aa F(a)}. If in a theory that ME B is legitimate (or reasonable), then the question m E M? becomes a paradox in that theory. This abstract paradox also can be regarded as unified schema for all paradoxes we have hnown. To get various concrete paradoxes we only need to give sets A, B and map F proper explanation. From the unified schema we find the common essential cause of all paradoxes, which creates a premise to solve the paradox problem satisfactorily. |
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| Keywords: | paradox Russell anti-diagonal set unified schema theorem quasi-anti-diagonal set strengthened unified schema theorem abstract paradox |
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