Semantics

chapter 4

Sentence

Relations

and Truth

4.1 Introduction

In the last chapter we looked at some of the semantic relations which hold between

words and at the network effect that this gives to the lexicon. In this chapter we move

on to semantic relations that may hold between sentences of a language. As we shall

see, sometimes these relations are the result of particular words in the sentences, but

in other cases the relations are the result of syntactic structure. As an example of an

attempt to represent these relations, we will look at an approach to meaning based

on the notion of truth, which has grown out of the study of logic. In particular we

examine how successfully a truth-based approach is in characterizing the semantic

relations of entailment and presupposition. We begin by going back to our early,

deceptively simple question: what is meaning?

Many linguists would argue (see for example J. D. Fodor 1983) that there is no

answer to this question and that in this it is like the question “what is a number?”

in mathematics; or “what is grammaticality?” in syntax. The only true answer to

such questions, it is argued, are whole theories: so one has to have a syntactic theory

to give a substantive answer to the question: “what is grammaticality?” Otherwise,

it is claimed, we are reduced to empty answers like: “Grammaticality is a prop-

erty assigned to sentences by a grammar” (J. D. Fodor 1983). One way around this

Semantics, Fourth Edition. John I. Saeed.

Sentence Relations and Truth 85

problem is to identify the kinds of phenomena a theory of semantics must cover.

As we have seen, generative linguists orient their explanation in terms of a native

speaker’s competence. In this approach, the question then becomes: what kind of

knowledge about the meaning of his or her language does the native speaker have?

Answers to this question differ but there is a consensus in the literature that for sen-

tence meaning, a semantic theory should reect an English speaker’s knowledge:

4.1 That a and b below are synonymous:

a. My brother is a bachelor.

b. My brother has never married.

4.2 That a below entails b:

a. The anarchist assassinated the emperor.

b. The emperor is dead.

4.3 That a below contradicts b:

a. My brother Sebastian has just come from Rome.

b. My brother Sebastian has never been to Rome.

4.4 That a below presupposes b, as c does d:

a. The Mayor of Manchester is a woman.

b. There is a Mayor of Manchester.

c. I regret eating your sandwich.

d. I ate your sandwich.

4.5 That a and b are necessarily true, i.e. tautologies:

a. Ireland is Ireland.

b. Rich people are rich.

4.6 That a and b are necessarily false, i.e. contradictions:

a. ?He is a murderer but he’s never killed anyone.

b. ?Now is not now.

We shall be looking at some of these relations in more detail in this chapter but for

now we can give a rough characterization of each, as follows:

4.7 A is synonymous with B: A has the same meaning as B.

4.8 A entails B: we know that if A then automatically B.

4.9 A contradicts B: A is inconsistent with B.

4.10 A presupposes B: B is part of the assumed background against which A is

said.

4.11 A is a tautology: A is automatically true by virtue of its own meaning, but

informationally empty.

4.12 A is a contradiction: A is inconsistent with itself, i.e. asserts and denies the

same thing.

86 Semantic Description

The problem for semantics is to provide a more rigorous account of these and

similar notions. In the following sections we look at how a notion of truth might be

used to do this.

4.2 Logic and Truth

In this section, we take a brief excursion into the realm of logic. In doing this we are

following a number of writers, like Richard Montague (1974), who have hypothe-

sized that the tools of logic can help us to represent sentence meaning. We won’t be

going very far on this excursion and the interested reader is referred to an excellent

introduction to logic in Allwood et al. (1977). We will go on to look at logic-based

semantics in more detail ourselves in chapter 10.

The study of logic, of course, comes down to us from the classical Greek world,

most famously from Aristotle. The beginnings of logic lie in a search for the prin-

ciples of valid argument and inference. A well-known example is Aristotle’s modus

ponens, a type of argument in three steps, like the following:

4.13

a. If Arnd left work early, then he is in the pub.

Arnd left work early.

c. Arnd is in the pub.

If steps a and b (called the premises) are true then step c (the conclusion) is also

guaranteed to be true. Here we follow the tradition of separating the premises from

the conclusion by a horizontal line. Other rules of valid inference include the modus

tollens exemplied in 4.14 below, the hypothetical syllogism in 4.15 and the

disjunctive syllogism in 4.16:

4.14

a. If Arnd has arrived, then he is in the pub.

Arnd is not in the pub.

c. Arnd has not arrived.

4.15

a. If Arnd is in the pub, then he is drinking beer.

If Arnd is drinking beer, then he is drinking Guinness.

c. If Arnd is in the pub, then he is drinking Guinness.

4.16

a. Arnd is in the public bar or he is in the lounge.

Arnd isn’t in the public bar.

c. Arnd is in the lounge.

A part of this study is a concern for the truth of statements and whether truth is

preserved or lost by putting sentences into different patterns. Truth here is taken

to mean a correspondence with facts, or in other words, correct descriptions of

states of affairs in the world.

