Revising a system of beliefs › Interchangeability and semantic rules

Another proposal identifies synonymous expressions by their interchangeability without changing truth value. Section 3 examines why this is difficult. We must first specify the contexts in which substitution is permitted. Quotations, for example, concern expressions themselves: the word "vixen" has five letters, while the phrase "female fox" does not. A qualification excluding such contexts is needed before the proposal even gets started.

More substantially, predicates can apply to exactly the same objects without meaning the same thing. In a fictional collection, every red folder might be a confidential folder, and every confidential folder red. Substituting these predicates in ordinary extensional statements about the collection would preserve truth. Nevertheless, discovering that coincidence is different from learning the meanings of "red" and "confidential."

An extensional context is one in which replacement by expressions with the same reference or extension preserves truth value. An extension is the collection of things to which a predicate applies. The folder example shows why agreement in extension is weaker than the kind of synonymy sought. The agreement might disappear if somebody changes a folder's colour without changing its confidentiality.

One might require substitution to preserve necessary truth instead. Quine's concern is that an unexplained appeal to necessity can reintroduce the semantic notions that the proposed test was meant to clarify. The issue is not a ban on using modal vocabulary. It is whether that vocabulary provides an independent explanation in this argument. Quine, §3.

Section 4 considers explicit semantic rules for constructed languages. A list can identify a class of sentences with perfect precision. Quine asks what makes the selected rules rules of meaning, and the selected truths analytic, rather than simply a designated class. His challenge concerns the interpretation of the classification, not our ability to manipulate a formally specified system. That distinction matters when assessing both his objection and replies to it.