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Review of  Modals and Conditionals

Reviewer: Eugenia Romanova
Book Title: Modals and Conditionals
Book Author: Angelika Kratzer
Publisher: Oxford University Press
Linguistic Field(s): Philosophy of Language
Issue Number: 23.5019

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AUTHOR: Angelika Kratzer
TITLE: Modals and Conditionals
SUBTITLE: New and Revised Perspectives
SERIES TITLE: Oxford Studies in Theoretical Linguistics. Vol. 36
PUBLISHER: Oxford University Press
YEAR: 2012

Eugenia Romanova, Department of Linguistics, Institute of International Relations, Yekaterinburg, Russia


The simple title of this book fully corresponds to its complicated contents: it is a collection of six classical articles on modality and conditionality written in the framework of formal semantics/language philosophy and published in different years (from 1977 to 2002). The articles have, however, been reviewed and updated.

Chapter 1. What ‘Must’ and ‘Can’ Must and Can Mean.

The opening lines of the first chapter point out that there are many modals and even more modal interpretations. But if we limit ourselves to just two - “must” and “can” - how do we know which interpretation to choose in every particular case? The answer is: all the readings have one common component of meaning, “in view of”:

1. All Maori children must learn the names of their ancestors. ((2), p. 4)

2. In view of what their tribal duties are, the Maori children must learn the names of their ancestors. (Kratzer’s (2’), p. 6)

3. The ancestors of the Maoris must have arrived from Tahiti. ((3), p. 4)

4. In view of what is known, the ancestors of the Maoris must have arrived from Tahiti. ((3’), p. 6)

The phrase “in view of” has two arguments: a free relative (“what is known”), which falls into the modal restriction of this operator, and a sentence (“the ancestors of the Maoris must have arrived from Tahiti”), which falls into its modal scope.

Any proposition in the scope of a modal operator should be identified with sets of possible worlds. A free relative “what is known” is a function from possible worlds to sets of propositions -- premise sets. It is important that a set of propositions be consistent -- only those can be considered in modal expressions. To interpret “must”, for every set we need a superset from which a certain proposition follows; for “can” the proposition must be compatible with some set and all of its supersets. The intricacies of structuring premise sets leads the author to the conclusion that such sets as {p, q} (where “p” and “q” are propositions) should be distinguished from the intersection of the two sets in the theory of modality.

Chapter 2. The Notion of Modality.

The second chapter deals with necessity and possibility modals, and analyses their epistemic and root (circumstantial) interpretations. Since there is no unique syntactic category expressing modality (it can be realized with the help of various morphemes, auxiliaries and even phrases), the question arises: What is modality?

First, the main two ingredients of a modal reading are a conversational background (a function from worlds to premise sets) and a modal relation determining the force of the conclusion. Modals express relations between conversational backgrounds and propositions. In the case of “simple” necessity the relation is “follows from f(w)'', where f is a conversational background (a function from worlds (w) to premise sets); in the case of “simple” possibility the relation is “compatible with f(w)” (p. 31). All modal operators are propositional operators.

Modal expressions are typically vague. Conversational backgrounds are defined by how a particular world is characterized and can be subdivided into realistic, informational, and stereotypical (or normative). While realistic conversational backgrounds are more context-independent, stereotypical conversational backgrounds should correspond to some contextual standard of normalcy, thus the two should be kept separate.

The appeal to normalcy as a contextual standard leads to one of the main proposals of this chapter, which was missing in the original article: modal interpretations can be graded. A notion of an ordering source is introduced here. When we induce the ordering ≤ on a set of worlds W, a world w is at least as close to an ideal or norm determined by a set of propositions A as a world z iff all propositions of A that are true in z are true in w as well. The ordering relation is reflexive and transitive but not necessarily antisymmetric (worlds don’t have to be compatible).

When necessity and possibility are considered through this ordering relation, possibility turns out to be the dual of necessity. There are cases where possibility and necessity collapse into each other (see pp. 44-45), yielding a modal without dual. “A modal without dual could also be a degree expression covering the upper end of a scale of degrees of probabilities or preferences” (p. 46). A “toy example” on p. 46 with concrete probability measures what an upper-degree modal may do. Such modals “could be used in situations where English would sometimes use ‘must’, and at other times ‘may’ or ‘might’” (p. 47); however there are languages (like St’át’imcets) where upper-end degree modals systematically take the place of necessity and possibility modals of any kind (epistemic, deontic, irrealis and future). The modal base is thus restricted by the ordering source requirements. The conclusion at this point is that the interpretations of modals depend on both a modal base and an ordering source, but either parameter can be fixed by an empty conversational background.

