لا شك أن مفارقات زينون في الحركة قد تم تناولها – تحليلاً ونقدًا – في كثيرٍ من أدبيات العلم والفلسفة قديمًا وحديثًا، حتى لقد ساد الظن بأن ملف المفارقات قد أغُلق تمامًا، لاسيما بعد أن نجح الحساب التحليلي في التعامل منطقيًا مع صعوبات الأعداد اللامتناهية، لكن الفرض الأساسي لهذا البحث يزعم عكس ذلك؛ أعني أن الملف مازال مفتوحًا وبقوة – خصوصًا على المستوى الرياضي الفيزيائي – وأن إغلاقه النهائي قد لا يتم في المستقبل القريب. من جهة أخرى، إذا كانت فكرة (...) وجود العالم ذاته – مصدر مشكلاتنا الفلسفية – لا معنى لها إلا في إطار نسقٍ من التصورات التي تُصاغ بالضرورة في لغة، ومن ثم يُصبح العالم كيانًا كوّنته أساليبنا اللغوية في وصفه، فإن ما يواجهنا دومًا هو السؤال الكانطي المُعضل: إذا كانت اللغة ليست مرآة عاكسة للواقع الفعلي – أو للشيء في ذاته – وإنما للواقع كما تدركه الذات وتؤسلبه، ألا يعني ذلك أن وجودنا ذاته ووجود العالم مجرد فكرة تقطع الصلة بين العوالم الممكنة والعالم الفعلي؟. (shrink)

It will be shown in this article that an ontological approach for some problems related to the interpretation of Quantum Mechanics (QM) could emerge from a re-evaluation of the main paradox of early Greek thought: the paradox of Being and non-Being, and the solutions presented to it by Plato and Aristotle. More well known are the derivative paradoxes of Zeno: the paradox of motion and the paradox of the One and the Many. They stem from what was perceived by (...) classical philosophy to be the fundamental enigma for thinking about the world: the seemingly contradictory results that followed from the co-incidence of being and non-being in the world of change and motion as we experience it, and the experience of absolute existence here and now. The most clear expression of both stances can be found, again following classical thought, in the thinking of Heraclitus of Ephesus and Parmenides of Elea. The problem put forward by these paradoxes reduces for both Plato and Aristotle to the possibility of the existence of stable objects as a necessary condition for knowledge. Hence the primarily ontological nature of the solutions they proposed: Plato’s Theory of Forms and Aristotle’s metaphysics and logic. Plato’s and Aristotle’s systems are argued here to do on the ontological level essentially the same: to introduce stability in the world by introducing the notion of a separable, stable object, for which a ‘principle of contradiction’ is valid: an object cannot be and not-be at the same place at the same time. So it becomes possible to forbid contradiction on an epistemological level, and thus to guarantee the certainty of knowledge that seemed to be threatened before. After leaving Aristotelian metaphysics, early modern science had to cope with these problems: it did so by introducing “space” as the seat of stability, and “time” as the theater of motion. But the ontological structure present in this solution remained the same. Therefore the fundamental notion ‘separable system’, related to the notions observation and measurement, themselves related to the modern concepts of space and time, appears to be intrinsically problematic, because it is inextricably connected to classical logic on the ontological level. We see therefore the problems dealt with by quantum logic not as merely formal, and the problem of ‘non-locality’ as related to it, indicating the need to re-think the notions system, entity, as well as the implications of the operation ‘measurement’, which is seen here as an application of classical logic (including its ontological consequences) on the material world. (shrink)

I examine the reasons Aristotle presents in Physics VIII 8 for denying a crucial assumption of Zeno’s dichotomy paradox: that every motion is composed of sub-motions. Aristotle claims that a unified motion is divisible into motions only in potentiality (δυνάμει). If it were actually divided at some point, the mobile would need to have arrived at and then have departed from this point, and that would require some interval of rest. Commentators have generally found Aristotle’s reasoning unconvincing. Against David (...) Bostock and Richard Sorabji, inter alia, I argue that Aristotle offers a plausible and internally consistent response to Zeno. I defend Aristotle’s reasoning by using his discussion of what to say about the mobile at boundary instants, transitions between change and rest. There Aristotle articulates what I call the Changes are Open, Rests are Closed Rule: what is true of something at a boundary instant is what is true of it over the time of its rest. By contrast, predications true of something over its period of change are not true of the thing at either of the boundary instants of that change. I argue that this rule issues from Aristotle’s general understanding of change, as laid out in Phys. III. It also fits well with Phys. VI, where Aristotle maintains that there is a first boundary instant included in the time of rest, but not a “first in which the mobile began to change.” I then show how this rule underlies Aristotle’s argument that a continuous motion cannot be composed of actual sub-motions. Aristotle distinguishes potential middles, points passed through en route to a terminus, from actual middles. The Changes are Open, Rests are Closed Rule only applies to actual middles, because only they are boundaries of change that the mobile must arrive at and then depart from. On my reading, Aristotle argues that the instant of arrival, the first instant at which the mobile has come to be at the actual middle, cannot belong to the time of the subsequent motion. If it did, the mobile would already be moving towards the next terminus and thus, per Phys. VI 6, would have already left. But it cannot have moved away from the midpoint at the very same moment it has arrived there. This means that the instant of arrival must be separated from the time of departure by an interval of rest. I show how Aristotle’s reasoning applies generally to rule out any continuous reflexive motion or continuous complex rectilinear motion. On my interpretation, however, the argument does not apply to every change of direction. When, as in the case of projectile motion, multiple movers and their relative powers explain why the mobile changes directions, distinct sub-motions are not involved. Aristotle holds that such motions cannot be continuous, not because they involve intervals of rest, but because they involve multiple causes of motion. My interpretation of the Changes are Open, Rests are Closed Rule allows us to make better sense of Aristotle’s argument than any previous interpretation. (shrink)

