Multiple Temporal Indexing in Early Formal Semantics ∗ David Rey LOGOS - University of Barcelona dareys@gmail.com The idea of double indexing is a familiar one in the philosophy of language and in formal semantics. Arguably, Kaplan was the author who contributed the most to its refinement and popularization. But by the time Kaplan was developing his theory of indexicals, double indexing had already been in the air for a few years and double-index logical systems were being studied by theorists such as Kamp (1967, 1971), Vlach (1973), Segerberg (1973), and Åqvist (1973). Interestingly, the motivations that these theorists had for adopting double indexing were subtly different from Kaplan’s. One important motivation concerned the possibility of expressing the truth-conditions of certain fragments of English using intensional operators. In this paper I discuss a family of arguments that rely on considera- tions about the expressibility of the truth-conditions of English sentences. I will call arguments of this family expressibility arguments. Kamp, Vlach, and Seger- berg motivated their double-index systems by appeal to arguments of this sort. 1 Expressibility arguments, as I will characterize them, may be invoked for many different purposes. But I will focus my attention here on some influential expressibility arguments from the literature on multiple indexing. Sections 1 and 2 provide a formal framework for my discussion. In section 3 I analyze the basic 1 ∗ Comments to this paper are welcome. Please do not quote it or circulate it without permission. 1 See Kamp 1971, pp. 230-232, Vlach 1973, pp. 2-5, 39-41, and Segerberg 1973, pp. 77-79. Åqvist’s motivation for adopting double indexing was to avoid theorem (9c) of his system Å, which he interpreted as precluding the possibility of non-contingent conditionals (see Åqvist 1973, pp. 29, 58-59). As it is well known, Kaplan (1977, section VII) argued for double indexing, and against the view that he called index-theory, by reflecting upon the modal and logical properties of sentences like I am here now. His argument did not rely on expressibility considerations. When Kaplan considered sentences which may give rise to an expressibility argument for double indexing (see Kaplan 1977, section V), he was presupposing the context/ circumstance distinction and was arguing for something different. Expressibility arguments are also absent in Lewis’ (1980) defense of the context/index distinction.