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This chapter argues that certain important lessons about truth can only be appreciated by approaching semantic circularity from the perspective of a compositional semanticist. It explains our need for a compositional semantics for semantic vocabulary like ‘true’. These reflections stress the need to explain, consistently with linguistic productivity facts, truth-value judgments concerning two classes of semantic circularities. The first involves claims like ‘Everything I say today will be true’, made when all other utterances by the speaker that day are true. The second involves claims about broad distributions of semantic properties like ‘A conjunction is true just in case both of its conjuncts are true’. We cannot explain the productive speaker judgments concerning the classes with a theory that gives ‘true’ an extension assignment as part of its semantic value. The chapter explains what shape semantic theories would need to take in order to avoid this circularity.

To have meaning is to stand in the meaning relation to a meaning, meanings taken to be characters*. This chapter is about the nature of the meaning relation. A theory of this relation requires saying what relation a person must bear to a language in order for that language to be her public language, and also what relation a person must bear to a language in order for that language to be her language of thought. The answers bear on questions about compositional semantics and about the supervenience of the intentional on the non-intentional.

Two general kinds of views have become prominent in contemporary metanormative theory: descriptivists hold that normative statements express descriptive beliefs about reality, whereas expressivists hold that normative statements express nondescriptive attitudes. This chapter argues that this should not be viewed as a debate about whether to assign truth conditions to normative sentences as part of our compositional semantics, but about how to interpret the truth condition assigned in our metasemantic theory. By more carefully understanding the project of truth-conditional approaches to compositional semantics and how it is open to various metasemantic interpretations, and by reorienting the design of a metanormative theory towards a focus on ought-statements, the stage is set for a view of normative statements that is neither descriptivist nor expressivist.

In this chapter, I argue that Fodor and Pylyshyn are justified in claiming that representational systematicity is an important aspect of cognitive activity, but they are wrong to suppose that a failure to explain it should substantially undermine a given architecture's promise or credibility. Fodor and Pylyshyn's argument assumes that the mind has a single basic cognitive architecture and representational system; thus, they assume that if systematicity is real, then it must be a fundamental feature of cognition. While this assumption has always been problematic, as various authors have noted, it has now been rejected by a growing crowd of investigators who have adopted different forms of architectural pluralism, such as dual process models. With pluralism, there is no reason to think that explaining representational systematicity is necessary for a viable theory of cognitive processes. Indeed, I suggest that when properly understood, some forms of connectionist processing should be treated as lacking not just representational states that are related systematically, but rather as lacking representational states altogether.

The representation of motion begins by discussing motion‐oriented extensions of the spatial calculi described in Chapter 3, including models of relative motion. It then describes a relatively new semantics for motion in language, based on Dynamic Interval Temporal Logic (DITL), where constructing meaning involves creating an executable program. The authors show how the compositional semantics for motion expressions discussed in Chapter 2 can be recast more formally in DITL, with the spatial primitives used now grounded in terms of primitives drawn from these qualitative calculi. The chapter then elaborates the motion verb classification in Chapter 2, with DITL motion expressions for each class. The authors argue that their treatment addresses most of the requirements specified at the beginning of the book.

For accommodating defective utterances within compositional semantics, truth-value gaps (Kleene's 3-valued logic) and gluts (Priest's LP) are equally efficient, but in terms of classical logic gaps yield harmless incompleteness, whereas gluts precipitate collapse; ex contradictione quodlibet. The discrepancy is less deep than first appears, however. A dialetheist dual to van Fraassen's supervaluationism, implicit in Ramsey's ‘Theories,’ counts sentences true if they are true in at least one acceptable model. Divergent illucutionary norms compensate for differing semantics. Subvaluationists (so-called by Varzi) replace the supervaluationist maxim, ‘Do not assert what is untrue,’ by ‘Do not assert what is false.’ Both predict the same verbal behavior.

