Recall from this post the following statement:
(T&W-3) Propositions have structure that parallels the logical structure of the sentences.
Hill notes that this is a strong claim and one that is not universally accepted (T&W, 3), but presents a defense of it in a footnote (127) . I will reproduce the argument he presents, verbatim in most places, but restructured slightly:
Premise 1: (T&W-127-A) When one uses the predicate “believes that S” to attribute a belief to someone, the embedded sentence S indicates the proposition that serves as the object of the belief.
Premise 2: (T&W-127-B) The proposition that S indicates when it occurs in the predicate “believes that S” is the same as the proposition that S expresses when it is used in other contexts.
(T&W-127-A) and (T&W-127-B) imply:
Lemma 1: (T&W-127-C) If predicates “believes that S” and “believes that S*” can be used to attribute different beliefs, then the propositions, then the propositions that are expressed by the sentences S and S* must be numerically distinct.
Premise 3: (T&W-127-D) If there are any logical differences between S and S* (including even differences in microstructure), then the predicates “believes that S” and “believes that S*” can be used to attribute1 different beliefs.
(T&W-127-C) and (T&W-127-D) imply:
Lemma 2: (T&W-127-E) Propositions are distinct when the sentences that express them are different in point of logical form.
Premise 4: (T&W-127-F) The best explanation of (T&W-127-E) is the hypothesis (T&W-127-G) .
Theorem: (T&W-127-G) Propositions have internal logical structures that reflect the logical structures of the sentences used to express them.
Corollary: (T&W-3) Propositions have structure that parallels the logical structure of the sentences.
1 The original uses “express” instead of “attribute” here, but I have edited this for the sake of consistency.