Results for 'Zeno's paradoxes'

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  1. Why Zeno’s Paradoxes of Motion Are Actually About Immobility.Bathfield Maël - 2018 - Foundations of Science 23 (4):649-679.
    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 (...)
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  2. Zeno's Paradoxes.Nicholas Huggett - 2002
    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), (...)
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  3.  11
    Did Frege Solve One of Zeno’s Paradoxes?Gregory Lavers - 2020 - In Maria Zack & Dirk Schlimm (eds.), Research in History and Philosophy of Mathematics: The CSHPM 2018 Volume. Springer Verlag. pp. 99--107.
    Of Zeno’s book of forty paradoxes, it was the first that attracted Socrates’ attention. This is the paradox of the like and the unlike. On contemporary assessments, this paradox is largely considered to be Zeno’s weakest surviving paradox. All of these assessments, however, rely heavily on reconstructions of the paradox. It is only relative to these reconstructions that there is nothing paradoxical involved, or that there is some rather obvious mistake being made. This paper puts forward and defends a (...)
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  4. Mathematics, Models and Zeno's Paradoxes.Joseph S. Alper & Mark Bridger - 1997 - Synthese 110 (1):143-166.
    A version of nonstandard analysis, Internal Set Theory, has been used to provide a resolution of Zeno's paradoxes of motion. This resolution is inadequate because the application of Internal Set Theory to the paradoxes requires a model of the world that is not in accordance with either experience or intuition. A model of standard mathematics in which the ordinary real numbers are defined in terms of rational intervals does provide a formalism for understanding the paradoxes. This (...)
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  5. Modern Science and Zeno's Paradoxes of Motion.Adolf Grünbaum - 1970 - In Wesley C. Salmon (ed.), Zeno’s Paradoxes. Bobbs-Merrill. pp. 200--250.
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  6.  99
    Zeno's Paradoxes: A Timely Solution.Peter Lynds - 2003 - PhilSci Archive.
    Zeno of Elea's motion and infinity paradoxes, excluding the Stadium, are stated (1), commented on (2), and their historical proposed solutions then discussed (3). Their correct solution, based on recent conclusions in physics associated with time and classical and quantum mechanics, and in particular, of there being a necessary trade off of all precisely determined physical values at a time (including relative position), for their continuity through time, is then explained (4). This article follows on from another, more physics (...)
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  7. Why Mathematical Solutions of Zeno’s Paradoxes Miss The Point: Zeno’s One and Many Relation and Parmenides’ Prohibition.Alba Papa-Grimaldi - 1996 - Review of Metaphysics 50 (2):299 - 314.
    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 (...)
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  8. Zeno's Paradoxes and the Cosmological Argument.Jan Dejnozka - 1989 - International Journal for Philosophy of Religion 25 (2):65 - 81.
    I SHOW THAT THE COSMOLOGICAL ARGUMENT OF AQUINAS FOR THE EXISTENCE OF GOD COMMITS A RATHER TRIVIAL LINGUISTIC FALLACY, BY SHOWING THAT (1) SOME OF ZENO'S PARADOXES COMMIT A TRIVIAL LINGUISTIC FALLACY, AND THAT (2) THE COSMOLOGICAL ARGUMENT IS SUFFICIENTLY SIMILAR TO THESE PARADOXES THAT IT COMMITS THE SAME FALLACY. COPLESTON'S VIEW THAT "MENTION OF THE MATHEMATICAL INFINITE SERIES IS IRRELEVANT" TO "ANY" OF AQUINAS'S ARGUMENTS FOR GOD'S EXISTENCE IS THUS SHOWN FALSE.
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  9.  93
    Zeno's Paradoxes. A Cardinal Problem. 1. On Zenonian Plurality.Karin Verelst - 2006 - In J. Šķilters (ed.), Paradox: Logical, Cognitive and Communicative Aspects. Proceedings of the First International Symposium of Cognition, Logic and Communication,. University of Latvia Press.
