LINGUIST List 23.5019

Sun Dec 02 2012

Review: Philosophy of Language; Semantics; Syntax: Kratzer (2012)

Editor for this issue: Monica Macaulay <>

Date: 02-Dec-2012
From: Eugenia Romanova <>
Subject: Modals and Conditionals: New and Revised Perspectives
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Book announced at

AUTHOR: Angelika KratzerTITLE: Modals and ConditionalsSUBTITLE: New and Revised PerspectivesSERIES TITLE: Oxford Studies in Theoretical Linguistics. Vol. 36PUBLISHER: Oxford University PressYEAR: 2012

Eugenia Romanova, Department of Linguistics, Institute of InternationalRelations, 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 conditionalitywritten in the framework of formal semantics/language philosophy and publishedin different years (from 1977 to 2002). The articles have, however, beenreviewed 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 modalsand even more modal interpretations. But if we limit ourselves to just two -“must” and “can” - how do we know which interpretation to choose in everyparticular case? The answer is: all the readings have one common component ofmeaning, “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 thenames 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 arrivedfrom 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 (“theancestors of the Maoris must have arrived from Tahiti”), which falls into itsmodal scope.

Any proposition in the scope of a modal operator should be identified withsets of possible worlds. A free relative “what is known” is a function frompossible worlds to sets of propositions -- premise sets. It is important thata set of propositions be consistent -- only those can be considered in modalexpressions. To interpret “must”, for every set we need a superset from whicha certain proposition follows; for “can” the proposition must be compatiblewith some set and all of its supersets. The intricacies of structuring premisesets 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 thetwo sets in the theory of modality.

Chapter 2. The Notion of Modality.

The second chapter deals with necessity and possibility modals, and analysestheir epistemic and root (circumstantial) interpretations. Since there is nounique syntactic category expressing modality (it can be realized with thehelp of various morphemes, auxiliaries and even phrases), the question arises:What is modality?

First, the main two ingredients of a modal reading are a conversationalbackground (a function from worlds to premise sets) and a modal relationdetermining the force of the conclusion. Modals express relations betweenconversational backgrounds and propositions. In the case of “simple” necessitythe 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 modaloperators are propositional operators.

Modal expressions are typically vague. Conversational backgrounds are definedby how a particular world is characterized and can be subdivided intorealistic, informational, and stereotypical (or normative). While realisticconversational backgrounds are more context-independent, stereotypicalconversational backgrounds should correspond to some contextual standard ofnormalcy, thus the two should be kept separate.

The appeal to normalcy as a contextual standard leads to one of the mainproposals of this chapter, which was missing in the original article: modalinterpretations can be graded. A notion of an ordering source is introducedhere. When we induce the ordering ≤ on a set of worlds W, a world w is atleast as close to an ideal or norm determined by a set of propositions A as aworld 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 necessarilyantisymmetric (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 wherepossibility and necessity collapse into each other (see pp. 44-45), yielding amodal without dual. “A modal without dual could also be a degree expressioncovering 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 anupper-degree modal may do. Such modals “could be used in situations whereEnglish would sometimes use ‘must’, and at other times ‘may’ or ‘might’” (p.47); however there are languages (like St’át’imcets) where upper-end degreemodals systematically take the place of necessity and possibility modals ofany kind (epistemic, deontic, irrealis and future). The modal base is thusrestricted by the ordering source requirements. The conclusion at this pointis that the interpretations of modals depend on both a modal base and anordering source, but either parameter can be fixed by an empty conversationalbackground.

Discussing circumstantial (root) and epistemic modals the author says thatboth types have non-empty realistic modal bases. The subtle semanticdifferences between the two types of modal come from their different syntacticpositions in the hierarchy of verbal inflectional heads (Hacquard 2006).Potentially non-realistic conversational backgrounds must function as orderingsources. Interacting with root modals they yield a number of differentinterpretations (deontic, bouletic, teleological, or propensity). The way itworks 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 andnot an upper-end degree modal, that wishes cannot override facts and thatordering sources can induce different partitions of modal bases, which is themain topic of the following chapter.

This chapter closes with an outlook of a theory describing how conditionalsrestrict modals where the subject of counterfactuals is also raised. Thesematters 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 isthe utterance of the whole sentence, and p depends on q and r; f is thefunction from the set of worlds W that assigns to every world the set of allthose propositions that are “the case in it” (p. 72). The analysis offered forp on p. 72 produces wrong truth conditions ((i) and (ii) on p. 73), followedby the Critical Argument, a step-by-step proof demonstrating where the truthconditions are wrong. So, a plausible analysis of counterfactuals is shown tohave implausible consequences. Out of two options -- to give up the analysisor check the argument -- the author prefers the second one.

Wittgenstein’s atomistic view is discarded, for it destroys the proposedanalysis. The notions worked out by Pollock (1976) are investigated in moredetail and adopted by the author. They are: simple (atomic) propositions,negated simple propositions, strong subjunctive generalizations (laws ofnature like the law of gravity) and weak subjunctive generalizations (actualnecessities, for example, anyone drinking from a particular bottle containingpoison would die).

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

Chapter 4. Conditionals.

