Parmenides believed that he had found the most reliable way of theorizing about ultimate reality. While natural philosophers conceptualized phenomenal differences to explain cosmic change, Parmenides used the least meaningful but most versatile verb in Ancient Greek to engage in a purely intellectual exploration of reality – one that transcended synchronous and asynchronous differences. In this article I explain how the verb εἰμί was useful to Parmenides in his attempt to overcome natural philosophy. First, I argue that the Eleatic philosopher (...) regarded νοεῖν and εἶναι as equivalent because εἰμί-clauses enabled him to express arguably any conceivable content without providing significant additional meaning. I then show that Parmenides’ concept of being implies the present tense and the imperfective aspect but is grounded in the lexical content of the verb εἰμί, which entails no inherent temporal limits. This explains why ἔστι, ἐόν, and εἶναι could be used to indicate unbounded actuality, regardless of whether these forms represented lexical predicates or auxiliaries for predication. Finally, I maintain that the suitability of εἰμί for talking about all kinds of things without introducing temporal limits allowed Parmenides to avoid what he saw as two mistakes made by natural philosophers: identifying ultimate reality with something that cannot cover the full extent of thought and confusing actuality with present occurrence. (shrink)

In this article, both Anaxagoras' theory of multiple worlds and the principles of his theory of matter are examined. It is argued that the five principles, which are set out explicitly in the extant fragments, (No Becoming, Indefinite Types, Universal Mixture, Predominance, and Infinite Divisibility) form a consistent set. Further, it is argued that the principle of Homoeomereity, which Anaxagoras attributes to Anaxagoras, is consistent with Anaxagoras' other principles and is likely to be a genuine principle of Anaxagoras' physics.

In the Timaeus, Plato says that the hypothesis of there being five worlds casts a reasonable doubt. Neither ancient commentators of Plato nor modern scholars have succeeded in unveiling the meaning of this hypothesis. I propose that five is the number of combinations with which the five platonic solids can be arranged in sets of four, each set making up a world. I discuss the question of whether Plato's mathematical skills made him equal to the task of calculating the correct (...) number of combinations, as well as the possible reasons why he rejected the hypothesis of there being five worlds. (shrink)

Does Anaxagoras admit that the world is destructible? Aëtius’ doxographical handbook says as much, and so does a doxographical scholion derived from Alexander of Aphrodisias’ lost commentary on Aristotle’sPhysics(Frag. 539 Rashed) according to the transmitted text. However, because of other difficulties occurring in the same scholion, Rashed was led to correct not only this text, thus making it contradict Aëtius’ testimony, but also the entry dedicated to Plato. My article suggests that while Rashed’s corrections are superfluous, the problems that triggered (...) them are of great interest for the history of the doxographical tradition, for the way in which this tradition was used by Alexander of Aphrodisias and Simplicius in their commentaries on Aristotle’sPhysicsand, last but not least, for the understanding of the difficulties that ancient interpreters had to confront when they had to make sense of the lines now known as Anaxagoras B12 DK – difficulties that modern interpreters have still to confront. (shrink)

Some classical authors ascribe to Anaximander of Miletus a belief in the existence of infinite worlds. Their testimonies have provoked an extensive discussion on the question of whether Anaximander spoke of successive or coexistent worlds, or perhaps only one world that undergoes changes. Of course, this subject is related to important aspects of archaic cosmologies. First, we need to investigate whether one can even speak of a notion of coexistent worlds prior to atomist theories. Second, the issue of infinite worlds (...) is closely linked to the nature of Anaximander's scheme of the universe and Ionian cosmologies in general. Finally, this matter has a bearing on the subject of the duration or perishing of the world. (shrink)

L’article réexamine la signification, dans la pensée de Phérécyde, du témoignage de Damascius sur la génération des dieux des cinq recoins par les trois éléments créés par Chronos. Les modèles par lesquels on explique la génération de cinq familles de dieux ou de cinq régions du monde à partir de ces trois éléments comportent des difficultés internes, ainsi que des anachronismes qui ont conduit à penser que Phérécyde préfigurerait par exemple les théories d’un Empédocle sur le mélange des éléments. Ces (...) difficultés sont issues d’une interprétation erronée du texte : rien n’indique que la génération des cinq recoins comporte cinq familles ni que ces familles ont des caractéristiques différentes. Lever ce faux problème permet de mieux apprécier le sens du témoignage dans l’entreprise de Phérécyde : il ne s’agit pas de rationaliser le mythe au sens d’une préfiguration de la pensée présocratique, mais de produire une généalogie mythique dont la structure rationalise la théogonie d’un Hésiode à l’intérieur de la pensée mythique. Loin de faire de feu, souffle et eau des éléments physiques (des στοιχεῖα), Phérécyde les traite ici comme des éléments naturels conçus de façon abstraite, sans qu’on ait besoin d’admettre un anachronisme. (shrink)

In this article, both Anaxagoras’ theory of multiple worlds and the principles of his theory of matter are examined. It is argued that the five principles, which are set out explicitly in the extant fragments, (No Becoming, Indefinite Types, Universal Mixture, Predominance, and Infinite Divisibility) form a consistent set. Further, it is argued that the principle of Homoeomereity, which Anaxagoras attributes to Anaxagoras, is consistent with Anaxagoras’ other principles and is likely to be a genuine principle of Anaxagoras’ physics.

In the analysis of Anaxagoras’ physics in view of the relation between his teachings on multitude and heterogeneity, two central questions emerge: 1) How can the structure of the universe considered purely mereo-topologically help us explain that at the first cosmic stage no qualitative difference is manifest in spite of the fact that the entire qualitative heterogeneity is supposedly already present there? 2) How can heterogeneity become manifest at the second stage, resulting from the noûs intervention, if according to fragment (...) B 6 such a possibility requires the existence of “the smallest”, while according to the general principle stated in fragment B 3 there is not “the smallest” but always only “a smaller”? This paper showcases the perplexity of these two questions but deals only with the former. The answer follows from Anaxagoras’ being a thoroughgoing infinitist in the way in which no Greek physicist was: the principle of space isotropy operative in geometry is extended to physics as well. So any two parts of the original mixture are similar to each other not only in view of the smaller-larger relation but also because each contains everything that the other one contains. This in effect means that at the stage of maximal possible heterogeneity each part of any part contains infinitely many heterogeneous parts of any kind whatsoever. So, neither can there be homogeneous parts in view of any qualitative property, nor can there be predominance in quantity of parts of any kind that would make some property manifest. (shrink)

Anaxagoras of Clazomenae (a major Greek city of Ionian Asia Minor), a Greek philosopher of the 5th century B.C.E. (born ca. 500–480), was the first of the Presocratic philosophers to live in Athens. He propounded a physical theory of “everything-in-everything,” and claimed that nous (intellect or mind) was the motive cause of the cosmos. He was the first to give a correct explanation of eclipses, and was both famous and notorious for his scientific theories, including the claims that the sun (...) is a mass of red-hot metal, that the moon is earthy, and that the stars are fiery stones. Anaxagoras maintained that the original state of the cosmos was a mixture of all its ingredients (the basic realities of his system). The ingredients are thoroughly mixed, so that no individual ingredient as such is evident, but the mixture is not entirely uniform or homogeneous. (shrink)