    In this paper the claim that Zeno's paradoxes have been solved is contested. Although "no one has ever touched Zeno without refuting him" (Whitehead), it will be our aim to show that, whatever it was that was refuted, it was certainly not Zeno. The paper is organised in two parts. In the first part we will demonstrate that upon direct analysis of the Greek sources, an underlying structure common to both the Paradoxes of Plurality and the (...) of Motion can be exposed. This structure bears on a correct - Zenonian - interpretation of the concept of “division through and through”. The key feature, generally overlooked but essential to a correct understanding of all his arguments, is that they do not presuppose time. Division takes place simultaneously. This holds true for both PP and PM. In the second part a mathematical representation will be set up that catches this common structure, hence the essence of all Zeno's arguments, however without refuting them. Its central tenet is an aequivalence proof for Zeno's procedure and Cantor's Continuum Hypothesis. Some number theoretic and geometric implications will be shortly discussed. Furthermore, it will be shown how the “Received View” on the motion-arguments can easely be derived by the introduction of time as a (non-Zenonian) premiss, thus causing their collapse into arguments which can be approached and refuted by Aristotle's limit-like concept of the “potentially infinite”, which remained — though in different disguises - at the core of the refutational strategies that have been in use up to the present. Finally, an interesting link to Newtonian mechanics via Cremona geometry can be established. (shrink)
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  10.  49
    Grünbaum's Solution to Zeno's Paradoxes.J. Q. Adams - 1973 - Philosophia 3 (1):43-50.
    Zeno's paradoxes of motion are considered as challenges to the practice of describing motion in terms of continuous functions. A brief description of some work of adolf gruenbaum toward the resolution of these paradoxes is given. A new form of zeno's dichotomy paradox is described, And it is claimed that the paradox, In this form, Is not amenable to the explanations of gruenbaum. This is demonstrated by giving the new form of the paradox a second, More (...)
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  11.  52
    The Persuasiveness of Zeno's Paradoxes.John R. Mckie - 1987 - Philosophy and Phenomenological Research 47 (4):631-639.
    It has been argued that we find zeno's paradoxes of motion persuasive because physical time is dense and continuous, While time as we experience it is discrete. But we do not experience time as a succession of distinct, Countable, Consecutively ordered mental "nows." nor is it common to attempt the futile mental task of traversing in thought the infinite number of spatial subintervals in zeno's paradoxes, As has also been suggested. Rather, We find the paradoxes (...)
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  12.  44
    Zeno's Paradoxes and Continuity.Ian Mueller - 1969 - Mind 78 (309):129-131.
    In this note i argue against harold n. lee's assertion ("mind," october, 1965) that resolution of zeno's paradoxes is closely connected with the modern mathematical distinction between density and continuity. zeno's paradoxes would arise as much if space or time is dense as they do if it is continuous. in fact the paradoxes only arise if one combines a mathematical analysis of space and time with a non-mathematical conception of motion.
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  13.  35
    Zeno's Paradoxes on Motion.John O. Nelson - 1963 - Review of Metaphysics 16 (3):486 - 490.
    The author argues that, Although zeno's paradoxes on motion cannot be resolved in their own terms, They are nonetheless illegitimate. Examining the paradox of achilles and the tortoise, He finds that the mechanism of zeno's argument consists in an equivocal concept of motion characterized at once by a constant rate and by proportionate segments of movement. He then contends it is illegitimate to treat the concept of motion and its subconcepts like the postulates of a deductive system. (...)
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  14.  23
    Modern Science and Zeno's Paradoxes.H. P. K. - 1967 - Review of Metaphysics 21 (1):158-159.
    "There are no paradoxes in mathematics," says Kurt Gödel. Moreover, Gödel seems to be right on this count. That is, there are no paradoxes, in the strict sense of the word, internal to the known and available body of mathematical knowledge. But while there are no paradoxes in mathematics, there certainly is an embarrassing bag of difficulties when we come to the application of mathematical concepts to the physical world. Of these, perhaps the most unruly offenders of (...)
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  15. Zeno’s Paradoxes.Bradley Dowden - 2009 - Internet Encyclopedia of Philosophy.
     
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  16.  2
    Are Zeno’s Arguments Unsound Paradoxes?Guido Calenda - 2013 - Peitho 4 (1):125-140.
    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 (...)
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  17.  36
    Another Look at Some of Zeno's Paradoxes.Flash qFiasco - 1980 - Canadian Journal of Philosophy 10 (1):119 - 130.
