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Logic

In Our Time

00:00

The Paradox of Classes

Russell was trying to define number in terms of classes of things. Some classes are members of the class of classes, okay? But some classes are class of teaspoons, and not themselves teaspoons. So you've got a contradiction. If this idea of classes can generate a paradox in that way, then you can't use it to try to define the basic notions of arithmetic. Remember that arithmetic can take translations from all the other branches of mathematics.

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