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

(6) If my hen has laid eggs today, then the Cologne Cathedral will collapsetomorrow 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 sentenceswith quantifiers, like “some” and “most,” and conditional sentences withquantifying adverbials, like “most of the time.” What can account for suchsentences is the theory of restrictive quantification. For instance, thesentence “Most porches have screens” has the following representation:

(9)(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 ahorse, 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 eventwhere 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 inthe logical representation of the sentences” (pp. 90-91) with quantificationaladverbials ((13), p. 89). “The function of if-clauses is invariably torestrict the domain of the adverb. We have to concede, then, that there areindicative conditionals that cannot be analyzed as material conditionals” (p.91).

Chapter 2 raised the issue of if-clauses and their ability to restrict modaloperators. They do so without operating over modals directly: “if-clausesaffect a modal base parameter that subsequent modals depend on” (p. 94).Conditionals are capable of restricting modals at a distance and there is noneed to reconstruct the if-clause for purposes of interpretation (but seeBhatt and Pancheva 2006).

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

In addition to conditionals that restrict various types of operators, thereare “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 tohave 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 setsdepending on what the circumstances of evaluation are; conversationalbackgrounds are rather functions than premise sets.

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

At the end of the chapter the author discusses apparent counterexamples to herproposal and concludes that if-clauses are still not two place if…thenconnectives, 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 insome cases more rewarding than a possible world semantics. Possible situationsare mereologically composed of states of affairs that are world-mates. Thequestion is whether different states of affairs represent different situationsor can be lumped together. For instance, my being tired and my being hungryrepresent identical time-slices of the same individual, but are differentuniversals and hence different situations. Thick particulars -- particularswith all the universals they instantiate -- are not always necessary, thinparticulars 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 thesituations containing s, it is persistent).

Such logical operations as conjunction, disjunction and existentialquantification are restated for a situation semantics, and universalquantification is given special treatment, depending on the type of situationat 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 asstrong lumpers, which means that they can be true only in worlds, not inparticular situations, whereas non-accidental universal quantification createspropositions that are very poor lumpers -- they are true in all or none of thesituations of a world. And only accidental universal quantification producespropositions with the desired lumping properties in all worlds where universalgeneralization is non-vacuously true.

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

Not all facts have equal weight: some are important, others are altogetherirrelevant. Different sorts of similarities matter in different counterfactualsituations, and when lumping relations are different inconsistency does notarise.

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

The chapter closes with a discussion of negated statements and the interactionof negation with focus. Interpretation of counterfactuals with negation alsodepends 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 factsand true propositions that facts exemplify. One way is through the semanticsof the verb “to know”: “A person knows p iff the person believes p de re ofsome fact exemplifying p” (p. 163), where the res is not a proposition, but asituation. Situations stand in a part-whole relation to each other, thus “apossible situation s (is a fact that) exemplifies a proposition p iff wheneverthere is a part of s where p is not true, s is a minimal situation where p istrue” (p. 166) (see the situation Mud on p. 167).

Interestingly, while we do not seem to have a de re belief about the factexemplifying 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 abouta temporal or spatial location (in our case the world as a whole).

Knowledge ascriptions have a modal semantics with realistic conversationalbackgrounds. Some scenarios rendered in the chapter are not about the res ofthe belief ascribed, but about the proposition claimed to be the content ofthe 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 thebelief and the res of the belief. Consequently, facts are not necessarily truepropositions and that plays an important role in the analysis ofcounterfactuals.


The book is primarily intended for formal semanticists and philosophers oflanguage with serious background in the subjects. It can be accessible tograduate students of semantics or syntacticians with some knowledge of theformalism used in the volume, but the extent of this accessibility willdefinitely vary. Nevertheless, the book is certainly worth reading, for it isa product of rare scientific beauty, reflecting years of serious intellectualenterprise undertaken by its renowned author, whose already classical workshave been studied and cited by generations of linguists. Prior acquaintancewith mathematical logic, philosophy, and intensional semantics would increasethe level of understanding of this important book and make reading it moreenjoyable.

I have a number of questions of a highly specialized semantic character. Themost difficult chapter was chapter 2, where the ingredients and main notionsof modality were introduced. For example, in the discussion of informationalconversational backgrounds, the following statement was made: “…If a testimonyis a salient body of facts that a realistic background is about, theaccessible worlds are those that have counterparts of that testimony. …If thatsame testimony is the salient source of information feeding an informationbackground, the accessible worlds are those that are compatible with theintentional content of the testimony” (p. 34). To me it is not quite clearwhat is a counterpart and what is meant under the term “compatible” in thisparticular case, though I see the main idea of the passage.

The clearest chapters are chapters 4 and 6. A big part of chapter 4 wasdedicated to answering a question about scope relations between possibilitymodals and conditionals, which is related to syntax, and chapter 6 deals withphilosophy 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, onp. 47, where examples from St’át’imcets are given, the glosses naturallycontain some abbreviations (DEIC, IMPF, FOC, COUNTER etc.), but there is nolist 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 ofmodality, conditionality and counterfactuality. These are highly complexmatters but even so the author writes about them in such a clear, logical andhonest manner, that it turns the process of reading into an excitingintellectual adventure, whether you hold a degree in mathematics or not.

For those who are familiar with the original articles it will be interestingto see how the author’s thought has developed since the date of their firstpublication 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: BlackwellPublishers, 638-87.

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

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

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

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


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

Page Updated: 02-Dec-2012