    This article is an analysis of the logical structure of zeno's arguments without mathematical or metaphysical diversions. Topics of discussion include achilles and the stadium, Achilles and the tortoise, Compositeness of objects, The flying arrow.
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  18.  12
    The Rhetoric of Zeno's Paradoxes.Livio Rossetti - 1988 - Philosophy and Rhetoric 21 (2):145 - 152.
    A whole set of rhetorical maneuvers are at work in zeno's subtle logical creatures. Specially prominent (and unquestionably rhetorical in character) is a rather perverse move allowing zeno to persuade his potential audience that it is up to the reader to supply the missing qualifications without which no paradoxicality could emerge from his 'banal' stories, And to find good reasons for dismissing the most intuitive objections. Foundations for something like a 'rhetoric of paradoxicality' are given.
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  19.  88
    Zeno's Paradoxes and the Tile Argument.Jean Paul Van Bendegem - 1987 - Philosophy of Science 54 (2):295-302.
    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.
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  20.  46
    Zeno's Paradoxes and the Tile Argument.Jean Paul Bendegevanm - 1987 - Philosophy of Science 54 (2):295-.
    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.
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  21. Zeno’s Paradoxes.Wesley C. Salmon (ed.) - 1970 - Bobbs-Merrill.
    ABNER SHIMONY of the Paradox A PHILOSOPHICAL PUPPET PLAY Dramatis personae: Zeno , Pupil, Lion Scene: The school of Zeno at Elea. Pup. Master! ...
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  22.  68
    Zeno's Paradoxes and Temporal Becoming in Dialectical Atomism.Hristo Smolenov - 1984 - Studia Logica 43 (1-2):169 - 180.
    The homogeneity of time (i.e. the fact that there are no privileged moments) underlies a fundamental symmetry relating to the energy conservation law. On the other hand the obvious asymmetry between past and future, expressed by the metaphor of the arrow of time or flow of time accounts for the irreversibility of what happens. One takes this for granted but the conceptual tension it creates against the background of time''s presumed homogeneity calls for an explanation of temporal becoming. Here, it (...)
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  23. On a Version of One of Zeno's Paradoxes.Graham George Priest - 1999 - Analysis 59 (1):1–2.
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  24.  26
    On a Version of One of Zeno's Paradoxes.Graham George Priest - 1999 - Analysis 59 (1):1-2.
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  25.  57
    Are Zeno's Paradoxes Based on a Mistake?Harold N. Lee - 1965 - Mind 74 (296):563-570.
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  26. Towards a Definitive Solution of Zeno's Paradoxes.Fazal Ahmad Shamsi - 1973 - Hamdard Academy.
     
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  27.  47
    Zeno’s Paradoxes Still in Motion.Wilbur R. Knorr - 1983 - Ancient Philosophy 3 (1):55-66.
  28.  42
    Zeno's Paradoxes - Rafael Ferber: Zenons Paradoxien der Bewegung und die Struktur von Raum und Zeit. Pp. vii + 100. Munich: C. H. Beck, 1981. Paper, DM. 32. [REVIEW]Malcolm Schofield - 1982 - The Classical Review 32 (02):188-189.
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  29.  26
    Reply to J. Q. Adams' “Grünbaum's Solution to Zeno's Paradoxes”.Adolf Grünbaum - 1973 - Philosophia 3 (1):51-57.
  30. Time and Paradox: Bertrand Russell and Slavoj Žižek on Zeno's Paradoxes of Motion.Jean P. Tan - 2007 - Budhi: A Journal of Ideas and Culture 11 (1):11-54.
     
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  31.  31
    Zeno's Paradoxes.Malcolm Schofield - 1982 - The Classical Review 32 (02):188-.
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    Zeno's Paradoxes.N. Booth - 1957 - Journal of Hellenic Studies 77 (2):187-201.
  33.  31
    Zeno's Paradoxes.Andrew Ushenko - 1946 - Mind 55 (218):151-165.
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  34.  10
    Zeno's Paradoxes[REVIEW]Malcolm Schofield - 1982 - The Classical Review 32 (2):188-189.