The four antinomies of Zeno of Elea continue to be provoking issues that remain relevant for the foundation of science. Aristotle used this antinomy to arrive at a deeper understanding of movement : it is a fluent continuum that he considers to be a whole. The parts, if any, are only potentially present. Similarly, quantum mechanics states that movement is quantized ; things move or change in nonreducible steps, the so-called quanta. This view is in contrast to classical (...) mechanics, where infinitesimally small steps are permitted. The objective of the present study is to show the merits of the Aristotelian approach. Examples from modern science serve to illustrate the philosophical statements. (shrink)

I propose that an irreducible property of physical space — consistency — is the origin of logic. I propose that an inconsistent space is inconceivable and that this inconceivability can be recognized as the force behind logical propositions. The implications of this argument are briefly explored and then applied to address two paradoxes: Zeno of Elea’s paradox regarding the race between Achilles and the Tortoise, and Lewis Carroll’s paradox regarding the Tortoise’s conversation with Achilles after the race. I (...) conclude that Achilles would have won on both accounts, in the race and the argument, by invoking the consistency of space as the foundation of both movement across space and logical argument. (shrink)

The strings of physics’ string theory are the binary digits of 1 and 0 used in computers and electronics. The digits are constantly switching between their representations of the “on” and “off” states. This switching is usually referred to as a flow or current. Currents in the two 2-dimensional programs called Mobius loops are connected into a four-dimensional figure-8 Klein bottle by the infinitely-long irrational and transcendental numbers. Such an infinite connection translates - via bosons being ultimately composed of 1’s (...) and 0’s depicting pi, e, √2 etc.; and fermions being given mass by bosons interacting in matter particles’ “wave packets” – into an infinite number of 8-Kleins. Each Klein 1) is one of the universe’s subuniverses (our own is 13.7 billion years old), 2) is made flexible through its binary digits which seamlessly, or almost seamlessly, join it to surrounding subuniverses and eliminate its central hole, and 3) possesses warped time and space because its foundation is the programmed curves in its mathematical Mobius loops (along with the twists they generate [p.7]). The universe functions according to the rules of fractal geometry. So the Mobius does not exist only at the cosmic level. It also manifests at the quantum scale, giving us photons and protons etc. Space and time are no longer separate, but are an indivisible space-time. So if space and the universe are infinite, how can time not be eternal? The past and the future must both extend forever (the idea of time being finite arises from confusion of our subuniverse with the one infinite universe). -/- BITS (Binary digiTS) only suggest existence of the divine if time is linear. Although a non-supernatural God is proposed via the inverse-square law coupled with eternal quantum entanglement, Einstein taught us that time is warped. Warped time is nonlinear, making it at least possible that the BITS composing space-time and all particles originate from the computer science of humans. -/- I suspect many readers will be content with reading this abstract. While there are more details, and mathematics, in the content; my natural style of writing is to avoid jargon and maths. I also tend to get philosophical. While I personally feel that there’s a lot of precious information in the content, I realize it won’t all be to everyone’s liking. Other subjects dealt with in this article are - the “Pioneer anomaly”, refinement of gravitational physics, dark energy and dark matter, quantum phenomena like mass and electric charge and quantum spin, Kepler’s laws of planetary motion, deflection of starlight by the sun, tides, falling bodies, Earth’s orbit, ancient Greek philosophers, Newton, Kepler, Galileo, Aristotle, Parmenides, Zeno of Elea, time travel into the past as well as the future, the elimination of distances in space, humanity’s construction of this universe we live in, The Law of Conservation of Matter-Energy, and support for the science-fiction-like idea of the electronic binary digits of 1 and 0 being the building blocks of our universe. (shrink)

The four antinomies of Zeno of Elea, especially Achilles and the tortoise continue to be provoking issues which are even now not always satisfactory solved. Aristotle himself used this antinomy to develop his understanding of movement: it is a fluent continuum that has to be treated as a whole. The parts, if any, are only potentially present in the whole. And that is exactly what quantum mechanics is claiming: movement is quantized in contrast to classical mechanics. The objective (...) of this study is to show the merits of the Aristotelian approach. It is a good candidate for serving as the philosophical background for understanding fundamental aspects of quantum mechanics. Especially mentioned are the influence of the final state in quantum mechanics that in philosophy could be correlated with the final cause. Like in the work of Aristotle also in this study examples from science are presented to illustrate the philosophical approach. But, in contrast to ancient Greek, the examples now relate to issues which are only fully accessible to the scientifically trained reader. As the main conclusion the dialogue between scientists and philosophers is strongly recommended which will result in progress in both disciplines. (shrink)

