James R. Shaw

I argue that on very weak assumptions about truth (in particular, that there are coherent norms governing the use of "true"), there is a proposition absolutely inexpressible with conventional language, or something very close. I argue for this claim "constructively": I use a variant of the Berry Paradox to reveal a particular thought for my readership to entertain that very strongly resists conventional expression. I gauge the severity of this expressive limitation within a taxonomy of expressive failures, and argue that despite its strength there is nothing incoherent about admitting its existence. The argument forms part of a project of clarifying precisely what trade-offs are required to secure the kinds of expressive power truth theorists typically want, in the process showing that the admission of very strong expressive limitations may ultimately prove to be the lesser of two evils.

The Sleeping Beauty puzzle has dramatized the divisive question of how de se beliefs should be integrated into formal theories of rational belief change. In this paper, I look ahead to a related question: how should de se beliefs be integrated into formal theories of rational choice? I argue that standard decision theoretic frameworks (e.g., Causal and Evidential Decision Theory) fail in special cases of de se uncertainty, like Sleeping Beauty. The nature of the failure reveals that sometimes rational choices are determined independently of one's credences in the kinds of "narrow" de se propositions that Sleepy Beauty has set in relief. Consequently, in addition to pinpointing a failure of standard decision theoretic frameworks, this result casts doubt on a large class of strategies for determining principles for the rational updating of de se beliefs in cases like Sleeping Beauty, and also calls into question the importance of making such a determination at all.

I argue for two theses about semantically anomalous utterances (more commonly called "category mistakes") like "sequestered slaps reel evergreen rights". First, semantic anomaly generates a unique form of semantically enforced quantifier domain restriction. Second, the best explanation for why anomaly interacts with quantifiers in this way is that anomalous utterances are truth-valueless. After arguing for these points, I trace out some further consequences these theses have in semantics and logic. In particular, I argue they reveal that truth-valueless material has a surprising positive role to play in the compositional semantics of truth-evaluable utterances. Moreover, the interaction of anomaly with quantifiers generates a unique form of classical inference failure, and also provides special motivations for reconceptualizing our logical consequence relations.

I argue that a formal theory of truth, of the sort usually developed to cope with paradox, should also act as a compositional semantics for semantic vocabulary, and that providing such a theory faces an under-appreciated problem. Foundational programs in the philosophy of language, as well as some basic empirical data, require a special "benign" reflexivity in uses of semantic vocabulary that forces their compositional semantic values to be highly non-standard. In particular their semantic values cannot be modeled using extensions. This shows that standard model-theoretic semantics has an inadequate structure to capture the compositional behavior of a very important class of natural language predicates. In the process, this result also rules out a wide range of formal theories of truth (including Tarskian and Kripkean) as structurally inadequate. I explore how our compositional theories must be liberalized to accommodate the peculiarities of semantic terms and extract some important lessons from this liberalization for our understanding of the relationship between foundational and compositional semantics, the nature of truth, expressive power, the structure of informational effects, context-sensitivity, and semantic paradox.

This paper develops a particular formal implementation of truth-proceduralism: the view that the meanings of semantic terms like "true" are given by special kinds of rules for making stepwise assignments of semantic properties to utterances. The paper formulates and deploys new evolving semantic dependence relations making use of supervaluations that are specially tailored to the truth-proceduralist program, and integrates tools, such as generalized quantifiers, suited to capturing general semantic claims in a trivalent setting. The non-standard assignment of semantic properties embodied by the procedural conception of truth interacts with the characterization of semantic dependence to create the need for a special analog of a consistency result, which is proved. The paper then explores the extent to which the resulting system is adequately able to state particular and general facts about its own semantic structure, including its own logic.

Truth-value gaps have received very little attention from a foundational perspective, a fact which has rightfully opened up gap theories to charges of vacuousness. This paper is an attempt to rectify this problem. I begin by reviewing and sharpening a powerful argument of Dummett's to dramatically constrain the options that gap theorists have to make sense of their views. I then show that within these strictures, we can give an account of gaps by drawing on elements of a broadly Stalnakerian framework for assertion and using gaps to track an amalgamation of assertoric effects. On this account, we can only make sense of gaps by drawing on some very special resources in our theories of assertion. These resources preclude gaps from being used in describing mentality, which I argue is actually an important virtue of the account. Additionally, the account organically gives rise to a combination of properties that gaps are often merely stipulated to have: strong projection behavior and falsity-like regulation of inferential schemes.