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Review of  Graded Modality

Reviewer: Kathryn P Bove
Book Title: Graded Modality
Book Author: Daniel Lassiter
Publisher: Oxford University Press
Linguistic Field(s): Pragmatics
Cognitive Science
Issue Number: 29.3485

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Chapter 1: Gradation, scales, and degree semantics

In this section, Lassiter introduces the reader to the concept of gradable modality, importantly drawing the distinction between a gradable analysis in adjectives, epistemic modals, and other modal elements. This section introduces some of the similarities between gradable semantics and modality. Lassiter communicates the purpose for the book: to build a detailed semantics for modal expressions similar to previous analyses of gradable adjectives.

Chapter 2: Measurement theory and the typology of scales

This chapter introduces the concept of Representational Theory of Measurement (also known as RTM or “measurement theory”), which allows researchers to take data and decide which mathematical operations could be supported by the data (rather than the other way around). Lassiters recommends Roberts (1979) for a good introduction to RTM. This chapter presents some of the basic concepts of RTM to be used in the analysis, initially without discussing numbers or degrees before moving onto examples of ratio and interval scales that include a more mathematical explanation. He dedicates a section to explaining the difference between interpretation of concatenation in natural language and in RTM, which he establishes are different. To conclude the chapter, Lassiter describes scale types, focusing on intermediate scales, which he revisits throughout the book.

Chapter 3: Previous work on graded modality: Lewis and Kratzer

This chapter gives an overview of two foundational theories in graded modality: Lewis (1973) and Kratzer (1981, 1991). The key to both theories is the idea that modality is the quantification over possible worlds, which, until recently, has been the primary approach to understanding gradable modality. Lassiter presents the fundamentals of the theories as well as a discussion of strengths and shortcomings of each. He concludes the chapter by highlighting the issue that while Lewis’ and Kratzer’s theories account for deontic modality, both lack adequate descriptions of epistemic modality. To account for these shortcomings, Lassiter posits that measurement theory, as described in Chapter 2, may be able to do what Lewis and Kratzer could not.

Chapter 4: Epistemic adjectives: “Likely” and “probable”

This chapter analyzes of epistemic adjectives “likely” and “probable” using measurement theory. Starting with a brief overview of qualities of scalar and ratio modifiers, Lassiter reviews previous accounts of several gradable adjectives. Kennedy (2007) suggests that “likely” and “probable”, as relative adjectives, should fall on an open scale, which Lassiter proves cannot be the case. Klecha (2012, 2014), who adopts Kennedy’s theory, restricts “likely” and “possible” to an open interval (0, 1) that lacks endpoints, but Klecha argues that endpoints can be coerced for “likely”. Lassiter points to the weakness in this argument, saying that “likely” “lacks endpoints until it has them” (Lassiter 2017:110) and argues that this account cannot explain cases of degree modifying readings of “completely”/“likely” “certain”. Lassiter concludes that instead of building on Kennedy’s theory or Klecha’s account, the most accurate conclusion with regards to “likely” and “probable” is that these epistemic adjectives are relative adjectives falling on an upper and lower bounded ratio scale.

Chapter 5: Certainty and possibility

This chapter begins with a presentation of the two adjectives “certain” and “sure”. Lassiter (2017:129) explores three possibilities for certainty and likelihood: (1) “Certain” is structurally identical to “likely”; (2) “Certain” differs from “likely” in that the former is not lower-bounded (Klecha 2012, 2014); (3) “Certain” orders objects of a different semantic type: sets of propositions rather than properties (cf. Uegaki 2016). He suggests that all possibilities have shortcomings and strengths, and he acknowledges the need for further development of these theories. In his discussion of “possible”, he argues that this adjective should be analyzed as scalar after presenting both opinions in favor of and against a scalar analysis. He ends the chapter with a comparison of possibility and likelihood, concluding that these adjectives are identical except in their behavior (“possible” is a minimum adjective while “likely” is a relative adjective).