NOTA PRELIMINAR: o texto a seguir representa a versão ampliada (e corrigida conforme as indicações dos pareceristas) do artigo homônimo, publicado na revista Archai em 2014. Por algum problema técnico, acabou sendo publicada, na época, a primeira versão, sem as melhorias sugeridas pelos avaliadores. Eis, então, a versão ‘definitiva’ do artigo “Zenão e a impossibilidade da analogia”: -/- A reductio ad absurdum foi elevada por Zenão de Eléia a único método que permitiria vislumbrar a verdadeira realidade, invisível tanto aos sentidos (...) quanto à maneira de pensar comum. Mostrando uma certa continuidade com os filósofos anteriores, não só na busca de um procedimento para que a especulação pudesse avançar, como também na mesma rota de afastamento daquilo que é mais próximo, conhecido e particular (visível) em direção àquilo que é menos conhecido, distante e universal (invisível), para dizê-lo em termos aristotélicos, Zenão utilizou-se de argumentos aporéticos como único caminho possível para poder entrever o ‘reino do Ser’. Esse, com efeito, é invisível não somente aos nossos sentidos, como também ao nosso raciocínio ordinário. Eis que somente a ‘via do não-ser’, a única que poderia ser trilhada após Parménides, como diz Wolff, nos permite ter uma ideia, por quanto vaga, daquilo que é ‘verdadeiramente invisível’. Tão invisível ao ponto de ser inalcançável até mesmo pelo pensamento. (shrink)

The main thesis of Michael Della Rocca’s outstanding Spinoza book (Della Rocca 2008a) is that at the very center of Spinoza’s philosophy stands the Principle of Sufficient Reason (PSR): the stipulation that everything must be explainable or, in other words, the rejection of any brute facts. Della Rocca rightly ascribes to Spinoza a strong version of the PSR. It is not only that the actual existence and features of all things must be explicable, but even the inexistence – as well (...) as the absence of any feature of any thing – demands an explanation. Della Rocca does not stop here, however. He feeds his PSR monster with some more powerful steroids and suggests that Spinoza advocates what he terms “the twofold use of the PSR.” It is not only that everything must be explained and made intelligible, but it must ultimately be explained in terms of explainability or intelligibility itself. This twofold use of the PSR is the key to the entire book. Della Roca’s strategy throughout the book is to argue that any key feature of Spinoza’s system – be it causality, inherence, essence, consciousness, existence, rejection of teleology, goodness or political right – must be explained, and ultimately it must be explained in terms of intelligibility. “Spinoza single-mindedly digs and digs until we find that the phenomenon in question is nothing but some form of intelligibility itself, of explicability itself” (Della Rocca 2008a: 2). Della Rocca’s book came out together with a cluster of articles in which he develops in detail his new reading of Spinoza. In one of these articles, he warns the reader: “Don’t let me start” (Dell Rocca 2010: 1). The train that is about to embark leads to very bizarre terrain, and thus one should think twice before embarking on the “PSR Express.” In this paper I argue that the train was hijacked. This was a perfect crime: without anyone noticing it, the engine driver diverted the train to a new route, and as with other perfect crimes, it is none but the criminal himself who is capable of, and indeed will, bring about his own demise. As I will later argue, Della Rocca’s “PSR-on-steroids” will eventually cripple reason itself. But let us not run too fast, and start at the very beginning. I happily – or at least, so I think - board the “PSR Express.” I believe Spinoza is strongly committed to the PSR and makes very significant use of this principle, but, unlike Della Rocca, I do not think the PSR is the key to all mysteries Spinozist, nor do I believe Spinoza was committed to the reductionist program of explaining all things through intelligibility (i.e., the second use of the PSR). (shrink)

Hume’s discussion of space in the Treatise addresses two main topics: divisibility and vacuum. It is widely recognized that his discussion of divisibility contains an answer to Bayle, whose Dictionary article “Zeno of Elea” presents arguments about divisibility as support for fideism. It is not so widely recognized that, elsewhere in the same article, Bayle presents arguments about vacuum as further support for fideism. This paper aims to show that Hume’s discussion of vacuum contains an answer to these (...) vacuum-based fideistic arguments. Key to this answer is a distinction between two ways in which vacuum was conceived in the early modern period: i) as a genuine thing that has spatial properties, and yet is immobile, indivisible, and penetrable ; ii) as a mere absence of spatial things. This paper also aims to provide a novel defense of Hume against the long-standing objection that he is inconsistent in denying that we can conceive of a vacuum, while allowing that we can conceive of “invisible and intangible distance.” As I interpret him, Hume consistently denies that we can conceive of a positive vacuum, while allowing that we can conceive of two or more objects’ being arranged so as to have privative vacuum between them. (shrink)

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)

Aspetti filosofico-matematici dei celebri paradossi di Zenone di Elea.

