Achilles and the Tortoise
The fastest runner alive can never catch a tortoise with a head start. The argument is airtight. So where does it go wrong?
c. 450 BCE15 min read
Era
Ancient
Before 500 CE
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Intermediate
Curious teenagers and general adult readers.
The Ship of Theseus
Replace a ship's planks one at a time until not one original piece is left. Is it still the same ship?
c. 75 CE (Plutarch's report of an older dispute)20 min read
The Paradox of the Court
A student agrees to pay for his lessons the day he wins his first case. He never takes a case. His teacher sues him for the money.
c. 420 BCE (traditional); earliest surviving account 2nd century CE20 min read
Meno's Paradox
How can you search for something you don't know? And how would you recognise it if you found it?
c. 380 BCE9 min read
Advanced
Undergraduate level in the relevant field.
The Liar Paradox
"This sentence is false." Decide whether you are looking at something true or something false, and see how far you get.
c. 600 BCE (the Epimenides line); c. 350 BCE (Eubulides' paradox)26 min read
Zeno's Dichotomy Paradox
To cross a room you must first cross half of it, then half of what is left, and so on without end. So how does anyone move?
c. 450 BCE18 min read
The Sorites Paradox
One grain of sand is not a heap. Adding a single grain never turns a non-heap into a heap. So heaps do not exist.
c. 350 BCE20 min read