Ancient research on conditionals are collected and revised. It is claimed, that the problem arises in analyzing of some methods of deduction. Five main ancient concepts of conditionals are analyzed, those of Aristotle, Diodorus Cronus, Philo of Megara, Chrysippus and an anonymous text concerned with a concept of 'dynamei'. It is argued, that this text should be identified with the one by Aristotle. Philo's concept is the classical, truth-functional one. It is suggested, that Aristotle's concept is close to the modern concept of entailment, but not identical. Chrysippus's concept is especially discussed. It is claimed, that, contrary to common opinion, it is not close to C. I. Lewis's modern concept of strict implication. Chrysippus' concept of implication seems to be a nomic or causal one, like Diodorus's concept of temporal implication, while Lewis's concept of strict implication is based on the concept of logical modality.
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