‘...if you learn to think like Peter Cave – with freshness, humour, objectivity and penetration – you will have been amply rewarded.’ :::: Prof. Felipe Fernandez-Armesto, University of Notre Dame __________________ Chapter Titles:>>> ___ 1 Lao Tzu: The Way to Tao >>> 2 Sappho: Lover >>> 3 Zeno of Elea: Tortoise Backer, Parmenidean Helper >>> 4 Gadfly: aka ‘Socrates’ >>> 5 Plato: Charioteer, Magnificent Footnote Inspirer – ‘Nobody Does It Better’ >>> 6 Aristotle: Earth-Bound, Walking >>> 7 Epicurus: (...) Gardener, Curing the Soul, Ably Assisted by Lucretius >>> 8 Avicenna: Flying Man, Unifier >>> 9 Descartes: With Princess, With Queen >>> 10 Spinoza: God-Intoxicated Atheist >>> 11 Leibniz: Monad Man >>> 12 Bishop Berkeley, ‘That Paradoxical Irishman’: Immaterialist, Tar-Water Advocate >>> 13 David Hume: The Great Infidel or Le Bon David >>> 14 Kant: Duty Calls, Categorically >>> 15 Schopenhauer: Pessimism With Flute >>> 16 John Stuart Mill: Utility Man, With Harriet, Soul-Mate >>> 17 Søren Kierkegaard: Who? >>> 18 Karl Marx: Hegelian, Freedom-Fighter >>> 19 Lewis Carroll: Curiouser and Curiouser >>> 20 Nietzsche: God-Slaying Jester, Trans-Valuer >>>> 21 Bertrand Russell: Radical, Aristocrat >>> 22 G. E. Moore: Common-Sense Defender, Bloomsbury’s Sage >>> 23 Heidegger: Hyphenater >>> 24 Jean-Paul Sartre: Existentialist, Novelist, French >>> 25 Simone Weil: Refuser and Would-Be Rescuer >>> 26 Simone de Beauvoir: Situated, Protester, Feminist >>> 27 Ludwig Wittgenstein: Therapist >>> 28 Hannah Arendt: Controversialist, Journalist? >>> 29 Iris Murdoch: Attender >>> 30 Samuel Beckett: Not I >>>. (shrink)

A familiar interpretation of quantum mechanics (one of a number of views sometimes labeled the "Copenhagen interpretation'"), takes its empirical apparatus at face value, holding that the quantum wave function evolves by the Schrödinger equation except on certain occasions of measurement, when it collapses into a new state according to the Born rule. This interpretation is widely rejected, primarily because it faces the measurement problem: "measurement" is too imprecise for use in a fundamental physical theory. We argue that this is (...) a weak objection, as there may be many ways of making "measurement" precise. However, measurement-collapse interpretations face a more serious objection: a dilemma tied to the quantum Zeno effect. Is measurement itself an observable that can enter superpositions? If yes, then the standard measurement-collapse dynamics is ill-defined. If no, then (at least if measurement is an observable), measurements can never start or finish. The best way out is to deny that measurement is an observable, but this leads to strong and revisionary consequences. This reinforces the view that there is no nonrevisionary interpretation of quantum mechanics. (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)

The article uses Zeno’s metrical paradox of extension, or Zeno’s fundamental paradox, as a thought-model for the mind-body problem. With the help of this model, the distinction contained between mental and physical phenomena can be formulated as sharply as possible. I formulate Zeno’s fundamental paradox and give a sketch of four different solutions to it. Then I construct a mind-body paradox corresponding to the fundamental paradox. Through that, it becomes possible to copy the solutions to the fundamental (...) paradox on the mind-body paradox. Three of them fail. But one of them – the Aristotelian one – gives us an interesting hint. Finally, this hint is pursued somewhat further and through comparison with Zeno’s fundamental paradox, the impossibility of a solution to the mind-body problem is shown again. The main new point of this article is the comparison of the mind-body problem with Zeno’s fundamental paradox. The article is a revised english version of an article published in: Allgemeine Zeitschrift für Philosophie, 23, 1998, p. 61-75. (shrink)

. In our research about Fuzzy Time and modeling time, "Unexpected Hanging Paradox" plays a major role. Here, we compare this paradox to the Zeno Paradox and the relations of them with our standard models of continuum and Fuzzy numbers. To do this, we review the project "Fuzzy Time and Possible Impacts of It on Science" and introduce a new way in order to approach the solutions for these paradoxes. Additionally, we have a more general discussion about paradoxes, as (...) Philosophical back ground of the subject and in this way, we introduce the concepts of General View, the first picture, BBF-General View. -/- . (shrink)

In our research about Fuzzy Time and modeling time, "Unexpected Hanging Paradox" plays a major role. Here, we compare this paradox to the Zeno Paradox and the relations of them with our standard models of continuum and Fuzzy numbers. To do this, we review the project "Fuzzy Time and Possible Impacts of It on Science" and introduce a new way in order to approach the solutions for these paradoxes. Additionally, we have a more general discussion about paradoxes, as Philosophical (...) back ground of the subject and in this way, we introduce the concepts of General View, the first picture, BBF-General View. (shrink)

Review of: "Zeno and Einstein".

This article attempts to elucidate the phenomenon of time and its relationship to consciousness. It defends the idea that time exists both as a psychological or illusory experience, and as an ontological property of spacetime that actually exists independently of human experience.

