Zeno's Paradoxes: The Birth of Logical Thinking

Ancient Greek philosopher Zeno (490-430 bce) proposed a number of paradoxes (aporias) challenging logical thinking. Will Achilles ever catch a tortoise? Can a traveller reach their destination? Does an arrow actually move? Many scientists and philosophers have proposed their solutions to Zeno’s paradoxes since ancient times. It took thousands of years of the development of mathematics to solve these seemingly simple statements, though philosophers are still questioning their answers.

This class will be delivered online via the online platform Zoom. Enrolling students need to ensure they have an email, a reliable internet connection, microphone/speakers and access to a tablet, smartphone or computer.


  • Lewis Carroll. What the Tortoise Said to Achilles
  • Raymond M. Smullyan. Satan, Cantor, and Infinity. Mind-Boggling Puzzle. Chapters VI, VII. Dover Publication, Mineola, New York, 1992.


  • Acquaintance with the history of appearance of Zeno’s paradoxes. List of Zeno’s aporias as known from the Ancient Greek sources. Achilles and tortoise paradox. Traveller’s paradox. Arrow’s paradox. Heap of sand’s paradox.
  • Acquaintance with the history of attempts to solve the main paradoxes. Mathematical notion of countable infinity. Summing the infinite sets. Philosophical questions to the paradoxes. Modifications of Zeno’s paradoxes in the modern physics. More elementary logical paradoxes.


By the end of this course, students should be able to:

  1. Become familiar with the historical overview of the first steps of the Ancient Greek logical thinking.
  2. Know the main Zeno’s aporias, understand the notions of finite and infinite sets and know historical attempts of finding solutions to Zeno’s paradoxes.
  3. Become acquainted with sets’ summation. Become familiar with other amusing logical paradoxes.

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