On Malcolm Schofield’s highly influential reading of the Similarity Regress in Part I of the Parmenides, the problem that the Regress poses is explanatory. Socrates posited the Similarity Form in order to explain why similar things are similar: similar things are similar because they participate in the Form Similarity as copies of the same original. Yet, the Similarity Regress generates an infinite series of Similarity Forms such that explanation is deferred ad infinitum. Schofield provides a philosophical incentive for adopting his (...) reading. He argues that the treatment of similarity in Part II of the dialogue yields a complete explanation of similarity. If we adopt this account, we can avoid the Similarity Regress altogether since a Form of Similarity is not needed in order to explain why similar things are similar. Thus, his interpretation has a hugely important philosophical pay-off. However, there is a different way to read the argument. Socrates claims that each Form is only one. Yet, the Similarity Regress is an argument that generates an infinite series of Similarity Forms. This results in a violation of the principle of non-contradiction: there is both only one Similarity Form and infinitely many Similarity Forms. Yet, anything that is incompatible with the principle of non-contradiction is surely absurd. Nobody, as far as I am aware, has explored whether this reading also has philosophical pay-off if we look at it together with similarity in Part II. However, should this interpretation pay off, it would be a viable alternative to Schofield’s. In this paper, I explore both views in the context of the treatment of similarity in Part II of the Parmenides. I argue for an account of similarity that differs from Schofield’s. Although my account is not wholly dismissive of Schofield’s, it renders the pay-off of Schofield’s account less appealing than he suggests. Furthermore, I show that the account of similarity in Part II also yields important lessons for the proponent of the alternative reading of the Similarity Regress: similarity as treated in Part II simply leads to further infinite regresses, thereby pushing us to consider rejecting the account of similarity in Part II too and to look for some other account intead. (shrink)

La figure complexe et même contradictoire du démiurge dans le Timée de Platon a suscité plusieurs interprétations de l’Antiquité jusqu’à nos jours, même si habituellement le démiurge est considéré comme un intellect : intellect de l’âme du monde, activité productrice des Formes, Premier Moteur, divinité réalisant un plan déterminée comme le dieu de la Genèse, instrument du Bien. Le débat se poursuit, mais il est important d’insister sur l’originalité du Timée : c’est la première cosmologie dans l’Antiquité, qui fait intervenir (...) un dieu qui travaille, et qui utilise les mathématiques comme instrument par excellent de la mise en ordre du sensible. (shrink)

What does Plato mean in saying that, for all forms, “F-ness is F”? In such claims, I argue, ‘F’ is being used metonymically to refer to the property of being productive of F-ness rather than to the property of being F, in a way consistent with univocity and the rejection of a genuine Self-Predication Assumption. I explain and defend this productive metonymy reading and show how it can resolve the troubling argument at Phaedo 74b7-c6.

In this paper, I argue that Plato conceives self-motion as non-spatial in Laws X. I demonstrate this by focusing on the textual evidence and by refuting interpretations according to which self-motion either is a specific type of spatial motion or is said to require space as a necessary condition for its occurrence. Moreover, I show that this non-spatial understanding differs from the identification of the soul’s motion with locomotion in the Timaeus. Consequently, I provide an explanation for this difference between (...) the Timaeus and Laws X by considering developmentalist and contextualist viewpoints. (shrink)

À partir d’un ouvrage récent de W. Kühn sur la fin du Phèdre de Platon (2000) et des critiques de Th. Szlezák, l’auteur met en parallèle, dans la première partie de cette étude, la lecture anti-ésotériste de Kühn et la lecture ésotériste de Szlezák du finale du Phèdre (274b-279c), pour en dégager trois antinomies herméneutiques. Dans la deuxième partie, il tente de résoudre ce conflit d’interprétations en empruntant la voie herméneutique et en faisant des observations critiques sur chacune de ces (...) antinomies. Dans la troisième partie de cette étude, l’auteur s’attaque au fondement historique des paradigmes d’interprétation adoptés par chacun des auteurs. Le paradigme anti-ésotériste repose sur le principe herméneutique de l’autarcie des dialogues dont le fondement historique est le Corpus Platonicum, tandis que le paradigme ésotériste repose sur le principe herméneutique de l’enseignement oral de Platon dont le fondement historique est constitué par les Testimonia Platonica. L’auteur montre, après un survol des Testimonia Platonica de Gaiser (1963), de Krämer (1982) et d’Isnardi Parente (1997 et 1998), que ceux-ci ne permettent pas encore d’établir des certitudes historiques sur le contenu de l’enseignement oral de Platon. (shrink)