We outline Brentano’s theory of boundaries, for instance between two neighboring subregions within a larger region of space. Does every such pair of regions contain points in common where they meet? Or is the boundary at which they meet somehow pointless? On Brentano’s view, two such subregions do not overlap; rather, along the line where they meet there are two sets of points which are not identical but rather spatially coincident. We outline Brentano’s theory of coincidence, and show how he (...) uses it to resolve a number of Zeno-like paradoxes. (shrink)

On Zeno Beach there are infinitely many grains of sand, each half the size of the last. Supposing Aristotle denied the possibility of Zeno Beach, did he have a good argument for the denial? Three arguments, each of ancient origin, are examined: the beach would be infinitely large; the beach would be impossible to walk across; the beach would contain a part equal to the whole, whereas parts must be lesser. It is attempted to show that none of (...) these arguments was Aristotle’s. Indeed, perhaps Aristotle’s finitism applied to magnitude only, not plurality. (shrink)

In der vorliegenden Arbeit soll eine Lösung der zenonischen Paradoxie des ruhenden Pfeils vorgestellt werden, die auf möglichen Implikationen des Kontiguumbegriffs beruht, wie ihn Leibniz in mehreren Arbeiten zu den Grundlagen der Dynamik entwickelt hat. Wesentlich sind dabei wechselseitige thematische Bezüge seiner Theoria Motus Abstracti und seines Dialogs Pacidius Philalethi. Aus der von Leibniz durchgeführten Analyse des Kontiguums als einer Voraussetzung der Möglichkeit von Bewegung ergibt sich, daß das (scheinbar zwischen Kontinuum und Diskretheit angesiedelte) Kontiguum - in heutiger Terminologie - (...) nicht durch solche Merkmale wie Mächtigkeit oder Dichte bestimmt werden kann, sondern vielmehr eine besondere (topologische) Zusammenhangsstruktur aufweisen muß. In der Arbeit wird gezeigt, daß die dynamisch begründeten Anforderungen an eine solche Zusammenhangsstruktur von geeigneten topologischen Modellen einer Kette erfüllt werden. (shrink)

Many philosophers accept a ‘layered’ world‐view according to which the facts about the higher ontological levels supervene on the facts about the lower levels. Advocates of such views often have in mind a version of atomism, according to which there is a fundamental level of indivisible objects known as simples or atoms upon whose spatiotemporal locations and intrinsic properties everything at the higher levels supervenes.1 Some, however, accept the possibility of ‘gunk’ worlds in which there are parts ‘all the way (...) down’ such that there are no simples and insofar as composite objects exist these are composed of smaller objects which in turn are composed of smaller objects, and so on. It may nonetheless still be claimed that the facts about each ontological level supervene on the facts about the lower levels. (shrink)

While Aristotle provides the crucial testimonies for the paradoxes of motion, topos, and the falling millet seed, surprisingly he shows almost no interest in the paradoxes of plurality. For Plato, by contrast, the plurality paradoxes seem to be the central paradoxes of Zeno and Simplicius is our primary source for those. This paper investigates why the plurality paradoxes are not examined by Aristotle and argues that a close look at the context in which Aristotle discusses Zeno holds the (...) answer to this question. (shrink)

There was a time in my school years when I have learned about Achilles and Tortoise “paradox” originated from Zeno. It was then clear that the ancient Greeks were arguing about this problem but contemporary science has clarified the issue. Yet to my surprise the problem is still debated over and over, despite the fact there exist mathematical proofs. I feel like reminding myself why this is not a paradox beyond reasonable doubt. This is a draft to a section (...) of a future publication. (shrink)

Zeno’s Arrow and Nāgārjuna’s Fundamental Wisdom of the Middle Way Chapter 2 contain paradoxical, dialectic arguments thought to indicate that there is no valid explanation of motion, hence there is no physical or generic motion. There are, however, diverse interpretations of the latter text, and I argue they apply to Zeno’s Arrow as well. I also find that many of the interpretations are dependent on a mathematical analysis of material motion through space and time. However, with modern philosophy (...) and physics we find that the link from no explanation to no phenomena is invalid and that there is a valid explanation and understanding of physical motion. Hence, those arguments are both invalid and false, which banishes the MMK/2 and The Arrow under this and derivative interpretations to merely the history of philosophy. However, a view that maintains their relevance is that each is used as a koan or sequence of koans designed to assist students in spiritual meditation practice. This view is partly justified by the realization that both Nāgārjuna and Zeno were likely meditation masters in addition to being logicians. The works are, therefore, not works that should be assessed as having valid arguments and true conclusions by the standards of modern analytic philosophy—contrary to some of the literature—but rather are therapeutic and perhaps more appropriately considered as part of an experientially focused philosophy such as existentialism, phenomenology or religion. (shrink)

- Applying the law of conservation of time to solve the Achilles and the tortoise paradox. - Applying the smallest unit of time T_min in the universe to solve the Dichotomy paradox. - Applying the disappearing property of matter when moving to solve the Arrow paradox.