Chapter 6: Implications for the epistemic auxiliaries

In this chapter, Lassiter shifts the discussion from scalar adjectives to auxiliaries. He begins by demonstrating that “ϕ must” is weaker than “ϕ is certain” stronger (contra von Fintel & Gillies 2010). Then, he presents a review of “might” and “must” according to several theories: strong quantificational theories (von Fintel & Gillies 2010), weak quantificational theories (Kratzer 1991b), both (Swanson 2005), and scalar (Yalcin 2005; Swanson 2006; Lassiter 2011a, 2016). In the end, he concludes that while a scalar analysis is not the only way this could be captured, it certainly presents the clearest explanation of “must” and “might”. In the following section, Lassiter discusses the role of context sensitivity and alternative sensitivity of “might” and “must”. Lassiter presents his own study of lottery winners to demonstrate the differences between “might” and “possible” and concludes that this highlights differences between ordinary language users and philosophers. He concludes the following modal strength:
θ possible < θ might < θ likely < θ must < θ certain.
With regards to the gradability of epistemic auxiliaries, Lassiter concludes that “must” may be gradable, but there needs to be more work before this conclusion can be reached; however, he does conclude that “might” lacks degree. He ends the chapter with a discussion of epistemic “ought”. This section introduces several ideas regarding epistemic “ought”, or as Yalcin (2016) calls it, “pseudo-epistemic,” and Lassiter argues that this can be understood through a scalar analysis but leaves final conclusions to future work.

Chapter 7: Scalar goodness

This chapter begins the conversation of deontic language with the adjectives “good” and “bad”. Lassiter argues that this sets up the scalar concept of goodness used in the following chapter. He begins by presenting “good” as a relative adjective that is context-dependent and suggests that is may also be sensitive to alternatives. Upon treating “good” as an interval scale, he rejects the idea that “goodness” is positive or maximal, suggesting intermediacy is the most logical possibility. In search of a semantics that treats “good” as a interval scale that is intermediate with respect to disjunction, Lassiter uses the concept of expected value, which applies possible worlds to real numbers. Using this approach, he concludes that “good” is intermediate, information-sensitive, and rich enough to support quantitative analyses.

Chapter 8: “Ought” and “should”

Building on the theory developed for “good” in Chapter 7, Lassiter extends this theory to deontic “ought” and “should”. He points out similarities between “ought”, “should”, and “better”, and while some researchers have suggested defining “ought” and “should” in terms of “better”, Lassiter concludes that this is problematic. Lassiter introduces three concepts to better understand the semantics of “ought”:
(1) Sloman’s (1970) Principle: ought(Φ)⇒∀ψ ≠ Φ ∈ ALT (Φ) : Φ >good ψ
(2) The Smith argument: [Φ ∨ ψ = W ∧ ought (Φ) ∧ ought (ψ) ]⇒ ought (Φ ∧ ψ)
(3) Weakening: [ ought (Φ) ∧ ought (ψ) ] ⇒ ought (Φ ∨ ψ) (Lassiter 2017:240).
Lassiter argues that “ought” and “should” validate the use of a combined approach involving his updated Sloman’s Principle and scalar goodness. He concludes the chapter by stating that there is still much to be done, but this analysis is a good first step towards better understanding the gradable nature of deontic predicates.


“Graded Modality” is a well-written book that explores a topic that, as the author notes, has been the subject of much debate. While the book is based on Lassiter’s 2011 NYU dissertation, he does an excellent job of revisiting the recent work published on the topic, which has been plentiful in recent years. Analyses of graded modality up to this point have primarily analogized these modals with quantifiers such as “some”, “all”, and “none”, but Lassiter successfully demonstrates that graded modals are more comparable to scalar adjectives like “big” or “full”. With this book, Lassiter aims to better explain the complex topic of graded modality by bringing together several semantic analyses of modals and graded adjectives as well as the mathematical notion of measurement theory. He states that “theories have much to gain by engaging with the rich, sophisticated literature on related topics from neighboring fields” (xiv). Lassiter is able to accomplish this, providing a novel analysis of frequently discussed topics using several notions from a variety of subfields within linguistics and from neighboring mathematics.