It is widely acknowledged that metaethical expressivism requires taking on some substantive commitments in the theory of meaning. Those commitments, however, do not require abandoning orthodox views in compositional semantics. Instead, they should be understood as bearing on one aspect of the metasemantic project, namely that of interpreting a compositional semantic theory—what is here called ‘semantic hermeneutics’. The nature of this project is spelled out and distinguished from that of explaining why words have the meanings that they do. The chapter concludes with an outline of a hermeneutics for orthodox compositional semantics that does justice to the expressivist’s distinctive views in the philosophy of mind.

Consider the idea that a natural language like English is in the first instance incorporated into the system of representation one thinks with. This ‘incorporation’ view is compared with a translation or ‘decoding’ view of communication. Compositional semantics makes sense only given the implausible decoding view.

Based on the review of in Chapter 3, this chapter develops the new formal logic ℒ_TU for hybrid semantics, that is both capable of dealing with the entire range of UCIs and overcomes some additional problems. The key advantage of ℒ_TU is that it embraces true multidimensionality, i.e. every natural language expression is represented by a three-dimensional meaning profile in the compositional semantics. The chapter shows how the core ideas of can naturally be reformulated and extended in such a framework, which employs a generalized composition rule called multidimensional application. It is shown how the restrictions that do not directly transfer to the new system can be recast as conditions on the lexicon—syntax interface of the logic by the use of lexical extension rules.

This chapter presents a theoretical framework that provides an answer to the question of how distributional representations of word meanings should be combined compositionally to produce distributional representations of larger phrases. More specifically, it describes the framework of Coecke et al. (2010) in a form designed to be accessible to computational linguists not familiar with the mathematics of category theory on which the framework is based. It also briefly introduces pregroup grammar, which is the syntactic framework underlying the compositional process. One question the framework does not answer is what the semantic type of a sentence should be; in other words, what vector space sentences should live in. The chapter presents two possible sentence spaces, the first for expository reasons and the second as an example of a sentence space that has been implemented and evaluated in a word-sense disambiguation task.

Most previous work on graded modality has relied on qualitative orderings, rather than degree semantics. This chapter introduces Representational Theory of Measurement (RTM), a framework which makes it possible to translate between qualitative and degree-based scales. I describe a way of using RTM to extend the compositional degree semantics introduced in chapter 1 to qualitative scales. English data are used to motivate the application of the RTM discussion between ordinal, interval, and ratio scales to scalar adjectives, with special attention to the kinds of statements that are semantically interpretable relative to different scale types. I also propose and motivate empirically a distinction between ‘additive’ and ‘intermediate’ scales, which interact differently with the algebraic join operation (realizing sum formation or disjunction, depending on the domain). This distinction is reflected in inferential properties of non-modal adjectives in English, and is also important for the analysis of graded modality in later chapters.

The chapter focuses on the question of whether internalism or externalism is true for talk about properties and propositions. Some of the standard arguments are discussed, in particular the substitution arguments. The role of semantic values in settling this question is brought out, and I argue against a close relationship between semantic values and reference. Instead, a proposal is made about the function of semantic values in a compositional semantics. Two large-scale pictures of the function of reference in natural language are formulated and discussed: the referential and the non-referential pictures of language. Overall, the chapter argues that that-clauses and property nominalizations are not referential, and that internalism should be accepted for talk about properties and propositions. A concluding section discusses how quantification over properties and propositions is to be formulated along internalist lines.

Concepts of motion in language introduces a qualitative model for natural language that captures static spatial descriptions expressing topological relations involving contact and inclusion, simple orientation relations, and qualitative distance. Extending a basic motion frame discussed in the literature, authors analyze path verbs in terms of transitions in spatial configurations over time, individuating them based on differences in the initial or final spatial configurations. The authors argue that manner is not a primitive parameter of motion, and they distinguish different manner‐of‐motion verbs based on topological constraints. The chapter illustrates the compositional analyses of a variety of different motion sentences.

