Zenón de Elea: Filósofo griego. (c. a. C.) -Escuela eleática. – Es conocido por sus paradojas, especialmente aquellas que niegan la. INSTITUTO DE EDUCACION Y PEDAGOGIA Cali – valle 03 / 10 / ZENON DE ELEA Fue un filosofo Griego de la escuela Elitista (Atenas). Paradojas de Zenón 1. paradoja de la dicotomía(o la carrera) 2. paradja de aquiles y la tortuga. Conclusion Discípulo de parménides de Elea.

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These works resolved the mathematics involving infinite processes. When asked about his accomplices, Zeno said he wished to whisper something privately to the tyrant.

Examines the possibility that a duration does not consist of points, that every part of time has a non-zero size, that real numbers cannot be used as coordinates of times, and that paradojsa are no instantaneous velocities at a point. It points out that, although Zeno was correct in saying that at any point or instant before reaching the goal there is always some as yet uncompleted path to cover, this does not imply that the goal is never reached.

Through history, several solutions have elra proposed, among the earliest recorded being those of Aristotle and Archimedes. The Problem of Infinity Considered Historically”. A continuum is too smooth to be composed of indivisible points. Journal of Mathematical Physics. Also argues that Greek mathematicians did ce originate the idea but learned of it from Parmenides and Zeno. The arguments were paradoxes for the ancient Greek philosophers.

Zeno is wrong in saying that there is no part of the millet that does not make a sound: Aristotle believed Zeno’s Paradoxes were trivial and easily resolved, but later philosophers have lss agreed on the triviality. Here are examples of each: If everything is motionless at every instant, and time is entirely composed of instants, then motion is impossible. Aristotle was influenced by Zeno to use the distinction between actual and potential infinity as a way out of the paradoxes, and careful attention to this distinction has influenced mathematicians ever since.


Zeno’s Paradoxes

The scientist and historian Sir Joseph Needhamin his Science and Civilisation in Chinadescribes an ancient Chinese paradox from the surviving Mohist School of Names book of logic which states, in the archaic ancient Chinese script”a one-foot stick, every day take away half of it, in a myriad ages it will not be exhausted.

Jean Paul Van Bendegem has argued that the Tile Argument can be resolved, and that discretization can therefore remove the paradox. Regarding the Dichotomy Paradox, Aristotle is to be applauded for his insight that Achilles has time to reach his goal because during the run ever shorter paths take correspondingly ever shorter times.

However, Aristotle merely asserted this and could give no detailed theory that enables the computation of the finite amount of time.

Other Issues Involving the Paradoxes a. Aristotle ‘s treatment said Zeno should have assumed instead that there are only potential infinitiesso that at any time the hypothetical division into parts produces only a finite number of parts, and the runner has time to complete all these parts. Thomas Aquinascommenting on Aristotle’s objection, wrote “Instants are not parts of time, for time is not made up of instants any more than a magnitude is made of points, as we have already proved.

However, most commentators suspect Zeno himself did not interpret his paradox this way. The Bs are moving paeadojas the right, and the Cs are moving with the same speed to the left. If so, then choice 2 above is the one to think about. His Method Before Zeno, Greek thinkers favored presenting their philosophical views by writing poetry. Here is how Eleaa expressed the point:. Suppose Homer wishes to walk to the end of a path. Peirce, James Thomson, Alfred North Whiteheadand Hermann Weyl argued in different ways that the standard mathematical account of continuity does not apply to physical processes, or is improper for describing those processes.

Argues that a declaration of death of the program of founding mathematics on an intuitionistic basis is premature. Aristotle claimed correctly that if Zeno were not to have used the concept of actual infinity and of indivisible point, then the paradoxes of motion such as the Achilles Paradox and the Dichotomy Paradox could not be created.


Robinson went on to create a nonstandard model of analysis using hyperreal numbers. This standard real analysis lacks infinitesimals, thanks to Cauchy and Weierstrass.

Zenón de Elea

Some of Zeno’s nine surviving paradoxes preserved in Aristotle’s Physics [3] [4] and Simplicius’s commentary thereon are essentially equivalent to one another.

Diels, Hermann and W. In the early fifth century B. Zeno was epea trying to directly support Parmenides. Aristotle’s treatment xe the paradoxes does not employ these fruitful concepts of mathematical physics.

Each body is the same distance from its neighbors along its track. Ds are moving along a linear path at constant speeds. See Dainton pp. If so, these can be further divided, and the process of division was not complete after all, which contradicts our assumption that the process was already complete.

Their calculus is a technique for treating continuous motion as being composed of an infinite number of infinitesimal steps. Zeno’s Arrow and Stadium paradoxes demonstrate that the concept of discontinuous change is paradoxical.

Paradojas de Zenón by gabriela montaña on Prezi

The first is his Paradox of Alike and Unlike. Lawvere in the s resurrected the infinitesimal as an infinitesimal magnitude. Is it concrete or abstract? Intuitively, a continuum is a paradoas entity; it is a whole thing that has no gaps.

Zeno’s paradoxes – Wikipedia

Similarly a distance cannot be composed of point places and a duration cannot be composed of instants. It assumes that physical processes are sets of point-events. Well, the parts cannot be so small as to have no size since adding such things together would never contribute anything to the whole so far elex size is concerned.