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Philosophy

The Philosophy of Mathematical Logic and the Foundations of Arithmetic

Quick fact

In 1931, Kurt Gödel proved that any consistent formal system powerful enough to express basic arithmetic cannot prove all true statements about numbers—there will always be true but unprovable arithmetic truths.

Why this is interesting

We all count things every day—but what exactly are numbers? Are they real objects, just useful fictions, or something in between? The answer turns out to shake the very foundations of mathematics.

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