In his commentary on Euclid, Proclus says both that the first principle of geometry are self-evident and that they are hypotheses received from the single, highest, unhypothetical science, which is probably dialectic. The implication of this seems to be that a geometer both does and does not know geometrical truths. This dilemma only exists if we assume that Proclus follows Aristotle in his understanding of these terms. This paper shows that this is not the case, and explains what Proclus himself (...) means by definition, hypothesis, axiom, postulate, and the self-evident, and how geometry is a science that receives its principles from dialectic. (shrink)

One of the hardest questions to answer for a (Neo)platonist is to what extent and how the changing and unreliable world of sense perception can itself be an object of scientific knowledge. My dissertation is a study of the answer given to that question by the Neoplatonist Proclus (Athens, 411-485) in his Commentary on Plato’s Timaeus. I present a new explanation of Proclus’ concept of nature and show that philosophy of nature consists of several related subdisciplines matching the ontological stratification (...) of nature. Moreover, I demonstrate that for Proclus philosophy of nature is a science, albeit a hypothetical one, which takes geometry as its methodological paradigm. I also offer an explanation of Proclus’ view of what is later called the mathematization of physics, i.e. the role of the substance of mathematics, as opposed to its method, in explaining the natural world. Finally, I discuss Proclus’ views of the discourse of philosophy of nature and its iconic character. (shrink)

Descartes croyait que le monde étendu ne se terminait pas par une borne, mais pourquoi? Après avoir expliqué la position de Descartes au §1, en suggérant que sa conception de l’étendue indéfinie de l’univers devrait être entendue comme actuelle, mais syncatégorématique, nous nous penchons sur son argument dans le §2 : toute postulation d’une surface extérieure au monde sera autodestructrice, parce que la simple contemplation d’une telle borne nous conduira à reconnaître l’existence d’une étendue allant au-delà. Au §3, nous identifions (...) l’hypothèse fondamentale qui sous-tend cet argument en comparant les conceptions respectives de Descartes et de Malebranche quant au statut ontologique des modes de l’étendue. (shrink)

My thesis reads Ernst Bloch’s materialist ontology with the aim of producing a utopian perspective on language’s materiality. As my Introduction outlines, set against the backdrop of a contemporary renewal in speculative philosophy, the present context is marked by a twofold limitation: (1) the perdurant marginalisation of Bloch’s form of utopian speculation, serving to couch contemporary materialism in thoroughly un-prospective tendencies; and (2), a relative failure of contemporary speculative philosophy to reflect on language, a failure attributable to the long drawn-out (...) dominance of post-structuralism’s linguistic form of relativism. To overcome these limitations I dedicate Chapter I of my thesis to expounding the core categories of Bloch’s materialism, casting a light on what I call its fundamental compositional structure: Incompleteness → Process → (possibility of an) Outfall, i.e. completion or arrival. In light of this, I argue that, placed within the horizon of Bloch’s materialism, incompleteness, process, and futural-directedness ought to be taken as cornerstones of language’s materiality. So as to better position what this means, in Chapter II a reading of the metaphysical Sens of Bloch’s materialism is given. There I consider Bloch’s materialism as a novel form of analogic metaphysics. Insofar as at the core of Bloch’s materialism there lies a metaphysical conception whereby being as such (e.g. Aristotle’s ontōs on) names an ultimate desire and not—pace the classical metaphysical tradition—an already existent beingness—a metaphysical conception Bloch proleptically terms the “ontology of not-yet being“—so then the essential dynamic of this materialism hinges on an incomplete analogy, for all things relate to that which is not-yet in existence; this not-yetness is the sustaining meaning of what is. In the final chapter I concretise my findings by turning to the question of language proper, reading “anacoluthon” as a speculative materialist figure of language which expressive this utopian analogic metaphysics. Anacoluthon denotes an interruption in syntactical flow (Greek: an-akóluthos, “not following“; German: Satzbruch, “sentence fracture/rupture“) and marginally features in Bloch’s corpus. But precisely because of its marginal status the figure possesses a real force in understanding language’s utopian materiality. Indeed, I read anacoluthia as expressive of the Blochian ontological composition. Anacoluthic discontinuities of speech are read as linguistic expressions of ontological incompleteness, ontological novelty, and ontological directedness to what is not yet. They linguistically express both the non-existence of ontological totality, but also, crucially, a real and open intending towards it: a utopian, creative, linguistically-based transgressiveness expressive of the world’s ontology. (shrink)

Discusses the importance of the early history of Greek mathematics to education and civic life through a study of the Parthenon and dialogues of Plato.