27
Jan
08

Hill’s Defense of (T&W-3)

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.

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