The goals of this paper are two-fold: I wish to clarify the Aristotelian conception of the law of non-contradiction as a metaphysical rather than a semantic or logical principle, and to defend the truth of the principle in this sense. First I will explain what it in fact means that the law of non-contradiction is a metaphysical principle. The core idea is that the law of non-contradiction is a general principle derived from how things are in the world. For example, (...) there are certain constraints as to what kind of properties an object can have, and especially: some of these properties are mutually exclusive. Given this characterisation, I will advance to examine what kind of challenges the law of non-contradiction faces; the main opponent here is Graham Priest. I will consider these challenges and conclude that they do not threaten the truth of the law of non-contradiction understood as a metaphysical principle. (shrink)

Extending on an earlier paper [Found. Phys. Ltt., 16(4) 343–355, (2003)], it is argued that instants of time and the instantaneous (including instantaneous relative position) do not actually exist. This conclusion, one which is also argued to represent the correct solution to Zeno’s motion paradoxes, has several implications for modern physics and for our philosophical view of time, including that time and space cannot be quantized; that contrary to common interpretation, motion and change are compatible with the “block” universe (...) and relativity; and that time, space, and space-time too, cannot exist. Instead, motion and change become the major players. (shrink)

Does consciousness collapse the quantum wave function? This idea was taken seriously by John von Neumann and Eugene Wigner but is now widely dismissed. We develop the idea by combining a mathematical theory of consciousness (integrated information theory) with an account of quantum collapse dynamics (continuous spontaneous localization). Simple versions of the theory are falsified by the quantum Zeno effect, but more complex versions remain compatible with empirical evidence. In principle, versions of the theory can be tested by experiments (...) with quantum computers. The upshot is not that consciousness-collapse interpretations are clearly correct, but that there is a research program here worth exploring. (shrink)

The many definitions of sophistry at the beginning of Plato’s Sophist have puzzled scholars just as much as they puzzled the dialogue’s main speakers: the Visitor from Elea and Theaetetus. The aim of this paper is to give an account of that puzzlement. This puzzlement, it is argued, stems not from a logical or epistemological problem, but from the metaphysical problem that, given the multiplicity of accounts, the interlocutors do not know what the sophist essentially is. It transpires that, (...) in order to properly account for this puzzle, one must jettison the traditional view of Plato’s method of division, on which divisions must be exclusive and mark out relations of essential predication. It is then shown on independent grounds that, although Platonic division in the Sophist must express predication relations and be transitive, it need not be dichotomous, exclusive, or express relations of essential predication. Once the requirements of exclusivity and essential predication are dropped, it is possible to make sense of the reasons that the Visitor from Elea and Theaetetus are puzzled. Moreover, with this in hand, it is possible to see Plato making an important methodological point in the dialogue: division on its own without any norms does not necessarily lead to the discovery of essences. (shrink)

This paper investigates the view that digital hypercomputing is a good reason for rejection or re-interpretation of the Church-Turing thesis. After suggestion that such re-interpretation is historically problematic and often involves attack on a straw man (the ‘maximality thesis’), it discusses proposals for digital hypercomputing with Zeno-machines , i.e. computing machines that compute an infinite number of computing steps in finite time, thus performing supertasks. It argues that effective computing with Zeno-machines falls into a dilemma: either they are (...) specified such that they do not have output states, or they are specified such that they do have output states, but involve contradiction. Repairs though non-effective methods or special rules for semi-decidable problems are sought, but not found. The paper concludes that hypercomputing supertasks are impossible in the actual world and thus no reason for rejection of the Church-Turing thesis in its traditional interpretation. (shrink)

I discuss the quantum mechanical theory of consciousness and freewill offered by Stapp (1993, 1995, 2000, 2004). First I show that decoherence-based arguments do not work against this theory. Then discuss a number of problems with the theory: Stapp's separate accounts of consciousness and freewill are incompatible, the interpretations of QM they are tied to are questionable, the Zeno effect could not enable freewill as he suggests because weakness of will would then be ubiquitous, and the holism of measurement (...) in QM is not a good explanation of the unity of consciousness for essentially the same reason that local interactions may seem incapable of accounting for it. (shrink)

This article presents the proposal of the principle of sound and light from mathematics and physics, as the origin of nature and the universe, using the Cartesian plane, together with the triadic plane of potential manifestation and complex organisation, starting from the contributions of four pre-Socratic philosophers, Pythagoras of Ephesus, Parmenides of Elea, Heraclitus of Samos and Democritus of Abdera, thus identifying essential principles of the origin of these, to conclude with the most important demonstrations of this theory, which (...) allow its articulation with current science. (shrink)

An analysis of the counter-intuitive properties of infinity as understood differently in mathematics, classical physics and quantum physics allows the consideration of various paradoxes under a new light (e.g. Zeno’s dichotomy, Torricelli’s trumpet, and the weirdness of quantum physics). It provides strong support for the reality of abstractness and mathematical Platonism, and a plausible reason why there is something rather than nothing in the concrete universe. The conclusions are far reaching for science and philosophy.

