This article examines the use of mathematical concepts in philosophy, focusing on topology, which may be viewed as a modern supplement to geometry. We show that Plato and Parmenides were already employing geometric ideas in their research, and discuss three examples of the application of topology to philosophical problems: the first concerns the analysis of the Cartesian distinction between res extensa and res cogitans, the second the ontology of possible worlds of Wittgenstein's Tractatus, and the third Leibniz's monadology. We also (...) consider the role of topology in mathematical explanations of the sort found in science, arguing that it can perform a role in philosophy that is of comparable importance. (shrink)

This essay explores a curious point of intersection in the historical pairing of becoming and negation, between two thinkers and two traditions: the Sophist Protagoras of fifth-century BCE Greece and the second-century CE South Asian Buddhist thinker Nāgārjuna. I offer a speculative account of how becoming and negation are linked in Protagoras—speculative because only so much can be deduced from the extant fragments and testimony. I compare that account to the more coherent picture offered by Nāgārjuna—more coherent because a complete (...) account of the logic that links becoming and negation is carefully preserved in the works attributed to Nāgārjuna. While no specific conclusions regarding the bridge that linked India and Greece may be reached, the similarities between these thinkers and the greater coherence of the Buddhist tradition nevertheless offer hypothetical possibilities for reconstructing the larger architecture of the world of sophistic thought that is now lost to us. (shrink)

Zeno’s paradoxes of motion, allegedly denying motion, have been conceived to reinforce the Parmenidean vision of an immutable world. The aim of this article is to demonstrate that these famous logical paradoxes should be seen instead as paradoxes of immobility. From this new point of view, motion is therefore no longer logically problematic, while immobility is. This is convenient since it is easy to conceive that immobility can actually conceal motion, and thus the proposition “immobility is mere illusion of the (...) senses” is much more credible than the reverse thesis supported by Parmenides. Moreover, this proposition is also supported by modern depiction of material bodies: the existence of a ceaseless random motion of atoms—the ‘thermal agitation’—in the scope of contemporary atomic theory, can offer a rational explanation of this ‘illusion of immobility’. Our new approach to Zeno’s paradoxes therefore leads to presenting the novel concept of ‘impermobility’, which we think is a more adequate description of physical reality. (shrink)