As the tenth book in the series “Oxford Studies in Semantics and Pragmatics”, this text makes an excellent contribution to the collection. Lassiter approaches modality by allowing several different theories to interact to better understand how modals behave. He is a part of the group of researchers that pioneer the idea of approaching modality with a gradable analysis. As such, there are many unanswered questions in the book, and, as the author notes, there is much left for future investigation; however, Lassiter’s discussion of these unanswered questions is sufficient for the purposes of this book, and the reader does not feel like Lassiter has left a topic without properly addressing it.

While this book is filled with complex topics from a variety of fields in and out of linguistics, Lassiter does a great job explaining the relevant information, giving natural language examples that enhance the descriptions. In two chapters (Chapters 6 and 9) he presents his own quantitative data collected through the Amazon Mechanical Turk Platform, which enhance his arguments; however, additional details including specifics of prompts seen by participants would make his explanations clearer. He consistently ties his conclusions into previous chapters, and his arguments, overall, are easy to follow. The writing would benefit from a consistency in notations; Lassiter provides what seems like an almost random assortment of extensive, paragraph-length notes to the reader within parenthesis as well as footnotes. An unexpected benefit in the book is the reading guide that Lassiter lays out in the preface (xvii); he gives suggestions for an abbreviated read for those with a solid foundation in degree semantics, those especially interested in epistemic modality, and those interested in deontic modality. While previous knowledge of modality or measurement theory would make for an easier read, Lassiter explains most concepts in depth, making the text appropriate for both student and professional semantics researchers.


Fintel, Kai von & Anthony Gillies. 2010. Must...stay...strong! Natural Language Semantics 18(4), 351-383.

Kennedy, Chis. 2007. Vagueness and grammar: The semantics of relative and absolutive gradable adjectives. Linguistics and Philosophy 30(1), 1-45.

Klecha, Peter. 2012. Positive and conditional semantics for gradable modals. In Anna Chernilovskaya Ana Aguilar Guevara, & Rick Nouwen (eds.), Sinn und Bedeutung 16, vol. 2, 363-376. MIT Press.

Klecha, Peter. 2014. Bridging the divide: Scalarity and modality. University of Chicago dissertation.

Kratzer, Angelika. 1981. The notional category of modality. In H.J. Eikmeyer & H. Rieser (eds.), Words, Worlds, and Context, 38-74. De Gruyter.

Kratzer, Angelika. 1991. Modality. In A. von Stechow & D. Wunderlich (eds.), Semantics: An international hanbook of contemporary research, 639-650. De Gruyter

Lassiter, Daniel. 2011. Measurement and modality: The scalar basis of modal semantics. New York University dissertation.

Lassiter, Daniel. 2016. Must, knowledge, and (in)directness. Natural Language Semantics 24(2), 117-163.

Lewis, David. 1973. Counterfactuals. Harvard University Press.

Lewis, David. 1979. Scorekeeping in a language game. Journal of Philosophical Logic 8(1), 339-359.

Roberts, Fred S. 1979. Measurement theory with applications to decisionmaking, utility, and the social sciences. Addison Wesley Publishing Company.

Sloman, Aaron. 1970. “Ought” and “Better”. Mind 75(315), 385-394.

Swanson, Eric. 2006. Interactions with context. MIT dissertation.

Uegaki, Wataru. 2016. Content nouns and the semantics of question-embedding. Journal of Semantics 33(4), 623-660

Yalcin, Seth. 2005. A puzzle about epistemic modals. MIT Working Papers in LInguistics 51, 231-272.

Yalcin, Seth. 2016. Modalities of normality. In Matthew Chrisman & Nate Charlow (eds.), Deontic modals, 230-255. Oxford University Press.
Kathryn Bove is a PhD candidate at the University of Georgia, currently finishing up her dissertation on mood and epistemic modality of Yucatec Spanish, a contact variety of Spanish spoken in Yucatán, Mexico. Her interests include semantics, the semantic/syntactic interface, language contact, bilingualism, and language documentation.

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