Dunning-Kruger Effect
The less you know, the more confident you feel. The more you know, the more you see how much you don't. Why?
19996 min read
Domain
Philosophy
Paradoxes that press on what exists, what we can know, and what words mean.
38 entriesFilter these further →
Beginner
Ages 8+, no background needed.
Hilbert's Grand Hotel
A hotel with infinitely many rooms is completely full. At two in the morning, one more guest arrives. The manager finds them a room.
1924 (lectures), 1947 (popularised)13 min read
Murphy's Law
If anything can go wrong, will it? The saying is a joke — but the engineering principle behind it is dead serious.
19497 min read
Occam's Razor
When two explanations fit the evidence equally, which should you believe? The one that assumes less.
c. 13206 min read
The Butterfly Effect
Can a butterfly in Brazil cause a tornado in Texas? Not by force — but by changing everything that follows.
1963 (discovery), 1972 (butterfly metaphor coined)7 min read
Amara's Law
Every major technology is overhyped on arrival and underestimated a decade later. Why does intuition fail in the same direction twice?
19776 min read
Baader-Meinhof Phenomenon
You learn a new word. Within a week, you hear it three times. Did the world start using it when you did — or did you just stop filtering it out?
20066 min read
Brandolini's Law
A tweet spreads a false claim to a million people. Correcting it requires essays and citations. Why does the truth always have to work harder?
20137 min read
Buridan's Ass
A donkey stands exactly halfway between two identical bales of hay. With no reason on earth to prefer either, does it starve?
c. 1340 (the attribution; the example is far older)14 min read
Chesterton's Fence
You find a fence in the middle of a field with no obvious purpose. Remove it? Chesterton says no — and the reason reveals something about reform.
19297 min read
Hanlon's Razor
They didn't do it to hurt you. Probably they just didn't think. How much does it matter?
19806 min read
Semmelweis Reflex
A doctor proved handwashing saved lives. He had the data. The medical profession ignored him for twenty years. Why does evidence trigger resistance?
18476 min read
The Barber Paradox
The barber shaves every man in town who does not shave himself, and no one else. So who shaves the barber?
1918 (Russell's lectures); the story circulated earlier11 min read
The Coastline Paradox
How long is the coastline of Britain? The answer depends on how you measure it. As the ruler gets shorter, the answer grows without bound.
1951 (Richardson), 1967 (Mandelbrot)7 min read
Intermediate
Curious teenagers and general adult readers.
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
Schrödinger's Cat
A cat sealed in a box, neither alive nor dead until somebody looks. The story was invented to show the idea was absurd.
193514 min read
The Fermi Paradox
The universe is ancient, enormous, and full of ordinary stars much like ours. So where is everybody?
1950 (Fermi's remark), 1975 (Hart's argument)22 min read
The Grandfather Paradox
Travel back in time and stop your own grandparents from ever meeting. Then who was it that went back?
1943 (Barjavel's novel), with antecedents from the 1920s18 min read
The Paradox of Tolerance
A society that tolerates absolutely everything, including those working to end it, does not remain tolerant for long.
19458 min read
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
Galileo's Paradox
There are exactly as many square numbers as there are numbers, even though almost every number is not a square.
163813 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
The Grelling-Nelson Paradox
Is the word "heterological" heterological? Either answer generates a contradiction.
19087 min read
The Tristram Shandy Paradox
A man writes his autobiography but keeps falling behind. If he had infinite time, would he ever catch up?
1759 (novel), 1903 (paradox formulated)8 min read
Advanced
Undergraduate level in the relevant field.
Russell's Paradox
Consider the set of all sets that do not contain themselves. Does that set contain itself? Either answer is wrong.
1901 (discovered), 1902 (letter to Frege), 1903 (published)19 min read
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
Newcomb's Problem
The boxes are already filled. Does choosing one still change what is in them?
c. 1960 (posed), 1969 (published)10 min read
The Sleeping Beauty Problem
Woken with no memory of having been woken before, how confident should you be that the coin came up heads?
1997 (posed), 2000 (named and popularised)24 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
The St. Petersburg Paradox
A coin-flipping game whose average winnings are infinite. How much of your own money would you actually pay to play?
1713 (posed by Nicolaus Bernoulli), 1738 (published by Daniel Bernoulli)19 min read
The Two Envelopes Problem
One envelope holds twice as much money as the other. The arithmetic says swap — then says swap back, forever.
1953 (Littlewood, crediting Schrödinger), 1989 (envelope form)19 min read
The Unexpected Hanging Paradox
A prisoner is told he will hang next week, on a day he cannot possibly predict. He proves it cannot happen. It happens.
1943 (in circulation), 1948 (first in print)21 min read
The Ross-Littlewood Paradox
You add ten balls and remove one, infinitely many times. At the end, the vase is empty. What happened to all the balls?
19887 min read
Expert
Graduate level or specialist readers.
Gödel's Incompleteness Theorems
In any system of arithmetic strong enough to be useful, there are true statements it can never prove. Including this one.
193125 min read
The Banach–Tarski Paradox
Cut a solid ball into five pieces, move them around, and you have two balls the same size as the first. Nothing was stretched.
192423 min read
The EPR Paradox
Measure one particle here and you instantly know something about its partner light-years away. Einstein thought this proved physics was unfinished.
1935 (argument), 1964 (Bell's theorem), 2015 (loophole-free tests)21 min read