Benardete presents a version of Zeno's dichotomy in which an infinite sequence of gods each intends to raise a barrier iff a traveller reaches the position where they intend to raise their barrier. In this paper, I demonstrate the abstract form of the Benardete Dichotomy. I show that the diagnosis based on that form can do philosophical work not done by earlier papers rejecting Priest's version of the Benardete Dichotomy, and that the diagnosis extends to a paradox not normally (...) classified as a dichotomy. I show how the form is exploited to generate paradox. Introduction The form of the Benardete dichotomy 2.1 The unsatisfiable pair diagnosis Applying the unsatisfiable pair diagnosis 3.1 Perez Laraudogoitia 3.2 Hawthorne 3.3 Angel 3.4 Yablo and Sorensen Exploiting the form. (shrink)

This paper examines the Stoic account of apprehension (κατάληψις) (a cognitive achievement similar to how we typically view knowledge). Following a seminal article by Michael Frede (1983), it is widely thought that the Stoics maintained a purely externalist causal account of apprehension wherein one may apprehend only if one stands in an appropriate causal relation to the object apprehended. An important but unanswered challenge to this view has been offered by David Sedley (2002) who offers reasons to suppose that the (...) Stoics (or at least Zeno, the founder of the Stoa) did not make such a causal stipulation. I offer a defence of the traditional, causal reading against the challenges raised by Sedley but also argue, against the traditional view, that the Stoic account incorporated an internalist element. On the hybrid account defended here, in order to apprehend not only must the agent stand in an appropriate causal relation to the object apprehended but the agent’s appearance of the object must also be clear (a feature which is accessible to the epistemic agent). The traditional scholarly view rejects internalist interpretations because it is thought that such interpretations cannot make sense of the Stoics’ discussion of the ‘automatic assent’ produced by kataleptic appearances and a purely externalist view is taken to be charitable insofar as it saves the Stoics from a vicious regress which they would otherwise face (were they internalists). I spell out how the regress might be taken to function and defend an internalist interpretation against both these charges. The internalist element embraced by the Stoics does not lead to the problems it is often thought to and the account defended here not only does justice to the textual evidence but also sheds light on the Stoic debates with their sceptical opponents and grants the Stoics an epistemic account fit for purpose. (shrink)

This textbook has been written to discuss the fundamental problems of Greek Philosophy. There has been many philosophical Problems which Greek philosophers has discussed and examined with rational approach. The philosophical problems which we have mentioned in this book are: Greek Rationalism, Greek Naturalism, Greek Idealism, Greeks on human mind, Number theory and Greek Metaphysics. We have defined some significant issues like Greek atomism, Nihilism, Solipsism, Dogmatism, Sophism and Pluralism. Philosophy is the subject which studies the fundamental Problems of the (...) world. The problems which Philosophy studies are reality, existence, mind, thought, language, essence, experience, perception, knowledge, God, and so on. This book ‘Problems of Greek Philosophy’ is divided into six chapters while first Chapter ‘Introduction to western Philosophy’ deals with overall discussion and argumentation of western philosophy and also some valuable introductory information on Greek Philosophy. Second Chapter ‘Greeks on Nature’ attempts to discuss the lonian classification and examination of natural elements like water, air, Aperion, fire and reality. This chapter deals with the ultimate constituents of the natural stuff. Third chapter ‘Greek Rationalism’ deals with the role of reason in explanation of the world. Greek rationalists have used reason as the fundamental constituent of the universe. Fourth chapter ‘Number theory and Greek Metaphysics’ deals with the contribution of great mathematicians like Pythagoras and Zeno to the world. This chapter has highlighted the philosophy of number and metaphysics. Fifth Chapter ‘Greek Idealism’ highlights the philosophy of Greek idealists; Protagoras, Socrates and Plato. Sixth Chapter ‘Mind in Greek Philosophy’ deals with the concept of mind and thought in Greek philosophy. This section examines the contribution of Anaxagoras and Empedocles. (shrink)

Epistemic approaches towards understanding ultimate reality proceed chiefly via the rational, the empirical, and the fideistic way, each yielding a theological view consistent to the approach chosen. Rational theologies tend to be ultimately monist in nature, while empirical theologies are pluralistic, e.g. polytheism. Fideism has its dangers as well where blind faith only hampers scientific research. However, Indian philosophy has suggested few criteria for verifying a source of authoritative testimony. This dissertation investigates why an authentic revelation would solve the ultimate (...) clash between reason and experience. (shrink)

According to the ancient Greek Stoics, the cosmos regularly transitions between periods of conflagration, during which only fire exists, and periods of cosmic order, during which the four elements exist. This paper examines the cosmogonic process by which conflagrations are extinguished and cosmic orders are restored, and it defends three main conclusions. First, I argue that not all the conflagration’s fire is extinguished during the cosmogony, against recent arguments by Ricardo Salles. Second, at least with respect to the cosmogony, it (...) is not necessary to posit the existence of proto-elements. Third, while scholars such as Salles and David Hahm have argued that Cleanthes held a distinct theory of cosmogony from Zeno and Chrysippus, I argue that each of these Stoics endorse the same cosmogonic theory. (shrink)

This submission constitutes six (core) pages in literary prose expounding the philosophy of Parmenides of Elea outside the reductionist framework based in formal logic that has become de rigeur in philosophy departments of the English language world — at least prior to Dr. Papa-Grimaldi’s research. To this end, my paper, in chronological order, by way of introduction simulates Plato’s Parmenides; in the main body reconstructs Taran’s argument in “Much Ado About ‘Nothing,’” in Apeiron, Vol. XXXV, No. 2, June 2002, (...) pp. 87-104; and in the final section which will be presented at the conference, breaks away into an original hermeneutics in dialogical format featuring Socrates as a guest dramatis personae charged with the task of reconstructing in a new key, on behalf of the author, Parmenides’s philosophy. (shrink)

