一个传统逻辑的难题

A Puzzle in Traditional Logic

在传统逻辑中,有一个熟知的难题,即SAP→SEP'→P'ES→P'AS'→S'IP'→S'OP,在这个推理串中,每一步推理都是符合规则的,但总的结果却是违反规则的:在前提中不周延的词项P在结论中却变成周延的!这一结果是由以下三个因素共同造成的:直言命题的主项存在假定,推理规则N:"在前提中不周延的词项在结论中不得周延",以及关于直言命题中主谓项周延性的四条规定。因此,要解决那个难题,我们至少有三种不同的选择:放弃主项存在假定,修改推理规则N,修改关于周延性的那些规定,而每一种选择都有可接受的后果和不可接受的后果,因而不是一个容易作出的选择。该难题仍然期待一个最终的系统解决方案。

There is a well-known puzzle in traditional logic,that is,SAP→SEP＇→P＇ES→P＇AS＇→S＇IP＇→S＇OP,which is valid in its every step,but is not valid from the beginning to the end,for P is not distributive in the premiss SAP,but is distributive in the conclusion S＇OP,which is against the rule of inference N.This result is made by the following three elements：the assumption of existence about the subject in catogorical propositions,the rule of inference N which says that if a term is not distributive in the premiss（es）,then it must be not distributive in the conclusion,and the four regulations about the distribution of the subject and predecate in categorecal propositions.So,if we want to solve the puzzle,we have at least three choices：refutating the assumption of existence,revising the rule of inference N,and revising the regulations about distribution.Every choice has its own acceptable results and also unacceptable results,so it is not an easy choice.Therefore,the puzzle still awaits a final systematic solution.