For the most part this truth is said to be empiri-

cal (or contingent), because we have to have some access to the facts of the world

to know whether a statement is true or not. Thus the truth or otherwise of the

sentence

4.17 My father was the rst man to visit Mars.

Sentence Relations and Truth 87

depends on facts about the life of the speaker’s father: if her father did go to Mars

and was the rst man there, then the sentence is true; otherwise it is false. In the

same way the empirical truth of 4.18 below:

4.18 The earth revolves around the sun.

depends upon the facts of the universe.

Semanticists call a sentence’s being true or false its truth-value,andthefacts

that would have to obtain in reality to make a sentence true or false, its truth con-

ditions. A simple example of a linguistic effect on truth-value comes from negating

a sentence. If we have a sentence like a below in English, adding not will reverse its

truth-value:

4.19

a. Your car has been stolen.

b. Your car has not been stolen.

If a is true then b is false; also if a is false then b is true. To show that this relationship

works for any statement, logicians use a schema called logical form, where a lower

case letter (p, q, r, etc.) stands for the statement and a special symbol for negation:

¬. So the logical form for 4.19a is 4.20a and for 4.19b is 4.20b:

4.20

a. p

b. ¬p

The effect of negation on the truth-value of a statement can be shown by a truth

table, where T represents “true” and F “false,” as below:

4.21 p ¬p

This table shows that when p is true (T), ¬p is false (F); when p is false (F), ¬p is

true (T). This is then a succinct way of describing the truth effect of negation.

The truth-value of other linguistic elements is studied in logic in the same way.

A number of connectives are especially important to logicians because they have a

predictable effect on the truth conditions of compound statements. For example the

truth-value of a compound formed by using and to join two statements is predictable

from the truth of the constituent statements. See, for example:

4.22

a. The house is on re.

b. The re brigade are on the way.

c. The house is on re and the re brigade are on the way.

If 4.22a and b above are true, then the compound c is also true. If however either

of a or b is false then the compound will be false. This can be shown by designing

a truth table for and, and representing it by a special symbol ∧:

4.23 pqp∧ q

TTT

TFF

FTF

FFF

88 Semantic Description

This table tells us that only when both statements connected by ∧ are true will the

compound be true. So 4.22c above will be false if the house is on re but the re

brigade are not on the way, and also false if the re brigade are on their way but to a

false alarm: the house is not on re. Most obviously of all, 4.22c is false if there is no

re and no re brigade on the way. This connective is called logical conjunction.

The study of the truth effects of connectives like ¬ and ∧, also called logical oper-

ators, is called propositional logic, and logicians have studied the truth effects of a

number of other connectives, for example those corresponding to the English words

or and if . . . then. We can look briey at these here and we will come back to them

again in chapter 10.

There are two logical connectives which can correspond to English or. The rst

is called disjunction (or alternatively inclusive or) and is symbolized as ∨, thus

giving logical forms like p ∨ q. The truth table for this connective is as follows:

4.24 pqp∨ q

TTT

TFT

FTT

FFF

Thus a compound created with ∨ is true if one or both of the constituent sentences

is true. This connective corresponds to the use of English or in sentences like the

following:

4.25 I’ll see you today or tomorrow.

Sentence 4.25 is true if either I’ll see you today or I’ll see you tomorrow is true, or both.

It is only false if both are false.

The second connective which can correspond to English or is called exclusive or,

XOR for short, which we can symbolize as ∨. This connective has the truth table

in 4.26 below:

4.26 pqp

∨ q

TTF

TFT

FTT

FFF

From 4.26 we can see that p

∨ q. This connective corresponds to the use of English

or in sentences like 4.27 below:

4.27 You will pay the ne or you will go to jail.

This use of or in English seems to have an implicit qualication of “but not both.”

Thus if a judge said sentence 4.27 to a defendant, it would seem very unfair if the

defendant paid the ne and then was still sent to jail, as would be consistent with

disjunction represented by the inclusive or. Thus the use in 4.27 seems to correspond

more closely to exclusive or.

Sentence Relations and Truth 89

The next connective we will look at here is the material implication, symbolized

as →. This connective has the truth table in 4.28

4.28 pqp→ q

TTT

TFF

FTT

FFT

As 4.28 shows, the expression p → q is only false when p (the antecedent)istrue

and q (the consequent) is false. This connective is something like my use of English

if...thenif I utter a sentence like 4.29:

4.29 If it rains, then I’ll go to the movies.

We can identify the if-clause in 4.29 as the antecedent and the then-clause as the

consequent. This conditional sentence can only be false if it rains and I don’t go to

the movies, that is p = T, q = F. If it doesn’t rain (p = F), my conditional claim

cannot be invalidated by whatever I do: whether I go to the movies (q = T) or not

(q = F). We can describe this relation by saying that p is a sufcient condition

for q (rain will cause me to go) but not a necessary condition (other things might

make me go; it might snow!).

