Talk:Zeno's paradoxes

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Former good articleZeno'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.
Article milestones
February 13, 2006Good article nomineeListed
September 14, 2006Good article reassessmentDelisted
Current status: Delisted good article


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.

  • Grünbaum, Adolf (1967). Modern science and Zeno's paradoxes. Wesleyan University Press. Retrieved 13 February 2010.
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)
  • Paul A. Fishwick, ed. (1 June 2007). "15.6 "Pathological Behavior Classes" in chapter 15 "Hybrid Dynamic Systems: Modeling and Execution" by Pieter J. Mosterman, The Mathworks, Inc.". Handbook of dynamic system modeling. Chapman & Hall/CRC Computer and Information Science (hardcover ed.). Boca Raton, Florida, USA: CRC Press. pp. 15–22 to 15–23. ISBN 9781584885658. Retrieved 5 March 2010.
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

Non-Standard (hyperreal) solutions[edit]

The turtle-like and arrow-like paradox is easily solved in Non Standard Analysis. Despite using "non-real", that is hyperreal numbers the solution holds for the "real" world.

The argument follows the general scheme that from the movement from one point to another, which are , however, at a distance of zero (0) apart from each other an infinite number of steps would be necessary, which could not be done. Let d be a real distance between start and finish. There must be infinite many points in between. An infinite number is not real, but can be written as a hyperreal number represented by the sequence [1;2;3;4;5;...] whereas a real number (e.g. 2) would be written as [2;2;2;2;...]. The infinite sequence of the infinite number surely is larger at almost all places than any sequence for a real number, hence it is realy infinite. By dividing the real distance [d;d;d;d;d;...] by [1;2;3;4;5;...] one yield the distance of two neighbouring points [d;d/2;d/3;d/4;d/5;...] which is clearly smaller than any real positive number, but also clearly larger than real zero.

Hence, in an instant - an infinitesimal small amount of time which can be represented by any infinitesimal small number like [1;1/2;1/3;1/4;...] the arrow indeed proceeds no space as [d;d/2;d/3;d/4...] is the nothingness of the distance of two neighbouring points. However, doing this flight infinite times one yields both, a real time needed to go from one starting point to a distant finish, and a real travelled distance.

The paradox is just a misconception of infinte (big) and infinitesimal (small, but not exactly zero). While the classical convergence criteria as the delta epsilon proof deliver a sound capture of defining a limit, they still do this with an aproximation to "infinite" although this quantity is nort part of the real number system. Those classical proofs still lack an universal proper treatment of infinity as they correctly state that "the usual algebraic rules" do not hold for infinity as "infinty + 1 is not more as infinity". Despite this limitation to standard rules these proofs use the operator "do this infinitively often". Weierstrass however argued correctly, as infinity + 1 shall equal infinity itself, a limit will exist if after doing something infinitively often and then do it once more the result is still the same. Non Standard Analysis prooves this to be not quite correct in the realm of hyperreals, however, the tranfer back to real numbers will exactly deliver the same result. — Preceding unsigned comment added by (talk) 15:27, 17 November 2016 (UTC)

"Chinese equivalents" IP-editor back[edit]

An IP-editor, using different IPs each time, has edited warred, without discussion, to make this edit. See previous discussions (now archived): Talk:Zeno's paradoxes/Archive 8#Chinese equivalents "Chinese equivalents" "Semi-protect needed". I've reverted but I expect the IP-editor to continue to insist on this edit with no discussion. The page will probably need to be semi-protected again (:@Materialscientist:). Paul August 11:24, 27 November 2016 (UTC)

(@Materialscientist:) And now again. Paul August 11:58, 2 December 2016 (UTC)
And again. I concur with Paul. --Bill Cherowitzo (talk) 17:08, 2 December 2016 (UTC)

New solution proposed for paradoxes of motion[edit]

I just want to inform the community about a new solution for paradoxes of motion, which was recently published in the journal Foundations of Science : (or full access here: )
I leave contributors decide on the relevance of adding this solution in the section 'Proposed solutions' of the article.

MaelBathfield (talk) 10:35, 23 November 2017 (UTC)

Fails to mention Differential Equations and multi-variable calculus[edit]

In most forms of physics that use differential equations, an object has several properties: Mass, location, direction, and spin. Each of these properties are independent. At any incident of time, the object has a vector and a spin. Keeping track of all of the above is the function of differential equations, which show that discrete slices of an object can be frozen in time while preserving the information for the vector. (talk) 05:48, 2 December 2017 (UTC)