罗素类型论研究(二)

类型论是罗素为解决逻辑悖论而构造的一个重要理论,它以恶性循环原则为前提,其核心思想是不把类当实体看,其总体思想是任一函项必定属于一定的类型和阶。类型论提供了一种对悖论的统一的解决办法,其排除悖论的实质是把引起悖论的表达式归于“无意义”。类型论本身并不完善,引来了争论,争论的焦点首先是可化归性公理,其次是恶性循环原则,引起争论的实质是在类的实在性问题上实在论和唯名论的对立。类型论尽管在总体上不那么令人满意,但它给逻辑和哲学都带来了重大的影响,这种影响是积极的。

Study on Russell's Theory of Types

The theory of types Russell put forward to solve logical paradoxes is very important.From the premise of the vicious-circle principle, the theory argued that classes should not be seen as substance and pointed out that every function belongs to one type and one order with no exception. Such were its central thoughts. The theory of types has successfully presented a general method to solve paradoxes by virtually ascribing the expressions, which would produce paradox, to"nonsense". Nevertheless, it is imperfect and causes many controversies.This thesis has pointed out that what cause controversies mainly lies in two points: the axiom of reducibility and the vicious-circle principle. The deep reason causing controversies is the opposition between Realists and Nominalists as to the reality of classes. Though the theory of types is not so satisfactory a theory in general, it has brought great and positive influences on logic and philosophy.