In this paper I show that one of the most fruitful ways of employing paradoxes has been as a philosophical method that forces us to reconsider basic assumptions. After a brief discussion of recent understandings of the notion of paradoxes, I show that Zeno of Elea was the inventor of paradoxes in this sense, against the background of Heraclitus’ and Parmenides’ way of argumentation: in contrast to Heraclitus, Zeno’s paradoxes do not ask us to embrace a paradoxical reality; and in (...) contrast to Parmenides, Zeno shows common assumptions to be internally problematic, not just in light of Eleatic positions. (shrink)

In Physics VI.9 Aristotle addresses Zeno's four paradoxes of motion and amongst them the arrow paradox. In his brief remarks on the paradox, Aristotle suggests what he takes to be a solution to the paradox.In two famous papers, both called 'A note on Zeno's arrow', Gregory Vlastos and Jonathan Lear each suggest an interpretation of Aristotle's proposed solution to the arrow paradox. In this paper, I argue that these two interpretations are unsatisfactory, and suggest an alternative interpretation. In particular, I (...) claim that what seems on the face of it to be Aristotle's solution to the paradox raises two puzzles to which my interpretation, as opposed to Lear's and Vlastos's, provides an adequate response. (shrink)

Perhaps the real paradox of Zeno's Arrow is that, although entirely stationary, it has, against all odds, successfully traversed over two millennia of human thought to trouble successive generations of philosophers. The prospects were not good: few original Zenonian fragments survive, and our access to the paradoxes has been for the most part through unsympathetic commentaries. Moreover, like its sister paradoxes of motion, the Arrow has repeatedly been dismissed as specious and easily dissolved. Even those commentators who have taken it (...) seriously have propounded solutions with which they profess themselves to be perfectly satisfied. So my question is: will Zeno's Arrow survive into the millennium just begun? (shrink)

The aim of my paper is to investigate Gorgias’ argument against motion, which is found in his Peri tou meontos and preserved only in MXG 980a18. I tried to shed new light both on this specific reflection and on the reliability of Pseudo-Aristotle’s version. By exploring the so called “change argument” and the “argument from divisibility”, I focused on the particular strategy used by the Sophist in his synthetike apodeixis, which should be investigated in relation to the dispute between monistic (...) and pluralistic ontology. In this regard, the puzzle from “divisibility everywhere” and its connection with the void as not-being can provide new elements to grasp the philosophical background in which the Sophist moves. On the one hand, Gorgias’ argument against motion is part of a broader dispute on the divisibility/indivisibility of being; on the other, his original elaboration of this puzzle seems to be perfectly understandable within the controversy between Eleatics and Atomists, and coherent with the argumentative style of the Sophist. (shrink)

Introduction“What reason is there to suppose that those who did know Parmenides’ poem necessarily thought that he had raised a real problem which they must try to deal with? Empedocles, perhaps also Anaxagoras, knew the poem, but they pursue a very different kind of philosophy from Zeno and Melissus: why, then, must we suppose that they are seeking an alternative answer to the problem posed by Parmenides, and that their ultimate material elements are to be seen as modifications of the (...) Eleatic ἓν έόν?“These rhetorical questions, taken from M. L. West's recent book,Early Greek Philosophy and the Orient,make a useful starting point for this inquiry. They are, of course, what the grammar books call “repudiating questions“: the answer hoped for is “no reason“. The argument with which Mr. West goes on to support his negative implication is not likely to convince many students of the Presocratics. He determinedly makes light of Parmenides’ chains of argument, apparently on the ground that “these were not the actual stages of Parmenides’ thinking” — as if Parmenides ought to have been writing his intellectual autobiography instead of a philosophical argument. (shrink)

Zeno’s arguments are generally regarded as ingenious but downright unsound paradoxes, worth of attention mainly to disclose why they go wrong or, alternatively, to recognise them as clever, even if crude, anticipations of modern views on the space, the infinite or the quantum view of matter. In either case, the arguments lose any connection with the scientific and philosophical problems of Zeno’s own time and environment. In the present paper, I argue that it is possible to make sense of Zeno’s (...) arguments if we recognise that Zeno was indeed a close follower of Parmenides, who wanted to show that, if the plurality of beings existed, then various absurd consequences would follow. He intended to highlight the compact and inarticulate nature of the being, and the human character of the system of world partitions producing the entities and the objects on which our knowledge is based. (shrink)