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  35.  11
    Modern Science and Zeno's Paradoxes.R. G. Swinburne - 1969 - Philosophical Books 10 (2):8-9.
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  36.  13
    Modern Science and Zeno's Paradoxes.Geometry and Chronometry in Philosophical Perspective.John North & Adolf Grunbaum - 1970 - Philosophical Quarterly 20 (80):296.
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  37.  10
    WESLEY C. SALMON: "Modern Science and Zeno's Paradoxes".Richard Norman - 1999 - Ratio 12 (2):178-194.
  38.  14
    Zeno's Paradoxes of Motion.James F. O'Brien - 1963 - Modern Schoolman 40 (2):105-137.
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  39.  9
    "Zeno's Paradoxes," Ed. Wesley C. Salmon.Martin D. O'Keefe - 1972 - Modern Schoolman 49 (3):291-291.
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  40.  16
    Zeno's Paradoxes.C. Mortensen - unknown
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  41. Zeno’s Paradoxes. A Cardinal Problem. I. On Zenonian Plurality.Karin Verelst - 2005 - The Baltic International Yearbook of Cognition, Logic and Communication 1.
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  42.  44
    Zeno’s Dichotomy and Achilles Paradoxes.J. A. Faris - 1986 - Irish Philosophical Journal 3 (1):3-26.
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  43. Another Note on Zeno's Arrow.Ofra Magidor - 2008 - Phronesis 53 (4-5):359-372.
    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. (...)
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  44.  60
    Time is Double the Trouble: Zeno’s Moving Rows.Barbara Sattler - 2015 - Ancient Philosophy 35 (1):1-22.
    Zeno’s Moving Rows paradox is the only paradox among his four paradoxes of motion that is usually skipped over as being of no philosophical interest. This paper aims to give a new diagnosis of the Moving Rows paradox, a diagnosis that allows us to see it as raising a philosophically interesting problem concerning the relationship of time, space, and motion. It shows the consequences of confusing time’s dependence on the space covered in a motion with time’s dependence on the (...)
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  45. Zeno's Metrical Paradox of Extension.Adolf Grünbaum - 1967 - In Wesley C. Salmon (ed.), Zeno’s Paradoxes. Bobbs-Merrill. pp. 176--199.
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  46.  32
    Zeno’s Boêtheia Tôi Logôi.Phil Hopkins - 2006 - Epoché: A Journal for the History of Philosophy 11 (1):1-25.
    This essay addresses two central issues that continue to trouble interpretation of Zeno’s paradoxes: 1) their solution, and 2) their place in the history of philosophy. I offer an account of Zeno’s work as pointing to an inevitable paradox generated by our ways of thinking and speaking about things, especially about things as existing in the continua of space and time. In so doing, I connect Zeno’s arguments to Parmenides’ critique of “naming” in Fragment 8, an approach that I (...)
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  47.  44
    Zeno's Arrow and the Significance of the Present.Robin LePoidevin - 2002 - Royal Institute of Philosophy Supplement 50:57-.
    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 (...)
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  48.  31
    Zeno’s Paradox for Colours.Barry Smith - 2000 - In O. K. Wiegand, R. J. Dostal, L. Embree, J. Kockelmans & J. N. Mohanty (eds.), Phenomenology of German Idealism, Hermeneutics, and Logic. Dordrecht. pp. 201-207.
    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 subregions such 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 (...)
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  49. Einstein’s “True” Discontinuity: With an Application to Zeno.Constantin Antonopoulos - 2008 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 23 (3):339-349.
    The question whether quantum discontinuity can or cannot provide an answer to Zeno’s Paradoxes is reopened. It is observed that what is usually understood by the term “discontinuity”, namely, Einstein’s conception of the photon as described by himself and all others, is unsuitable to the task because, essentially, it reduces to the trivial ‘discontinuity’ of objects scattered in space. By contrast, quantization of energy levels, which are not in space but can only alternate in time, provide the right sort (...)
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  50. Modern Science and the Refutation of the Paradoxes of Zeno.Adolf Grünbaum - 1955 - In Wesley C. Salmon (ed.), Zeno’s Paradoxes. Bobbs-Merrill. pp. 164--175.
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