Books M and N of Aristotle's Metaphysics receive relatively little careful attention. Even scholars who give detailed analyses of the arguments in M-N dismiss many of them as hopelessly flawed and biased, and find Aristotle's critique to be riddled with mistakes and question-begging. This assessment of the quality of Aristotle's critique of his predecessors (and of the Platonists in particular), is widespread. The series of arguments in M 2 (1077a14-b11) that targets separate mathematical objects is the subject of particularly strong (...) criticism by Annas and Ross. Two related arguments in this series (1077a14-20 and 1077a24-31) will serve as cases in point. The principal charges made against these arguments (that Aristotle misunderstands or misrepresents his opponents' views, and that he engages in question-begging because he presupposes his own metaphysical views) are frequently made against Aristotle's critique of Platonist positions more generally. If, as I argue, these charges are false for our two test case arguments, then there is good reason to think that they might also be false when they are leveled against the other arguments in this M 2 series. And, although presenting an argument for this is beyond the scope of this paper, this suggests that these two charges are more often than not false when applied to Aristotle's critique of Platonist mathematical views in M-N and beyond. (shrink)

Anaximenes is usually considered to be a material monist recognizing transparent atmospheric air as a principle (ἀρχή). In the cosmogonic explanation of the origin of the earth and the heavenly bodies, the Greek term ἀήρ turns out to mean rather ‘opaque damp mist’. However, Not only does it accord with archaic usage, but also with how it was used in his mentor, Anaximander. Yet, in cosmology ἀήρ means ‘air’ serving as stuff on which the earth and the heavenly bodies float. (...) Hence, in keeping with contemporary usage, Anaximenes recognised two kinds of ἀήρ, distinguishing them functionally. Whereas mist is conceived of as a generating substance, air functions only as carrying stuff. (shrink)

In Philolaus’ cosmology, the earth revolves around a central fire along with the other heavenly bodies, including a planet called the counter-earth which orbits below the earth. His theory can account for most astronomical phenomena. A common criticism of his theory since ancient times is that his counter-earth does no work in the system. Yet ancient sources say the planet was supposed to account for some lunar eclipses. A reconstruction of Philolaus’ cosmology shows how lunar eclipses occurring at certain times (...) of day cannot be explained by earth blocking the sun’s light. The counter-earth could explain these eclipses. (shrink)

L’article met en lumière la continuité intellectuelle de l’Académie à propos d’une question précise, les rapports entre philosophie et géométrie. On soutient d’abord que, dans les livres VI-VII de la République, Platon ne cherche pas à réformer les pratiques des géomètres mais identifie les contraintes incontournables de leurs raisonnements (constructions, hypothèses), qui constituent et limitent leur objectivité. On montre ensuite que cette analyse constitue le cadre des réflexions académiciennes ultérieures sur la géométrie. Speusippe reprend et développe l’analyse platonicienne des constructions (...) géométriques, qui est appliquée (de Speusippe à Crantor) à la cosmologie et même à la doctrine des principes, afin d’expliquer comment elles saisissent leurs objets éternels depuis le devenir, de manière indirecte. Si la Nouvelle Académie d’Arcésilas et de Carnéade critique les mathématiques, on fait l’hypothèse qu’il s’agissait pour elle – dans le contexte des débats philosophiques hellénistiques sur les usages des mathématiques –, de rappeler les limites de leur objectivité contre toute idéalisation dogmatique de la méthode géométrique. (shrink)

As a crucial source for Presocratic theories of sense perception, Theophrastus’ De sensibus deserves a closer scrutiny than the placement among A-fragments, as often suggested or instigated. This paper proposes to refine our terminology for labelling the varying quality of reporting within the A-fragments has. It supplements the existing criticism of Diels’ division by analysing neglected features. A reassessment of the assumptions underlying the terms ‘fragment’ and ‘paraphrase’ can contribute to dissolving the sharp distinction between A- and B-fragments in DK. (...) It advocates, not equality for A-fragments, but a more inclusive and accurate evaluation of the passages. (shrink)