摘要
类型论是为解决悖论问题提出的。通过对命题函项的分层以及对类型的限制,许多悖论就可以避免,类型论的限制很强,罗素又引入还原公理使数学成为可能。类型论可以解决日常语言与传统哲学中的许多问题,还原公理则使日常语言成为可能。但是,类型论面临现实中的复杂情况所带来的困难,还原公理则面临自身存在的合法性的困难,而罗素没有完全解决这些困难。
Theory of types was put forward to solve logic paradox. Through the hierarchy of proposi- tional function and the constraint on types, many paradoxes could be avoided. The constraint of theory of types is very strong. Russell introduced the axiom of reducibility to make mathematics possible. Theory of types could solve many problems of everyday language and traditional philosophy, and the axiom of reducibility makes everyday language possible. But theory of types faces the difficulty of complex circumstances of real life, and the axiom of reducibility faces the difficulty of its own legiti- macy, but Russell did not completely solve these difficulties.
出处
《重庆理工大学学报（社会科学）》
CAS
2013年第9期53-59,共7页
Journal of Chongqing University of Technology（Social Science）
关键词
悖论
类型论
还原公理
paradox
theory of types
the axiom of reducibility
