Mathilde Bremond

This chapter shows that Aristotelian reception often attributes to the Eleatics, as a group or individuals, arguments that the author of the chapter calls ‘antilogies’ (i.e. a reductio ad absurdum based on a dichotomy). The chapter traces back this structure of reasoning to Gorgias, who in his treatise On Not-Being was the first to reformulate the Eleatic arguments as antilogies. Not only did some authors, like Aristotle, borrow arguments from Gorgias to attribute them to the Eleatics, but it also led to a widespread tendency to reformulate the Eleatic arguments as antilogies, even independently of Gorgias’ treatise. This reveals a deep and so far unnoticed influence of Gorgias on the way the Eleatics were interpreted.

Melissus’ fragment B9, where he claims that being has no body and no thickness, raises the question of how being can be extended and full and at the same time incorporeal. Most recent interpretations tried to avoid lending to “body” the meaning of “physical body”. My aim in this paper is to reconstruct Melissus’ notion of body, by examining its connection to “thickness”. I show that Melissus meant by “thick” something that has distinct parts and therefore supports in B9 the indivisibility of being. I then indicate that he relied on the contrast between soul and body for his conception of corporeality, by highlighting that by Presocratic thinkers, the soul was considered as “thin” and regarded as something that could be exempt of the division into parts. I conclude that even though Melissus’ notion of incorporeality is very different from the one Plato will develop, he made a huge step toward its conceptualization.

This paper examines two doxographies present in Ḥunayn’s summaries to Galen’s treatise On the Elements. We track the origin of these doxographies back, from Greek scolia to Galen’s treatise to Simplicius’ Commentary on Aristotle’s Physics, which we show to be the ultimate source. We also point out that Simplicius’ Commentary inspired an interpretation of Parmenides and Melissus that we find in Ḥunayn’s texts. This allows us to see remnants of Simplicius’ Commentary in the Arabic world and to shed some light on the production of these summaries to Galen’s work called Summaria Alexandrinorum.

There is discussion among critics about the authenticity of Pseudo-Aristotle’s account on Melissus in the De Melisso, Xenophane, Gorgia, and especially about the refutation of mixture that he attributes to the latter. For there is no clue in the other testimonies and in the fragments that the Eleatic made such a refutation. In this article, I aim to show that the argument as it is presented is not genuinely Melissean, but inspired by some of Aristotle’s considerations on colour-mixture in the De sensu. I then claim that taking this source into account solves many of the difficulties inherent to this demonstration against mixture, and reveals something on Pseudo-Aristotle’s doxographical approach.

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.

This paper challenges the possible connection in Early Greek thinking between cosmic areas and elements. I criticize the idea that the universe was originally divided into four great areas and that Empedocles’ only innovation was to match this preexisting division with his elementary theory. I will demonstrate that although Empedocles was indeed the first to match the cosmic and elementary levels, his work is the first to mention a division of the universe into distinct and equal areas. To identify the novelty in Empedocles’ theory, I will emphasize the various ways in which thinkers structured the universe since Homer and illustrate the kind of relationship they established between cosmic areas and elements.

Cet article examine l’influence sur la première hypothèse du Parménide de deux penseurs dont l’importance a été négligée par les critiques : Mélissos et Gorgias. Après avoir observé que les prédicats attribués à l’un ainsi que la forme démonstrative sont plus représentatifs de l’éléatisme de Mélissos que de celui de Parménide, nous expliquons ce constat par le fait que Platon reprenne une partie du Traité du Non-être de Gorgias qui vise elle-même essentiellement Mélissos. Nous démontrons alors que la première hypothèse, et même l’ensemble de la seconde partie du Parménide, est un pastiche du Traité du Non-être, et nous en tirons des conclusions sur le statut de l’exercice dialectique mis en œuvre dans le Parménide.

In this paper, I investigate how Xenophanes was ‘eleaticised’, i.e. attributed theses and arguments that belong to Parmenides and Melissus. I examine texts of Plato, Aristotle and Theophrastus in order to determine if they considered Xenophanes as a philosopher and a monist. I show that neither Plato nor Aristotle regarded him as a philosopher, but rather as a pantheist poet who claimed, in a vague way, that everything is one. But Theophrastus interpreted too literally Aristotle’s claims and was the first to make Xenophanes a proper monist philosopher.