Hilbert's fully-booked hotel always finds room for one more
David Hilbert's 1924 thought experiment of a hotel with infinite rooms shows how infinity breaks the ordinary rules of counting.
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Brillo Box: the Warhol that made Arthur Danto end art's story
In 1964 Arthur Danto saw Warhol's Brillo boxes and could not tell them from the real thing. He concluded that art's story, though not art, had ended.
A pope's letter set Roger Bacon writing the Opus Majus
In 1266 Pope Clement IV asked a confined Franciscan friar for his writings. Roger Bacon had none, so he spent a year writing the Opus Majus.
A donkey with no reason to choose starves where it stands
Buridan's ass starves between two equal piles of hay because it has no reason to choose. The tale is usually read as an argument against free will.
Advaita Vedanta holds that your self and reality are one
The Indian school holds that the self, atman, is brahman. Maya makes the one reality look like many, and grasping this ends the cycle of rebirth.
Marcus Aurelius may not have been the Stoic he described
Marcus Aurelius left a notebook of Stoic reminders. He spared a rebel's backers, but made Commodus co-emperor at sixteen and sought to destroy the Iazyges.
Anthropic's alignment lead puts AI extinction risk above 10%
In a 2024 survey of nearly 3,000 AI researchers, over half put the odds of AI causing human extinction or disempowerment at 10 per cent or more.
Judith Jarvis Thomson named the trolley problem, then doubted it
The philosopher who named the trolley problem later said you may not pull the switch unless you would steer it into yourself. West Point still teaches it.
Sandel's Justice was the first Harvard course put online free
The lectures reached tens of millions of viewers. Critics called the edX version, JusticeX, old footage with quizzes, no better than assigning a book.
Alan Turing swapped 'Can machines think?' for a game
Alan Turing's 1950 imitation game asks a judge to tell human from machine by typed questions. His own sample machine got a sum wrong.
Wittgenstein argued a truly private word can never be corrected
Wittgenstein argued a language only one person could understand fails, because nothing outside that person could catch a wrong use of a word.
Bernard Williams used Gauguin to put luck into morality
In his 1976 essay on moral luck, Bernard Williams asked if Gauguin's success could justify leaving his family. Critics say it barely weighs the harm done.
The panopticon was designed so no one had to watch all the time
Bentham's panopticon put a tower inside a ring of cells. Prisoners could not see the watchman, so they had to assume someone was looking, at minimal cost.