Since many modal expressions in English are overtly gradable, we need to understand gradability in general if we are to understand their semantics. This chapter introduces a number of core notions in the lexical and compositional semantics of gradable expressions, including the distinction between gradability and scalarity, key notions around adjective type and scale structure, and discusses some background issues such as the treatment of comparison classes and vagueness.

This chapter argues that the difference between indicative and counterfactual conditionals traces to the overt difference in verb forms and not to any alleged covert ambiguity or context-dependence in ‘if’. ‘Would’ has a life beyond conditionals; the best hypothesis is that it is a necessity modal restricted to contextually relevant worlds. In standard counterfactual conditionals, ‘would’ scopes over ‘if’; given the invariant truth-functional semantics of ‘if’, the compositional semantics then makes counterfactual conditionals contextually restricted strict conditionals. The chapter explores the consequences of this for the logic of counterfactuals: principles such as transitivity, contraposition, and strengthening the antecedent hold, with appearances to the contrary being explained by context-shifting caused by the application of the suppositional heuristic. However, modus ponens fails because the contextual restriction may exclude the actual world.

The compositional functional logical models of natural language are recast as compact closed categories. Composition is based on the geometrical representation of information flow characteristic for these categories. The functional logical interpretation of (strings of) words is carried over to projectors in a finite tensor product of two-dimensional spaces such that the truth of a sentence is equivalent to the truth of the corresponding projector. Examples include sentences with compound noun phrases involving quantifiers, adjectives, and negation.

“Phonetics, phonology, and prosody” do not, as might be thought, constitute a set of three separate subsystems of language: linguistic sound systems have both phonetic and phonological aspects, and this applies as much to “prosody” as to other areas of language. The distinction between phonetics and phonology is most often applied to segmental sounds (i.e., sounds that are typically represented by individual letters in alphabetic writing systems), and “prosody” is often used to refer to any nonsegmental phenomena. However, there is little justification for defining prosody as some kind of separate channel that accompanies segmental sounds; prosody so conceived is no more than a loose collection of theoretical leftovers. Moreover, it is easy to identify phonetic and phonological aspects of at least some phenomena that are often thought of as prosodic (e.g., lexical tone). Nevertheless, various properties might motivate talking about a separate subsystem “prosody.” In particular, there are good reasons to think that the essence of prosody is the structuring of the stream of speech into syllables, phrases, and other constituents of various sizes, which may have internal structure, e.g., a head or nucleus of some sort. Rather than looking for specific local acoustic cues that mark a boundary or a stressed syllable—a quest motivated by a linear view of sound structure—we should be looking for cues that lead the perceiver to infer structures in which a boundary or a given stressed syllable are present. Clear analogs in music abound (e.g., harmonic cues to meter mean that a note can be structurally prominent without being louder or longer or otherwise acoustically salient). It is thus likely that our understanding of music should inform research on linguistic prosody rather than the reverse. The existence of abstract hierarchical structure in what is superficially a linear acoustic signal unfolding in time is a key aspect of what music and language share. Much the same is true of signed languages, though of course they are based on a stream of visible movements rather than an acoustic signal. These issues are relevant to the notion of duality of patterning: the building up of meaningful units (e.g., words) out of meaningless ones (e.g., phonemes). This is said to be a central design feature of language and may be absent from music and, for example, birdsong. However, the division between meaningful and meaningless elements is less sharp than it appears, and the fact that words are composed of phonemes is arguably just a special case of the pervasive abstract hierarchical structure of language. If this view can be upheld, the issue of whether music exhibits duality of patterning can be seen as the wrong question, along with the question of whether birdsong is more like phonology or more like syntax. Instead, it suggests that, evolutionarily, music and language are both built on the ability to assemble elements of sound into complex patterns, and that what is unique about human language is that this elaborate combinatoric system incorporates compositional referential semantics. Published in the Strungmann Forum Reports Series.