Discussing circumstantial (root) and epistemic modals the author says that both types have non-empty realistic modal bases. The subtle semantic differences between the two types of modal come from their different syntactic positions in the hierarchy of verbal inflectional heads (Hacquard 2006). Potentially non-realistic conversational backgrounds must function as ordering sources. Interacting with root modals they yield a number of different interpretations (deontic, bouletic, teleological, or propensity). The way it works is shown with the example of German modals like “darf, kann, muss” and “soll”. Further, it is shown that “should” in English is a necessity modal and not an upper-end degree modal, that wishes cannot override facts and that ordering sources can induce different partitions of modal bases, which is the main topic of the following chapter.

This chapter closes with an outlook of a theory describing how conditionals restrict modals where the subject of counterfactuals is also raised. These matters are raised again in chapter 4.

Chapter 3. Partition and Revision: The Semantics of Counterfactuals.

In a conditional sentence of the form:

(5) If it were the case that alpha, then it would be the case that beta (p. 72),

q and r are the propositions expressed by alpha and beta respectively, p is the utterance of the whole sentence, and p depends on q and r; f is the function from the set of worlds W that assigns to every world the set of all those propositions that are “the case in it” (p. 72). The analysis offered for p on p. 72 produces wrong truth conditions ((i) and (ii) on p. 73), followed by the Critical Argument, a step-by-step proof demonstrating where the truth conditions are wrong. So, a plausible analysis of counterfactuals is shown to have implausible consequences. Out of two options -- to give up the analysis or check the argument -- the author prefers the second one.

Wittgenstein’s atomistic view is discarded, for it destroys the proposed analysis. The notions worked out by Pollock (1976) are investigated in more detail and adopted by the author. They are: simple (atomic) propositions, negated simple propositions, strong subjunctive generalizations (laws of nature like the law of gravity) and weak subjunctive generalizations (actual necessities, for example, anyone drinking from a particular bottle containing poison would die).

In counterfactual reasoning, laws of nature have priority over actual necessities and actual necessities have priorities over simple facts. Contra Pollock’s analysis, “there are examples that show that Pollock’s partitioning of the world cannot be the one underlying counterfactual reasoning in general” (p. 76). The alternative partitioning of the world is provided by the context of conversation, which makes counterfactual propositions invariably vague. Thus the analysis that seemed faulty at the beginning of the chapter remains viable.

Chapter 4. Conditionals.

In his Lecture IV, Grice (1989:58-85) analyzes indicative conditionals in terms of material implication: there must be some non-accidental connection between the antecedent and the consequent. As a result, (6) is true just in case (7) or (8) is true:

(6) If my hen has laid eggs today, then the Cologne Cathedral will collapse tomorrow morning.

(7) My hen hasn’t laid eggs today.

(8) The Cologne Cathedral will collapse tomorrow ((1), (2) and (3), p. 86).

The analysis in terms of material implication fails to account for sentences with quantifiers, like “some” and “most,” and conditional sentences with quantifying adverbials, like “most of the time.” What can account for such sentences is the theory of restrictive quantification. For instance, the sentence “Most porches have screens” has the following representation:

(most x: x is a porch) (x has screens)
quantifier restriction nuclear scope ((12), p. 89)

(9) is true iff most individuals satisfying the restriction ‘x is a porch’ also satisfy ‘x has screens’ (the nuclear scope) (Heim 1982).

A conditional with a quantifying adverbial (“Most of the time, if a man buys a horse, he pays cash for it” ((15), p. 90)) is then analyzed as (10):

(10) (Most e: e is an event where a man buys a horse) (e is part of an event where the man in e pays cash for the horse in e). ((16), p. 90)

“On such an account there is no such thing as a two-place if… then operator in the logical representation of the sentences” (pp. 90-91) with quantificational adverbials ((13), p. 89). “The function of if-clauses is invariably to restrict the domain of the adverb. We have to concede, then, that there are indicative conditionals that cannot be analyzed as material conditionals” (p. 91).