We provide a new interpretation of Zeno’s Paradox of Measure that begins by giving a substantive account, drawn from Aristotle’s text, of the fact that points lack magnitude. The main elements of this account are (1) the Axiom of Archimedes which states that there are no infinitesimal magnitudes, and (2) the principle that all assignments of magnitude, or lack thereof, must be grounded in the magnitude of line segments, the primary objects to which the notion of linear magnitude applies. (...) Armed with this account, we are ineluctably driven to introduce a highly constructive notion of (outer) measure based exclusively on the total magnitude of potentially infinite collections of line segments. The Paradox of Measure then consists in the proof that every finite or potentially infinite collection of points lacks magnitude with respect to this notion of measure. We observe that the Paradox of Measure, thus understood, troubled analysts into the 1880’s, despite their knowledge that the linear continuum is uncountable. The Paradox was ultimately resolved by Borel in his thesis of 1893, as a corollary to his celebrated result that every countable open cover of a closed line segment has a finite sub-cover, a result he later called the “First Fundamental Theorem of Measure Theory.” This achievement of Borel has not been sufficiently appreciated. We conclude with a metamathematical analysis of the resolution of the paradox made possible by recent results in reverse mathematics. (shrink)

Some philosophers contend that the past must be finite in duration, because otherwise reaching the present would have involved the sequential occurrence of an actual infinity of events, which they regard as impossible. I recently developed a new objection to this finitist argument, to which Andrew Ter Ern Loke and Travis Dumsday have replied. Here I respond to the three main points raised in their replies.

The intention of this critical review of McTaggart’s 1908 paper is to bring about a distinction between Time and Motion . This distinction is crucial to our understanding of both time as well as motion because so far they have ben treated by all as one and the same. McTaggart, by at least recognizing two different “series” which he calls the A-series and the B-series, has given us a starting point to further understand this distinction. In the process of establishing (...) this distinction we will find ourselves encountering new concepts hitherto unrecognized in philosophy and physics and eventually understand the basis of the numerous paradoxes that time and motion involve dating all the way back to Zeno. (shrink)

a simple derivation of the effect induced from repeated measurements on quantum unstable systems is obtained by using the regularized incomplete beta - function .

This work deals with problems involving infinities and infinitesimals. It explores the ideas behind zero, its relationship to ontological nothingness, finititude (such as finite numbers and quantities), and the infinite. The idea of infinity and zero are closely related, despite what many perceive as an intuitive inverse relationship. The symbol 0 generally refers to nothingness, whereas the symbol infinity refers to ``so much'' that it cannot be quantified or captured. The notion of finititude rests somewhere between complete nothingness and something (...) having no end. -/- My concern is that many of the philosophers arguing for or against the ontology (or possibility) of an actual infinite set are unaware or unfamiliar with the mathematical literature attempting to clearly and rigorously define these terms. I believe it is a mistake to leave mathematicians out of this conversation, as analysts in particular have defined (and used) infinity in a way that is relevant to the ongoing debate between philosophers. -/- For this paper, I have selected examples from Principles of Analysis by Walter Rudin, which has become a standard text for Real Analysis classes taken by pure mathematicians and engineers. I will also restrict the scope of examples to Euclidean spaces for simplicity. Finally, I will be using addition, + and multiplication * in their usual way. (shrink)

What is so special and mysterious about the Continuum, this ancient, always topical, and alongside the concept of integers, most intuitively transparent and omnipresent conceptual and formal medium for mathematical constructions and the battle field of mathematical inquiries ? And why it resists the century long siege by best mathematical minds of all times committed to penetrate once and for all its set-theoretical enigma ? -/- The double-edged purpose of the present study is to save from the transfinite deadlock of (...) higher set theory the jewel of mathematical Continuum -- this genuine, even if mostly forgotten today raison d'etre of all set-theoretical enterprises to Infinity and beyond, from Georg Cantor to W. Hugh Woodin to Buzz Lightyear, by simultaneously exhibiting the limits and pitfalls of all old and new reductionist foundational approaches to mathematical truth: be it Cantor's or post-Cantorian Idealism, Brouwer's or post-Brouwerian Constructivism, Hilbert's or post-Hilbertian Formalism, Goedel's or post-Goedelian Platonism. -/- In the spirit of Zeno's paradoxes, but with the enormous historical advantage of hindsight, we claim that Cantor's set-theoretical methodology, powerful and reach in proof-theoretic and similar applications as it might be, is inherently limited by its epistemological framework of transfinite local causality, and neither can be held accountable for the properties of the Continuum already acquired through geometrical, analytical, and arithmetical studies, nor can it be used for an adequate, conceptually sensible, operationally workable, and axiomatically sustainable re-creation of the Continuum. -/- From a strictly mathematical point of view, this intrinsic limitation of the constative and explicative power of higher set theory finds its explanation in the identified in this study ultimate phenomenological obstacle to Cantor's transfinite construction, similar to topological obstacles in homotopy theory and theoretical physics: the entanglement capacity of the mathematical Continuum. (shrink)

From classical mechanics, in particular the motion in a straight line, together set theory and ordinal number theory, we prove a not-classical behaviour, a discontinuous motion and emission.