Plato’s instructions entail that the line of Republic VI is divided so that the middle two segments are of equal length. Yet I argue that Plato’s elaboration of the significance of this analogy shows he believes that these segments are of unequal length because the domains they represent are not of equally clear mental states, nor perhaps of objects of equal reality. I label this inconsistency between Plato’s instructions and his explanation the “overdetermination problem.” The overdetermination problem has been a perennial concern, and a substantial amount of work has been produced which attempts to deal with it. I offer a classification of approaches to the overdetermination problem as a way of documenting the problem’s significance, and show why these approaches are all inadequate as solutions. My novel resolution of the overdetermination problem rests upon a demonstration that the contradiction is intentional. The later recapitulation of the ratio at 534a reveals that Plato was himself aware that the middle two segments are equal. I argue that this contradiction is a sophisticated device designed to lead the reader of the Republic through the four epistemic stages represented by the line itself. Most significantly, recognition of this mathematical contradiction acts as a goad, spurring independent philosophical reflection just in the way that Plato advocates in the Republic more generally.
What Aristotle’s main concern is in Metaphysics H 6 has long puzzled commentators. In this paper I argued for a novel, deflationary interpretation of that chapter: Aristotle's main concern is to argue for the causeless unity of the definitions of form and of composite substance. The problem he is grappling with arises from a combination of (a) speaking about the parts of form and the parts of composite substances, and (b) the principle that parts of a whole need a unifying cause in order to be one and not many. If both form and composite particulars need a unifying cause, form cannot be primary substance, and composite substances, as composites of form and matter, cannot be true unities, but must be mere heaps of material parts which need a third unifying cause. Aristotle argues that although (a) and (b) seemingly threaten his theory of substance with incoherence, the problem can be easily solved if the unity of definitions of form and of composite substance are properly seen as causeless. In the course of clarifying and defending this reading of H6, a number of alternative interpretations are exposed and criticized.
It is shown that Aristotle’s references to automata in his biological treatises are meant to invoke the principle behind the ancient conception of the lever, i.e. that points on the rotating radius of a circle all move at different speeds proportional to their distances from the center. This principle is mathematical and explains a phenomenon taken as whole. Automata do not signify for him primarily a succession of material movers in contact, the modern model for mechanism. For animal locomotion and embryological development, Aristotle models his dunamis concept on the idea of mechanical potential that the lever principle displays.
Descartes maintained substance dualism, the thesis that no substance has both mental and material properties. His main argument for this thesis, the so-called separability argument from the Sixth Meditation (AT VII: 78) has long puzzled readers. In this paper I argue that Descartes’ independence conception of substance (which Descartes presents in article 51 of the Principles) is crucial for the success of the separability argument and that Descartes used this conception of substance to defend his argument for substance dualism from an important objection.
The Cartesians have often been read as if they denied spatial presence to incorporeal substances, reserving it for extended things alone. This article explores whether this common interpretation is accurate, examining the cases of both created minds and the divine substance of God Himself. Through scrutiny of the relevant texts of both Descartes himself and his followers, it demonstrates that, in the divine case, this common interpretation is incorrect, and that the Cartesians did believe that God’s own substance really was omnipresent in a literal sense. In the case of created minds, by contrast, the article suggests that the standard reading is probably correct after all, and that these substances were indeed excluded from the spatial world: but it also suggests that, in the hands of at least some of the Cartesians, this position caused certain philosophical tensions and potential inconsistencies within their systems.
La contribution de Berkeley à l'histoire de la métaphysique n'a que rarement été étudiée par ses commentateurs français ou anglo-saxons. La présente étude se propose de revenir sur la définition berkeleyenne de la métaphysique, sur la place qu'elle occupe dans l'économie de sa pensée, et tente ainsi d'éclairer la contribution de Berkeley à l'histoire de la notion de métaphysique à l'époque moderne. Nous montrons que la critique berkeleyenne de la métaphysique n'empêche pas Berkeley de maintenir sa pertinence théorique, si l'on rapporte sa conception de la métaphysique à la transformation qui affecte celle-ci après Descartes, et qui en fait la science des principes de la connaissance humaine. Cette étude entend donc réévaluer la place de la métaphysique dans l'oeuvre de Berkeley, et, simultanément, de mesurer l'apport de Berkeley à l'histoire de la métaphysique.
This paper reconstructs the evolution of Novalis’ thought concerning being, nature, and knowledge. In his earlier writings (above all the Fichte-Studies) he argues that unitary being underlies finite phenomena and that we can never know, but only strive towards knowledge of, being. In contrast, his later writings, principally the Allgemeine Brouillon, maintain that the unitary reality underlying finite things can be known, because it is an organic whole which develops and organises itself according to an intelligible pattern. Novalis equates this whole with nature. However, because this organic whole exercises spontaneity in assuming particular forms of organisation, we can never know why it assumes just these particular forms; nature therefore remains partly unintelligible to us. I argue that Novalis’ intellectual shift towards the idea that the whole can be known is motivated by his concern to explain how the modern, “disenchanted,” view of nature could be overcome. I also argue that by recognising this shift, we can resolve the dispute between Frank and Beiser as to whether Novalis thinks that the absolute can be known.