Chapter 2 raised the issue of if-clauses and their ability to restrict modal operators. They do so without operating over modals directly: “if-clauses affect a modal base parameter that subsequent modals depend on” (p. 94). Conditionals are capable of restricting modals at a distance and there is no need to reconstruct the if-clause for purposes of interpretation (but see Bhatt and Pancheva 2006).

Grice’s game of chess paradox is discussed at length to demonstrate that the modal base by itself “does not yet gives us a suitable set of worlds for a suitable probability measure” (p. 97). Therefore a particular partition of the set of accessible worlds has to be invoked as a “reflection of what is often called ‘question under discussion’ or ‘discourse topic’” (p. 97).

In addition to conditionals that restrict various types of operators, there are “bare” conditionals as well. Bare conditionals are implicitly modalized:

(11) a. If the lights in his study are on, Roger is home.

b. (MUST (epistemic): the lights in his study are on) (Roger is home) ((34), p. 98)

“…If there is a non-overt modal in bare conditionals, it is not expected to have exactly the same meaning as its overt counterpart” (p. 98):

(12) If the lights in his study are on, Roger must be home ((37) on p. 98).

Here “must” indicates that the speaker uses a particular piece of evidence. The covert MUST in (11b) does not involve any evidence to rely upon.

One and the same conversational background might yield different premise sets depending on what the circumstances of evaluation are; conversational backgrounds are rather functions than premise sets.

If circumstances of evaluation for conversational backgrounds are no longer whole worlds, but can be smaller entities like situations or spatio-temporal locations, modal claims are expected to be context-dependent, and the context is usually underdetermined and vague. Premise-sets representing the available evidence can change as time goes by, the modal base remaining the same.

At the end of the chapter the author discusses apparent counterexamples to her proposal and concludes that if-clauses are still not two place if…then connectives, but rather tripartite operator restrictors.

Chapter 5. An Investigation of the Lumps of Thought.

Here, situations are studied in greater detail. A situation semantics is in some cases more rewarding than a possible world semantics. Possible situations are mereologically composed of states of affairs that are world-mates. The question is whether different states of affairs represent different situations or can be lumped together. For instance, my being tired and my being hungry represent identical time-slices of the same individual, but are different universals and hence different situations. Thick particulars -- particulars with all the universals they instantiate -- are not always necessary, thin particulars would do.

Ingredients of a situation semantics include a part-relation and persistence (if a proposition p is true in a situation s and remains true in all the situations containing s, it is persistent).

Such logical operations as conjunction, disjunction and existential quantification are restated for a situation semantics, and universal quantification is given special treatment, depending on the type of situation at hand. There are different types of universal quantification: non-persistent, radical, non-accidental and accidental. For example, propositions assigned by radical universal quantification are characterized as strong lumpers, which means that they can be true only in worlds, not in particular situations, whereas non-accidental universal quantification creates propositions that are very poor lumpers -- they are true in all or none of the situations of a world. And only accidental universal quantification produces propositions with the desired lumping properties in all worlds where universal generalization is non-vacuously true.

According to the author, her view about counterfactuals had been wrong for a long time. She used to state that adding propositions to a counterfactual can be an almost endless process until we reach a point where the resulting set of propositions logically implies the consequent. But now, keeping in mind lumping properties of propositions, she argues that they never come alone: whenever we add a proposition, it will bring along all propositions lumped by it in the evaluation world. Therefore inconsistency easily arises on adding new propositions to such lumps (and the process of adding propositions stops here).

Not all facts have equal weight: some are important, others are altogether irrelevant. Different sorts of similarities matter in different counterfactual situations, and when lumping relations are different inconsistency does not arise.

Structuring Base Sets for counterfactuals (subsets of propositions assigned to a world), we privilege sets that logically imply confirming propositions for the non-accidental generalizations they contain. Some experimental data cited in the chapter also support this argumentation.

The chapter closes with a discussion of negated statements and the interaction of negation with focus. Interpretation of counterfactuals with negation also depends on the way propositions are lumped.

Chapter 6. Facts: Particulars or Information Units?