The interpretation of Parmenides’ Περί Φύσεως is a fascinating topic to which philosophers, historians of philosophy and scientists have dedicated many studies along the history of Western thought. The aim of this paper is to present the reading of Parmenides’s work offered by Federigo Enriques. It is based on several original theses: (1) Parmenides was the discoverer of abstract geometry; (2) his critics was addressed against the Pythagoreans rather than against Heraclitus; (3) Parmenides discovered and applied the contradiction and the (...) third excluded principles in the context of his research on foundation of geometry; (4) Parmenides’s metaphysical and physical conceptions have their bases in his speculation on geometry; (5) Parmenides used the principle of sufficient reason. Enriques’s reading is worth being expounded and discussed within the historical, philosophical and scientific context in which it is inserted. Since Enriques’s ideas are not widely known and discussed, my research has the purpose to fill this gap. The article also aims to provide elements to illustrate the discussion on Parmenides in the first half of the last century. (shrink)

Is it logically possible to perform a "superfeat"? That is, is it logically possible to complete, in a finite time, an infinite sequence of distinct acts? In opposition to the received view, I argue that all physical superfeats have kinematic features that make them logically impossible.

There are two no-change objections that can be raised against the B-theory of time. One stems from the observation that in a B-theoretic scenario changes of determinations can only be represented by propositions which have eternal truth values. The other derives from the principle that nothing can vary over a period of time if it doesn’t instantiate a state of change at all the instants of time which compose it. Here I argue that both objections apply to all comparative conceptions (...) of change, regardless of whether they take tense seriously or not. It follows that, contrary to what is widely believed, A-theoretic accounts of time are not immune to no-change objections, just in virtue of being realist about tense. A-theorists must either accept the conclusion that time, according to their account, does not flow, or put forward an account of flow that is not comparative. A number of difficulties with both of these options are discussed. (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)

This catalogue is divided into two parts. Part 1 presents basic bibliographical information on books and journal issues that consist exclusively or in large part in papers devoted to the Presocratics and the Sophists. Part 2 lists the papers on Presocratic and Sophistic topics found in the volumes, providing name of author, title, and page numbers, and in the case of reprinted papers, the year of original publication. In some cases Part 2 lists the complete contents of volumes, not only (...) the Presocratic and Sophistic-related papers. Annual updates are submitted as additional files below. (shrink)

I reconstruct the original versions of Zeno's Racetrack and Achilles paradoxes, along with Aristotle's responses thereto. Along the way I consider some of the consequences for modern analyses of the paradoxes. It turns out that the Racetrack and the Achilles were oral two-party question-and-answer dialectical paradoxes. One consequence is that the arguments needed to be comprehensible to the average person, and did not employ theses or concepts familiar only to philosophical specialists. I rely on this fact in reconstructing the original (...) dialectical versions of the paradoxes. I show that both paradoxes rely for their success on forcing the dialectical answerer to reflect on his own potentially unending experience of imagination, and show that this renders the most popular contemporary critique of each paradox unworkable in an ancient dialectical context. In responding to the Racetrack, Aristotle seeks to replace the answerer's first-person experience with something more objective, a visible diagram. He then argues that the Racetrack involves an equivocation, an equivocation resulting from the fact that one and the same visible diagram can be interpreted in two ways. He frames his charge of equivocation in standard dialectical fashion, but his use of a diagram is his own innovation. While first employing his response to the Racetrack to construct a response to the somewhat different Achilles paradox, Aristotle later proceeds to offer a revised critique of the Racetrack itself. His revised critique is heavily influenced by his reaction to a variant pre-Aristotelian version of the paradox, a version involving counting. This leads him to reflect on the possibility of mentally experiencing an infinite collection. He also reflects on his earlier diagrammatic methodology, and on the conditions that individuate points, especially halfway-points. He concludes that points which are individuated in diagrams need not represent points that are individuated in reality. His revised critique of the Racetrack hinges on the distinction between actual points and potential points, and I show that this critique maintains the dialectical form of its predecessor, while constituting a reflection on the potentially misleading nature of diagrams. (shrink)