Governments and other groups interested in the views of citizens require the means to present justifications of proposed actions, and the means to solicit public opinion concerning these justifications. Although Internet technologies provide the means for such dialogues, system designers usually face a choice between allowing unstructured dialogues, through, for example, bulletin boards, or requiring citizens to acquire a knowledge of some argumentation schema or theory, as in, for example, ZENO. Both of these options present usability problems. In this paper, (...) we describe an implemented system called PARMENIDES which allows structured argument over a proposed course of action, without requiring knowledge of the underlying argumentation theory. (shrink)

In Plato's Parmenides , Socrates proposes a 'Day' analogy to express one possible model of part/whole relations. His analogy is swiftly rejected and replaced with another analogy, that of the 'Sail'. In this paper, it is argued that there is a profound difference between these two analogies and that the 'Day' represents a distinct way to think about part/whole relations. This way of thinking, I argue, is the standard way of thinking in East Asian Buddhism. Plato's 'Day' analogy can then (...) be used to illuminate the meaning of an opaque but very important concept in East Asian Buddhism: li , which in this paper is developed as a modal concept of 'Wholeness'. (shrink)

I argue here that a properly Platonic theory of the nature of number is still viable today. By properly Platonic, I mean one consistent with Plato's own theory, with appropriate extensions to take into account subsequent developments in mathematics. At Parmenides 143a-4a the existence of numbers is proven from our capacity to count, whereby I establish as Plato's the theory that numbers are originally ordinal, a sequence of forms differentiated by position. I defend and interpret Aristotle's report of a Platonic (...) distinction between form and mathematical numbers, arguing that mathematical numbers alone are cardinals, by reference to certain non-technical features of a set-theoretical approach and other considerations in philosophy of mathematics. Finally I respond to the objections that such a conception of number was unavailable in antiquity and that this theory is contradicted by Aristotle's report in Metaph . XIII that Platonic numbers are collections of units. I argue that Aristotle reveals his own misinterpretation of the terms in which Plato's theory was expressed. (shrink)

The Eleatic Principle or causal criterion is a causal test that entities must pass in order to gain admission to some philosophers’ ontology.1 This principle justifies belief in only those entities to which causal power can be attributed, that is, to those entities which can bring about changes in the world. The idea of such a test is rather important in modern ontology, since it is neither without intuitive appeal nor without influential supporters. Its supporters have included David Armstrong (1978, (...) Vol 2, 5), Brian Ellis (1990, 22) and Hartry Field2 (1989, 68) to name but a few. (shrink)

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. (shrink)

: Given Descartes's conception of extension, space and body, there are deep problems about how there can be any real motion. The argument here is that in fact Descartes takes motion to be only phenomenal. The paper sets out the problems generated by taking motion to be real, the solution to them found in the Cartesian texts, and an explanation of those texts in which Descartes appears on the contrary to regard motion as real.

In his great poem, Parmenides uses an argument by elimination to select the correct "way of inquiry" from a pool of two, the ways of is and of is not , joined later by a third, "mixed" way of is and is not . Parmenides' first two ways are soon given modal upgrades - is becomes cannot not be , and is not becomes necessarily is not (B2, 3-6) - and these are no longer contradictories of one another. And is (...) the common view right, that Parmenides rejects the "mixed" way because it is a contradiction? I argue that the modal upgrades are the product of an illicit modal shift. This same shift, built into two Exclusion Arguments, gives Parmenides a novel argument to show that the "mixed" way fails. Given the independent failure of the way of is not , Parmenides' argument by elimination is complete. (shrink)

Wittgenstein’s Tractatus Logico-Philosophicus famously ends with a remark that, as he says in the book’s “Preface,” could also summarize the sense of the book as a whole: Whereof one cannot speak, thereof one must be silent. Passing over, for the moment, the difference between speaking and knowing, the remark can be read almost as a paraphrase of one written almost 2500 years ago: You could not know what is not – that cannot be done – nor indicate it. (KR 291).

Rational epistemics is the line of reasoning inclined to reason separated from reliance on experience that ultimately leads to monism or non-dualism.

The Parmenides is notorious for the criticisms it directs against Plato's own Theory of Forms, as presented in the middle period. But the second and major portion of the dialogue has generally been avoided, despite its being offered as Plato's response to the problems; the text seems intractably obscure, appearing to consist of a series of bad arguments leading to contradictory conclusions. Carefully analyzing these arguments and the methodological remarks which precede them, Meinwald shows that to understand Plato's response we (...) need to recognize his important distinction between two kinds of predication. Read in the light of this distinction, the arguments can be seen to be sound, and the contradictions merely apparent. Meinwald then proceeds to demonstrate the direct application of Plato's crucial innovation in solving the problems of the first part of the dialogue, including the infamous Third Man. On Meinwald's interpretation, the new distinction is associated with developments in metaphysics which take Plato well beyond the problems commonly thought to tell against Platonism. (shrink)

John Palmer presents a new and original account of Plato's uses and understanding of his most important Presocratic predecessor, Parmenides. Adopting an innovative approach to the appraisal of intellectual influence, Palmer first explores the Eleatic underpinnings of central elements in Plato's middle-period epistemology and metaphysics and then shows how in the later dialogues Plato confronts various sophistic appropriations of Parmenides.

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. (shrink)

It’s well known that one way to cure a hangover is by a “hair of the dog” — another alcoholic drink. The drawback of this method is that, so it would appear, it cannot be used to completely cure a hangover, since the cure simply induces a further hangover at a later time, which must in turn either be cured or suffered through.