Talk:Zeno's paradoxes

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Former good article Zeno's paradoxes was one of the Philosophy and religion good articles, but it has been removed from the list. There are suggestions below for improving the article to meet the good article criteria. Once these issues have been addressed, the article can be renominated. Editors may also seek a reassessment of the decision if they believe there was a mistake.


Bibliography[edit]

This list is intended to collect references thought to be relevant for the article. Delete entries only when they are blatantly and obviously inappropriate. In general, we want not only to collect useful references, but also be able to check new additions against previous discussions that lead to exclusion. Provide diffs, and update section links when they get archived.

The 2001 edition of Salmon's anthology lists at least 218 sources, so it is safe to say that this bibliography cannot be considered anywhere near comprehensive before we have passed the 200 mark.

Salmon's book is one of the best on the subject. Huggett, in his article "Zeno's Paradoxes" in the Stanford Encyclopedia of Philosophy [1] writes: After the relevant entries in this encyclopedia, the place to begin any further investigation is Salmon (2001), which contains some of the most important articles on Zeno up to 1970, and an impressively comprehensive bibliography of works in English in the Twentieth Century . Paul August 14:22, 13 February 2010 (UTC)
The bibliography of my 1970 hardcover edition has 143 entries, the 2001 edition cited above has at least 218 (preview limit, sorry). Paradoctor (talk) 08:32, 25 February 2010 (UTC)
Abstract from the official page at Springer: "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 model suggests that in discussing motion, only intervals, rather than instants, of time are meaningful. The approach presented here reconciles resolutions of the paradoxes based on considering a finite number of acts with those based on analysis of the full infinite set Zeno seems to require. The paper concludes with a brief discussion of the classical and quantum mechanics of performing an infinite number of acts in a finite time."
Pages 14-15 (section 3 "Infinite Time" of chapter 1 "the Container of All Things") discuss the arrow paradox.
Footnote 10 on page 410 (for page 15 in section 3 "Infinite Time" of chapter 1 "the Container of All Things") discusses "proposals at the ability to cross an infinite provided infinite acceleration is assumed".
From Amazon's author page (WebCite): 'Kip Sewell holds an MLIS from the University of South Carolina and currently works as an information professional. He has also received BA and MA degrees in Philosophy and has been a college lecturer. "The Cosmic Sphere" (1999) is Sewell's first work on the subject of cosmology. He is currently revising the book and continues to explore issues in science, philosophy, and theology as an independent researcher.'
Apart from this book, Scirus, Google Scholar and WorldCat turned up nothing by Sewell.
IMO, a minor primary source, apparently not peer-reviewed, by a philosopher very early in his career. Paradoctor (talk) 01:17, 2 March 2010 (UTC)
Defines "Zeno behavior", a concept from the field of verification and design of timed event and hybrid systems.
Criticizes the "Received View" on Zeno as untenable. Maintains that a "generally overlooked" key to Zeno arguments is that "they do not presuppose space, neither time". Paradoctor (talk) 17:33, 5 March 2010 (UTC)
Her official homepage (5 March 2010) Paradoctor (talk) 19:52, 5 March 2010 (UTC)

to do[edit]

  • Paul Hornschemeier's most recent graphic novel, The Three Paradoxes, contains a comic version of Zeno presenting his three paradoxes to his fellow philosophers.
  • Zadie Smith references Zeno's arrow paradox, and, more briefly, Zeno's Achilles and tortoise paradox, at the end of Chapter 17 in her novel White Teeth.
  • Brian Massumi shoots Zeno's "philosophical arrow" in the opening chapter of Parables for the Virtual: Movement, Affect, Sensation.
  • Philip K. Dick's short science-fiction story "The Indefatigable Frog" concerns an experiment to determine whether a frog which continually leaps half the distance to the top of a well will ever be able to get out of the well.
  • Allama Iqbal's book The Reconstruction of Religious Thought in Islam discusses the paradox in Lecture II The Philosophical Test of the Revelations of Religious Experience, and suggests that motion is not continuous but discrete.
  • Ursula K. Le Guin's character of Shevek in The Dispossessed discusses the arrow paradox in great amusement with his un-understanding classmates as a child.
  • add missing refs from Rucker section below
  • add refs deleted with this edit

Dichotomy paradox[edit]

"Suppose Homer wants to catch a stationary bus." As in, Homer Simpson? Can we do no better? --Thrissel (talk) 20:24, 5 July 2013 (UTC)

No. As in Homer. You know? The famous Greek epic author? 96.251.85.48 (talk) 05:34, 27 August 2013 (UTC)

Misconception?[edit]

Zeno's arguments are often misrepresented in the popular literature. That is, Zeno is often said to have argued that the sum of an infinite number of terms must itself be infinite–with the result that not only the time, but also the distance to be travelled, become infinite.[33] However, none of the original ancient sources has Zeno discussing the sum of any infinite series. Simplicius has Zeno saying "it is impossible to traverse an infinite number of things in a finite time". This presents Zeno's problem not with finding the sum, but rather with finishing a task with an infinite number of steps: how can one ever get from A to B, if an infinite number of (non-instantaneous) events can be identified that need to precede the arrival at B, and one cannot reach even the beginning of a "last event"?[4][5][6][34]

However, this "misconception" is mathematically the same as what Zeno says. "it is impossible to traverse an infinite number of things in a finite time" is equivalent to saying if we sum an infinite number of finite times, we end up with infinite time. And since Achilles is traveling at fixed speed, there is a fixed coorespondance between distance and time, and so we arrive at infinite distance. The only difference is that Zeno did not know what an infinite series was to state his objection in terms of a sum. 96.251.85.48 (talk) 05:30, 27 August 2013 (UTC)

Infinite Series[edit]

I've just deleted two sentences [2]. The first was an opinion - it is not task of an entry to tell what is evident, and the second nonsense. Infinite series converge. Full stop. At least some of them (The harmonic series doesn't). They do not converge with "precision", and quanta have certainly nothing to do with any mathematical proof that series converge (or not). Ansgarf (talk) 17:46, 23 September 2013 (UTC) Ansgarf (talk) 17:48, 23 September 2013 (UTC)

The last bit "particularly since there is in fact minimum expanses of time and space (quanta)" makes me think that Steaphen is back. It was added early September [3] Ansgarf (talk) 17:48, 23 September 2013 (UTC)

Merger proposal[edit]

I propose that Millet paradox be merged into Zeno's paradoxes. I think that the content in the Millet paradox article can easily be explained in the context of Zeno's paradoxes, and the Zeno's paradoxes article is of a reasonable size that the merging of Millet paradox will not cause any problems as far as article size or undue weight is concerned. Tco03displays (talk) 01:04, 4 December 2013 (UTC)

Yes check.svg Done
Support I see no objections. Be WP:BOLD. ;) Paradoctor (talk) 01:35, 4 December 2013 (UTC)×
It is already included in Zeno's paradoxes#Three other paradoxes as given by Aristotle--JimWae (talk) 21:04, 4 December 2013 (UTC)