The History of Zeno's Arguments on Motion: Phases in the Development of the Theory of Limits

Jul 9, 2026

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Historical analysis of Zeno’s arguments on motion and their role in shaping continuity, the infinite, and the infinite/infinitesimal. Florian Cajori surveys how interpretations evolved from ancient sources to later mathematical frameworks, noting that Zeno’s original writings survive only indirectly through critics and commentators such as Plato, Aristotle, and Simplicius. The discussion contrasts differing views on Zeno’s purpose and presents Aristotle’s condensed assessment of major paradoxes—Dichotomy, Achilles, Arrow, and Stade.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages62

Reading Time2 h 36 min

A. The Purpose of Zeno's Arguments

Introduction

Aristotle’s Interpretation of Zeno's Arguments

# THE HISTORY OF ZENO'S ARGUMENTS ON MOTION:PHASES IN THE DEVELOPMENT OF THE THEORY OF LIMITS.By FLORIAN CAJORI,Colorado College.SSI-X.(Yes:all in one complete document.)The American Mathematical Monthby 22(1915). Early Journal Content on JSTOR,Free to Anyone in the World This article is one of nearly 500,000 scholarly works digitized and made freely available to everyone inthe world by JSTOR. Known as the Early Journal Content,this set of works include research articles,news,letters,and otherwritings published in more than 200 of the oldest leading academicjournals.The works date from themid-seventeenth to the early twentieth centuries. We encourage people to read and share the Early Journal Content openly and to tell others that thisresource exists.People may post this content online or redistribute in any way for non-commercialpurposes. Read more about Early Journal Content at http://about.jstor.org/participate-jstor/individuals/early- journal-content. JSTOR is a digital library of academic journals,books,and primary source objects.JSTOR helps peoplediscover,use,and build upon a wide range of content through a powerful research and teachingplatform,and preserves this content for future generations.JSTOR is part of ITHAKA,a not-for-profitorganization that also includes Ithaka S+R and Portico.For more information about JSTOR,pleasecontact support@jstor.org. THE AMERICANMATHEMATICAL MONTHLY | VoLUME XXII | | JANUARY,1915 | NUMBER 1 | | | --- | --- | --- | --- | --- | # THE HISTORY OF ZENO'S ARGUMENTS ON MOTION: PHASE3 IN THE DEVELOPMENT OF THE THEORY OF LIMITS. By FLORIAN CAJORI,Colorado College. I. ## A.THE PURPOSE OF ZENo's ARGUMENTS. Introduction.No questions on the foundations of mathematics are as oldand of such perennial interest,reaching into the most recent speculations on thephilosophy of mathematics,as are Zeno's arguments on motion.Zeno flourishedin the fifth century before Christ,but only recently has G.Cantor's Mengenlehrebeen applied to the fuller elucidation of Zeno's paradoxes.The history of theseparadoxes is largely the history of concepts of continuity,of the infinite andinfinitesimal. There has been great difference of opinion as to the exact nature and purposeof Zeno's arguments.None of Zeno's writings have come down to us.We knowof his tenets only through his critics and commentators—Plato,Aristotle andSimplicius.Plato was born about 60 years after Zeno,Aristotle about 100 yearsafter.Simplicius lived nearly 1,000 years after Zeno.Plato does not reproduceZeno's arguments,but discusses their purpose,which was"to protect the argu-ments of Parmenides against those who make fun of him and seek to show themany ridiculous and contradictory results which they suppose to follow fromthe affirmation of the one”;Zeno argues that“there is no many,"he“deniesplurality.” Aristotle's Interpretation of Zeno's Arguments.Aristotle gives in very com-pressed form the arguments on motion,as they were handed down to him,inthese words:2 ZENO's ARGUMENTS ON MOTION “Zeno reasons here incorrectly;for,he says that everything,when in a uniform state,iscontinually either at rest or in motion,and that a body moving in space is continually in theNow [the instant],hence the arrow in its flight is at rest.But this is false,for the reason thattime is not composed of individual,indivisible Nows,as also no other quantity is so composed.There are four proofs advanced by Zeno against motion,which present many difficuties to thosewho try to refute them.The first is the one on the impossibility of motion,on the ground that athing moving in space must arrive at the mid-point before it reaches the end-point.We havegone into the details oi this matter in our previous discussion.The second is the so-called Achilles;it consists in this that in a race the faster cannot overtake the slower;for,the pursuer must alwaysfirst arrive at the point from which the one pursued has just de

FAQs

Why are Zeno’s arguments on motion considered historically significant?

They have remained a perennial topic because they connect ancient debates to modern foundations of mathematics, especially issues of continuity and the infinite/infinitesimal.

What is the source basis for understanding Zeno’s original arguments?

No Zeno writings have survived; the arguments are known through critics and commentators including Plato, Aristotle, and Simplicius.

How does Aristotle summarize key difficulties in Zeno’s reasoning about motion?

Aristotle argues that Zeno’s conclusions rely on treating time as made of indivisible “Nows,” which undermines claims such as the moving arrow being at rest, and he groups four main proofs (Dichotomy, Achilles, Arrow, and Stade).

Jul 9, 2026

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