It is often assumed that Aristotle, Boethius, Chrysippus, and other ancient logicians advocated a connexive conception of implication according to which no proposition entails, or is entailed by, its own negation. Thus Aristotle claimed that the proposition ‘if B is not great, B itself is great […] is impossible’. Similarly, Boethius maintained that two implications of the type ‘If p then r’ and ‘If p then not-r’ are incompatible. Furthermore, Chrysippus proclaimed a conditional to be ‘sound when the contradictory of its consequent is incompatible with its antecedent’, a view which, in the opinion of S. McCall, entails the aforementioned theses of Aristotle and Boethius. Now a critical examination of the historical sources shows that the ancient logicians most likely meant their theses as applicable only to ‘normal’ conditionals with antecedents which are not self-contradictory. The corresponding restrictions of Aristotle’s and Boethius’ theses to such self-consistent antecedents, however, turn out to be theorems of ordinary modal logic and thus don’t give rise to any non-classical system of genuinely connexive logic.

中文翻译：

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联结逻辑历史渊源的批判性考察

人们常常假设亚里士多德、波伊修斯、克利西普斯和其他古代逻辑学家提倡一种蕴涵的连接概念，根据该概念，没有任何命题包含或被其自身的否定所包含。因此，亚里士多德声称命题“如果 B 不是伟大的，那么 B 本身就是伟大的 [……] 是不可能的”。类似地，Boethius 认为“If p then r”和“If p then not-r”类型的两个含义是不相容的。此外，Chrysippus 宣称一个条件是“当其结果的矛盾与其前件不相容时是合理的”，在 S. McCall 看来，这种观点包含上述亚里士多德和波埃修斯的论点。现在，对历史资料的批判性检查表明，古代逻辑学家很可能意味着他们的论点仅适用于“正常”条件，其前提不是自相矛盾的。然而，亚里士多德和波伊修斯的论题对这种自洽前因的相应限制，结果是普通模态逻辑的定理，因此不会产生任何真正连通逻辑的非经典系统。