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In this sentence, Semantically 'his' and 'John' come to refer to the same person.

Hence, both "his" and "John" are co-indexed.

However,Principle C states that an R-expression like "John" needs to be free and not bound to an antecedent.

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Well, either that or, more likely, an account that makes "John" bound is mistaken. It is pretty obvious that "John" in the example is not a bound variable.

There is parallelism here between "command" and "C-command". Backwards pronominalization within the same sentence is okay when antecedent does not command the pro-form and neither does the pro-form command the antecedent. E.g., "The man who first saw her (= Mary) took charge of the donkey Mary was riding." In your example backwards pronominalization in the same sentence is okay when the antecedent does not C-command the pro-form, and neither does the pro-form C-command the antecedent.

Backwards pronominalization is also sometimes okay when the antecedent does command or C-command the pro-form:

"The man who first saw her followed Mary closely."  
"His mother always loved John best."

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