Hypothetical syllogism and modus tollens in Proclus' epicheiremes on the nature of names

In this paper, we carried out the reconstruction of the logical reasoning of ancient authors in the so-called «Democritus' epicheiremes» and counter arguments (refutations), presented in the alleged Proclus' «Commentary» on the «Cratylus». The term «epicheireme», used by Proclus in relation to Democritus' arguments, has a very broad meaning. It is a well-known interpretation of epicheireme, based on the categorical syllogism, consisting of two enthymemes. However, epicheireme could also be treated as the advanced version of modus ponens, modus tollens (hypothetical syllogisms), or polysyllogism (multi-premise), sorites, lemmatic inference or even inductive hypothesis. The difficulty lies in the fact that over time, especially after Aristotle's rhetoric, the concept of enthymeme and epicheireme have gone beyond the logic to the poorly defined rhetorical discourse, dealing with certain ways of «dialectical» reasoning, probabilistic statements or rhetorical figures, losing a direct connection with demonstrative syllogisms. In our view, the arguments of Democritus and the Proclus' subsequent refutation can be considered from a logical point of view; understanding epicheireme more logically than rhetorically. In this paper, we develop arguments for such a reconstruction. If we take into account that ancient authors often did not distinguish enthymeme and epicheireme, then at least we have a certain stratum of deductive arguments and refutations, which may be explicated by identifying the necessary structural units implicitly involved in the argumentation. The paper reveals the structure of four epicheiremes, arranged in modus tollens of Theophrastus' hypothetical syllogism, as well as Proclus' criticism, asserting the categorical premises of hypothetical reasoning expressed by negative statements. The conceptual features of ancient linguistic naturalism and relativism in regard to the semantics of names are analyzed. The article focuses on the awakening of research interest to the ancient heritage of logic and philosophy of language.

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