Tag Archives: Anti-foundation Axiom

A paradox, and where it led

What is the difference between a contradiction and a paradox? A contradiction is a dead end, a sign that the road leads nowhere and you should turn back and take the other road. A paradox, however, is an invitation to … Continue reading

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The random graph and anti-foundation

Last year, Bea Adam-Day, one of my undergraduate project students, settled a question that had been bugging me for years. According to the downward Löwenheim–Skolem Theorem of first-order logic (a consequence of the proof of Gödel’s Completeness Theorem), if a … Continue reading

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