In mathematical languages and in predicate logic coreferential terms can be interchanged in any sentence without altering the truth value of that sentence. Replacing 3 + 5 by 12 − 4 in any formula of arithmetic will never lead from truth to falsity or from falsity to truth. But natural languages are different in this respect. While in some contexts it is always allowed to interchange coreferential terms, other contexts do not admit this. An example of the first sort of context is likes bananas: for any two coreferential noun phrases A and B the sentence A likes bananas is true if and only if B likes bananas is. A context that does not allow intersubstitution of coreferents is The Ancients knew that appears at dawn. If we fill the hole with the noun phrase the Morning Star we get the true (1a), while if we plug in the Evening Star we get the false (1b). Yet the Morning Star and the Evening Star both refer to the planet Venus and are thus coreferential.
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