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Logic

In Our Time: Philosophy

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Defining Number in a Numerical Way

Russell was trying toa define number in terms of classes of things. Some, some classes are ar members of the class of classes, ok? But some classes, or a class oftea ns ard, not themselves. You've got a contradiction. To avoid it, you have to introduce this rather adhock manoeuvr of inventing a hierarchy. And and that the higher levels of the hierarchy can take as members members of the lower levels,. but they can't take members at the same level.

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