Compositionality and Context in Indexicals — Epoche C2
Two semantic values, and a question about which of them composes Kaplan's semantics for indexicals assigns every expression two semantic values rather than one: a character, which is a rule taking a context of utterance to a content, and a content, which is what the expression contributes to the proposition expressed on that occasion. The character of the first-person pronoun is fixed by the language and never varies; its content varies with every mouth that utters it. The question this essay presses is which of those two objects semantic composition actually operates on, and the answer turns out not to be a matter of convenience or notation. It is settled by a substantive empirical hypothesis about natural languages, and where that hypothesis fails, composition has to be run on characters. A qualification about the content of a subsentential expression is needed before anything else, because an earlier version of this essay identified content with the proposition expressed. That holds only for whole sentences. The content of the first-person pronoun in a context is an individual; the content of a predicate is a property, or a function from individuals to truth values at a circumstance; only a sentence has a proposition as its content. The two-value architecture applies at every level, and it is precisely the fact that it applies below the sentence that makes the question of composition live. A correction: there is no "Ascension Principle" An earlier version of this essay asserted that the satisfaction conditions of the Principle of Compositionality are standardly taken to reduce to something called the Ascension Principle, glossed as the claim that if a sentence is true then the proposition it expresses is true. No principle of that name exists in the semantics literature, and the sentence offered as its content is a disquotational triviality with no consequences for compositional structure at all — it is satisfied by any assignment of propositions to sentences whatsoever, including a wholly arbitrary one. Nothing in what follows depends on the discarded claim, but the gap it leaves has to be filled, because the formal statement of compositionality is what the rest of the argument is measured against. That statement is Montague's (1970). Take the syntax to be an algebra: a set of expressions $A$ together with a family of partial operations $F_\gamma$ that build complex expressions from simpler ones. Take the semantics to be a second algebra: a set of meanings $B$ with a family of operations $G_\gamma$ indexed by the same set. A meaning assignment $m: A \to B$ is compositional exactly when it is a homomorphism between them: $$m(F_\gamma(a_1,\ldots,a_n)) = G_\gamma(m(a_1),\ldots,m(a_n))$$ This is the whole content of the principle, and its bite lies in the indexing. Each syntactic operation must be matched by one semantic operation, the same one every time it is used, so that the meaning of a complex expression depends on the meanings of its immediate parts and on nothing else about them — not on their form, not on the meanings of expressions that are not among the parts, and not on the context of use except insofar as the whole assignment $m$ has been relativised to it. The immediate consequence, and the one that will matter, is substitutional: if two expressions have the same meaning, replacing one by the other in any larger expression leaves that expression's meaning unchanged. The attribution to Frege should also be loosened. Pelletier (2001) went through the texts and found that Frege nowhere states the principle, and argued that the doctrine Frege did state repeatedly — that a word has a meaning only in the context of a sentence — sits awkwardly with it, since it makes the sentence prior to the word rather than the other way about. Nothing here depends on the historical question; but "Frege's Principle" is a name, not a citation. Kaplan's machinery, written out The formal system in which Kaplan (1989) works is the Logic of Demonstratives. It evaluates expressions relative to two parameters that are kept rigorously apart. A context is a concrete occasion of use, and in the formal system it is a quadruple $c = \langle c_A, c_T, c_P, c_W \rangle$: an agent, a time, a position, and a world. A circumstance of evaluation is a world–time pair $\langle w, t\rangle$ at which a content is assessed for truth or reference. The two-stage semantics is then: $$\mathrm{Char}(\alpha): c \mapsto \mathrm{Cont}(\alpha, c), \qquad \mathrm{Cont}(\alpha, c): \langle w,t \rangle \mapsto \mathrm{Ext}(\alpha, c, \langle w,t \rangle)$$ Two features of this are load-bearing. The first is a constraint on which quadruples count as contexts: Kaplan requires them to be proper, meaning that the agent $c_A$ must be located at the position $c_P$ at the time $c_T$ in the world $c_W$. Improper quadruples — an agent somewhere other than where the context puts him — are excluded from the model, not merely deprecated. The second is the thesis of direct reference: the content of the first-person pronoun in a context is not a descriptive condition but the individual $c_A$ himself, so that its content is the constant function $\lambda w.\, c_A$, which returns that individual at every circumstance. This is why the pronoun is rigid, and why replacing it with a definite description that happens to pick out the same person changes what proposition is expressed. One further correction to the earlier version of this essay: the character of the first-person pronoun is best given as "the agent of the context", not "the speaker". Kaplan's agent coordinate is not defined as whoever is speaking, and the difference matters for written notes, recordings and other cases where the producer of a token is not uttering anything at the time it is encountered. Why the two levels are not notational variants If character and content always moved together, the choice between them would be a question of bookkeeping. The sentence "I am here now" sho