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Walter Burley (c. 1275-1344/5) provides a humorous example of the failure of the chain rule (P -> Q and Q -> R implies P -> R):
1. If I say you are a donkey, I say that you are an animal.
2. If I say that you are an animal, I say something true.
3. If I say you are a donkey, I say something true.
<smirk>
1. If I say you are a donkey, I say that you are an animal.
2. If I say that you are an animal, I say something true.
3. If I say you are a donkey, I say something true.
<smirk>