关于悖论的统一模式——纪念罗素悖论发现100周年

    On the Unified Schema of Paradoxes

    • 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=aA|aF∉(a),如果在某个理论中MB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AB就可以将所有已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.

       

      Abstract: We give an abstract paradox in mathematical language. Let F be a bijection from set A to set B. Denote M=aA|aF∉(a). If in a theory that MB is legitimate (or reasonable), then the question mM? 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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