If you have a systematic language with a large vocabulary, you will end up with a lot of nonsense. For example, besides sentences like ‘The number two is a prime’ and ‘Julius Caesar conquered Gaul’, you also get ‘The number two conquered Gaul’ and ‘Julius Caesar is a prime’. Since Gilbert Ryle's 1949 The Concept of Mind, philosophers have referred to these absurd sentences as category mistakes. The idea is that their subjects pick out an entity of the kind to which their predicate cannot be applied.

Alas, this gloss doesn't really single out category mistakes. We could say that ‘Napoleon's white horse was true’ is a category mistake because Napoleon's white horse is not the kind of thing that could be true. But then why is ‘Napoleon's white horse was blue’ not a category mistake? After all, a white horse is...

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