对集合论公理化方法悖性的审思

公理化集合论理论的创立．解决了康托尔素朴集合论因其概括原则的前提预设而导致的一系列悖论。在公理化集合论中人们没有发现新的悖论，学界因此而视其为成功的解悖方案。公理化的本质是重构集合论的演绎系统，演绎方法具有保真性，能够导出可靠知识。公理化集合论的两个准等价的系统却是从相互矛盾的前提建构得来的。如果这两个公理系统导出的结论是可靠的，就说明可靠知识可以由不可靠的公理化方法导出的。这就对公理化方法的可靠性构成了质疑。

Speculation on the Methodical Paradox of Axiomatic Set Theory

The axiomatic set theory solves the paradoxes of Cantor generalization principle of presupposition. As no new paradox has been theory is regarded by the academic circle as a successful solutions naive set theory due to its found, within, the axiomatic set However, though the nature of axiomatic is to reconstruct the set theory＇s deductive system which, due to its fidelity, yields to reliable knowledge, the two equivalent systems of axiomatic set theory is derived from contradictory premises. If conclusions of the both system were reliable, it would suggest that reliable knowledge may be deduced from unreliable axiomatic method, which is a questioning to the reliability, of axiomatic method.