The main question raised in this chapter is how to distinguish between facts and true propositions that facts exemplify. One way is through the semantics of the verb “to know”: “A person knows p iff the person believes p de re of some fact exemplifying p” (p. 163), where the res is not a proposition, but a situation. Situations stand in a part-whole relation to each other, thus “a possible situation s (is a fact that) exemplifies a proposition p iff whenever there is a part of s where p is not true, s is a minimal situation where p is true” (p. 166) (see the situation Mud on p. 167).

Interestingly, while we do not seem to have a de re belief about the fact exemplifying the proposition ‘A child was born yesterday’, we still know it. The account is based on the nature of the subject, a weak indefinite (interpreted as a thetic statement), which means that the predication is about a temporal or spatial location (in our case the world as a whole).

Knowledge ascriptions have a modal semantics with realistic conversational backgrounds. Some scenarios rendered in the chapter are not about the res of the belief ascribed, but about the proposition claimed to be the content of the belief (e.g., the mix-up about the butler, Milford and the judge on p. 177), so it is crucial to distinguish between the propositional content of the belief and the res of the belief. Consequently, facts are not necessarily true propositions and that plays an important role in the analysis of counterfactuals.


The book is primarily intended for formal semanticists and philosophers of language with serious background in the subjects. It can be accessible to graduate students of semantics or syntacticians with some knowledge of the formalism used in the volume, but the extent of this accessibility will definitely vary. Nevertheless, the book is certainly worth reading, for it is a product of rare scientific beauty, reflecting years of serious intellectual enterprise undertaken by its renowned author, whose already classical works have been studied and cited by generations of linguists. Prior acquaintance with mathematical logic, philosophy, and intensional semantics would increase the level of understanding of this important book and make reading it more enjoyable.

I have a number of questions of a highly specialized semantic character. The most difficult chapter was chapter 2, where the ingredients and main notions of modality were introduced. For example, in the discussion of informational conversational backgrounds, the following statement was made: “…If a testimony is a salient body of facts that a realistic background is about, the accessible worlds are those that have counterparts of that testimony. …If that same testimony is the salient source of information feeding an information background, the accessible worlds are those that are compatible with the intentional content of the testimony” (p. 34). To me it is not quite clear what is a counterpart and what is meant under the term “compatible” in this particular case, though I see the main idea of the passage.

The clearest chapters are chapters 4 and 6. A big part of chapter 4 was dedicated to answering a question about scope relations between possibility modals and conditionals, which is related to syntax, and chapter 6 deals with philosophy of thought, which makes it the most general of all the chapters.

There are two or three minor technical drawbacks in the text. For instance, on p. 47, where examples from St’át’imcets are given, the glosses naturally contain some abbreviations (DEIC, IMPF, FOC, COUNTER etc.), but there is no list of abbreviations in the book.

Another problem is connected with the mix-up of example numbers on pp. 180-182. The sentence “Now consider (34):” on p. 181 is followed by example (35).

To conclude, I recommend the book to all linguists interested in matters of modality, conditionality and counterfactuality. These are highly complex matters but even so the author writes about them in such a clear, logical and honest manner, that it turns the process of reading into an exciting intellectual adventure, whether you hold a degree in mathematics or not.

For those who are familiar with the original articles it will be interesting to see how the author’s thought has developed since the date of their first publication and what changes she has made as a result.


Bhatt, Rajesh and Roumyana Pancheva. 2006. Conditionals. In M. Everaert and H. v. Riemsdijk (eds.), The Blackwell Companion to Syntax. Oxford: Blackwell Publishers, 638-87.

Grice, H. Paul. 1989. Studies in the Way of Words. Cambridge, Mass.: Harvard University Press.

Hacquard, Valentine. 2006. Aspects of Modality. PhD dissertation. MIT, Cambridge, Mass.

Heim, Irene. 1982. The Semantics of Definite and Indefinite Noun Phrases. PhD dissertation. University of Massachusetts, Amherst.

Pollock, John L. 1976. Subjunctive Reasoning. Dordrecht: Reidel.

Eugenia Romanova holds a PhD from Tromsø University in Norway. Her thesis deals with the problems of verbal prefixation, event and argument structure and syntax-semantics interface in the Russian language. At present she is a lecturer in linguistics at a private university in Yekaterinburg, Russia.

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