Online research in philosophy

There is an intriguing recent effort to develop a valid cosmological argument on the basis of quite minimal assumptions.1 Indeed, the basis of the new cosmological argument is so slight that it is likely to make even a conscientious theist suspicious – to say nothing of our vigilant atheists. In Section 1 we present the background assumptions and central premises of the new cosmological argument. We are sympathetic to the conclusion that there necessarily exists an intelligent and powerful creator of the actual universe, but we show in Section 2 that the new cosmological argument cannot establish this claim. Specifically, we show by reductio ad absurdum that the new argument is unsound, and that every plausibly modified version of the argument is also unsound.2 We close our discussion with a diagnosis of what went wrong in the new cosmological argument. Our conclusion is that this intriguing new argument promises considerably more than it can show.

``No one has ever touched Zeno without refuting him''. We will not refute Zeno in this paper. Instead we review some unexpected encounters of Zeno with modern science. The paper begins with a brief biography of Zeno of Elea followed by his famous paradoxes of motion. Reflections on continuity of space and time lead us to Banach and Tarski and to their celebrated paradox, which is in fact not a paradox at all but a strict mathematical theorem, although very counterintuitive. Quantum mechanics brings another flavour in Zeno paradoxes. Quantum Zeno and anti-Zeno effects are really paradoxical but now experimental facts. Then we discuss supertasks and bifurcated supertasks. The concept of localization leads us to Newton and Wigner and to interesting phenomenon of quantum revivals. At last we note that the paradoxical idea of timeless universe, defended by Zeno and Parmenides at ancient times, is still alive in quantum gravity. The list of references that follows is necessarily incomplete but we hope it will assist interested reader to fill in details.

Zeno's paradoxes of motion have been puzzling human's understanding of nature for twenty-five centuries. While the assumption of continuous space-time has been overwhelmingly believed, modern physic findings suggest the possibility of the other case. The ultimate truth still remains an unsolved mystery. This paper presents a proof that space-time is discrete by resolving the discreteness-based paradoxes of Zeno, in particular the Stadium, with the help of the Special Relativity Theory. The key work is the proof that the only speed at which motions on the Zeno's Stadium can be is the speed of light. Lorentz transformation then provides sufficient information to resolve the paradox.

ABNER SHIMONY of the Paradox A PHILOSOPHICAL PUPPET PLAY Dramatis personae: Zeno , Pupil, Lion Scene: The school of Zeno at Elea. Pup. Master! ...

Zeno''s paradoxes of motion and the semantic paradoxes of the Liar have long been thought to have metaphorical affinities. There are, in fact, isomorphisms between variations of Zeno''s paradoxes and variations of the Liar paradox in infinite-valued logic. Representing these paradoxes in dynamical systems theory reveals fractal images and provides other geometric ways of visualizing and conceptualizing the paradoxes.

A solution of the Zeno paradoxes in terms of a discrete space is usually rejected on the basis of an argument formulated by Hermann Weyl, the so-called tile argument. This note shows that, given a set of reasonable assumptions for a discrete geometry, the Weyl argument does not apply. The crucial step is to stress the importance of the nonzero width of a line. The Pythagorean theorem is shown to hold for arbitrary right triangles.

MATHEMATICAL RESOLUTIONS OF ZENO’s PARADOXES of motion have been offered on a regular basis since the paradoxes were first formulated. In this paper I will argue that such mathematical “solutions” miss, and always will miss, the point of Zeno’s arguments. I do not think that any mathematical solution can provide the much sought after answers to any of the paradoxes of Zeno. In fact all mathematical attempts to resolve these paradoxes share a common feature, a feature that makes them consistently miss the fundamental point which is Zeno’s concern for the one-many relation, or it would be better to say, lack of relation. This takes us back to the ancient dispute between the Eleatic school and the Pluralists. The first, following Parmenide’s teaching, claimed that only the One or identical can be thought and is therefore real, the second held that the Many of becoming is rational and real.1 I will show that these mathematical “solutions” do not actually touch Zeno’s argument and make no metaphysical contribution to the problem of understanding what is motion against immobility, or multiplicity against identity, which was Zeno’s challenge. I would like to point out at this stage that my contention.

Almost everything that we know about Zeno of Elea is to be found in the opening pages of Plato's Parmenides. There we learn that Zeno was nearly 40 years old when Socrates was a young man, say 20. Since Socrates was born in 469 BC we can estimate a birth date for Zeno around 490 BC. Beyond this, really all we know is that he was close to Parmenides (Plato reports the gossip that they were lovers when Zeno was young), and that he wrote a book of paradoxes defending Parmenides' philosophy. Sadly this book has not survived, and what we know of his arguments is second-hand, principally through Aristotle and his commentators (here I have drawn particularly on Simplicius, who, though writing a thousand years after Zeno, apparently possessed at least some of his book). There were apparently 40 ‘paradoxes of plurality’, attempting to show that ontological pluralism — a belief in the existence of many things rather than only one — leads to absurd conclusions; of these paradoxes only two definitely survive, though a third argument can probably be attributed to Zeno. Aristotle speaks of a further four arguments against motion (and by extension change generally), all of which he gives and attempts to refute. In addition Aristotle attributes two other paradoxes to Zeno. Sadly again, almost none of these paradoxes are quoted in Zeno's original words by their various commentators, but in paraphrase.