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This paper explores the prosaic deductive style developed by Melissus and Zeno. It first emphasizes the authors’ use of a systematic and reduced vocabulary solely dedicated to a priori deduction. In a second time, the paper delves into the systematic role of reductio ad absurdum in their reasoning and distinguishes several kinds of reductio employed by the authors. Through this analysis, the study shows how Melissus and Zeno not only developed and systematized certain aspects of Parmenides’ style but also introduced original features that significantly influenced the philosophical writing style.

According to the Eleatic Principle, only items which have the capacity to affect or be affected are. Recently, there has been a question about what, if anything, is Eleatic about the Eleatic Principle (EP). I examine the purported origins of the EP in Plato’s Sophist and argue that the text presents three ways in which something can affect or be affected: (1) as tangible contact, (2) as Cambridge change, and (3) by being responsible for the way something else is. Next, I look to the historical Eleatics in search of precursors to the EP. Against recent work in this area, I argue that elements of the EP are present in Parmenides, Zeno, and Melissus. The poem of Parmenides is compatible with (1) and (2) through the interaction of Light and Night, and the characterization of what-is as knowable. Zeno’s moving arrow paradox employs elements of (2), while his argument from complete divisibility adds preconditions to (3). Finally, against the traditional view that Melissus denies the existence of the sensible world, I show that for Melissus, the sensible world exists alongside what-is. The causal link between what-is and the sensible world, along with Melissus’ commitment to what-is as the object of knowledge renders Melissus the Eleatic whose Eleaticism is most represented in the Eleatic Principle. Alternatives for the application of the EP in contemporary metaphysics and reasons for the inclusion of an Eleatic visitor as the main interlocutor of a dialogue that is often taken as a criticism of Eleaticism emerge.

The present paper makes the following points. (1) The summary given in Sextus Emp. Math. VII is of much greater value than usually acknowledged, since it preserves several key elements of Gorgias’ communicational strategy. (2) A sketchy trilemma is available in the opening sentence of Philolaos (DK 44B2) as well as in a passage of Plato’s Parmenides. This is evidence in favor of the hypothesis that the very first known trilemma was devised by Gorgias and not by Sextus himself or Aenesidemus. (3) Not unlike Zeno, Gorgias enjoyed to be neither serious nor joking, but remained somewhat halfway. This point is seldom acknowledged, though it is crucial in order to understand that he pretends to claim (e.g. that p), but his claims do not amount to any points of doctrine. (4) That he remains halfway should not prevent us from appreciating some of his ideas, but, at the same time, we should not expect full intellectual adhesion to what he tells us. Besides, something similar occurs in most of Plato’s dialogues. (5). Gorgias owes a lot to Melissus.