This relation is a little hard to grasp and the reason is because we intuitively try

to match it with our ordinary use of conditional sentences in English. However,

conditionals in real languages often have more to them than this truth-conditional

connective shows. For example, there is often an assumption of a causal connection

between the antecedent clause (the if-clause) and the consequent (the then-clause),

as in 4.30 below:

4.30 If Patricia goes to the party, then Emmet will go too.

A natural implication of sentence 4.30 is that Emmet is going because Patricia is.

This is partly like our connective → because if Patricia goes to the party but Emmet

doesn’t (p = T, q = F) then the conditional sentence 4.30 is false, as the truth

table for → suggests. However, because of the causal implication, we might feel that

if Patricia doesn’t go (p = F) the conditional 4.30 implies that Emmet won’t go.

Thus we might feel that if he does go (q = T), the claim is invalidated. The logical

connective, however, doesn’t work like this: as 4.28 shows, if the antecedent is false,

the compound is true, whatever the truth-value of the consequent.

This truth-conditional relation also seems to miss our intuitions about another

ordinary language use of conditional if...thenconstructions: counterfactuals,

where the speaker overtly signals that the antecedent is false, for example:

4.31 If wishes were money, then we’d all be rich.

The lack of t here with our intuitions can be shown by the sentences in 4.32 below:

4.32

a. If I were an ostrich, then I would be a bird.

b. If I were an ostrich, then I would not be a bird.

90 Semantic Description

Let us interpret each of these conditionals as the p → q relation: since I am not in

fact an ostrich, we might take p in 4.32a to be false, and if we follow the reasoning

of the conditional then q might seem to be true. Thus, by the truth table in 4.28 the

sentence 4.32a is true. This seems a reasonable t with our intuition about 4.32a.

The problem is that assuming the same antecedent p in 4.32b to be false means that

4.32b also has to be true, according to our truth table 4.28. Even if we accept the

less likely 4.32b as true, it is uncomfortable to try and hold both 4.32a and b to be

true for the same speaker in the same context. It seems likely that the material impli-

cation relation simply doesn’t t our use of counterfactuals. We will not follow this

issue any further here; for a discussion of logical implication and ordinary language

conditionals, see Lewis (1973) and the overview in Haack (1978). What we can say

is that the logical relation of material implication captures some but not all aspects

of our use of if . ..thenin English.

There is one other related connective we might mention here, the bi-conditional,

symbolized by ≡ (or alternatively ↔). This connective has the truth table in 4.30

below:

4.33 pqp≡ q

TTT

TFF

FTF

FFT

As 4.33 shows, a statement p ≡ q is true when p and q have the same truth-value. The

name “bi-conditional” reects the fact that the p ≡ q is equivalent to the compound

conditional expression (p → q) ∧ (q → p), which we can paraphrase as “if p then q

and if q then p.” This connective corresponds to the English words if and only if as

in 4.34:

4.34 We’ll leave if and only if we’re forced to.

If we reverse the English clause order and identify the condition if and only if we

are forced to as p, and the consequent We’ll leave as q, then we can say that p is a

necessary condition for q,thatis,p is the only possible cause for q. Given this, this

connector is a plausible translation of the intended meaning of our earlier example

4.30 with if … then. In logic this relation “p if and only if q” is often abbreviated to

“p iff q.”

This has been just a brief look at logical connectives and their English counter-

parts. As we have mentioned, in logic these connectives are important for the estab-

lishment of valid arguments and correct inductive reasoning. Using the symbols we

have introduced in this section, we can represent the types of valid inference exem-

plied earlier in 4.13–16, as follows:

4.35 Modus ponens

p → q

Sentence Relations and Truth 91

4.36 Modus tollens

p → q

¬q

¬p

4.37 Hypothetical syllogism

p → q

q → r

p → r

4.38 Disjunctive syllogism

p ∨ q

¬p

For our current purposes, what we need to hold onto are these ideas from logic: that

statements have a truth-value; that this truth-value depends upon a correspondence

to facts, and that different ways of connecting statements have different effects on

the truth-value of the compounds produced.

4.3 Necessary Tr uth, APrioriTruth, and Analyticity

As we have seen, the notion of empirical truth depends on a correlation to states

of affairs in reality. Philosophers and logicians have identied another type of truth

which seems instead to be a function of linguistic structure. For example, we know

that the tautology

4.39 My father is my father.

is always true (in its literal meaning) without having to refer to the facts of the world,

as is a sentence like:

4.40 Either he’s still alive or he’s dead.

We do not have to check a pulse to nd out whether this sentence is true.

In the same way, contradictions are false simply by virtue of their own meaning,

for example:

4.41 ?She was assassinated last week but fortunately she’s still alive.

This second kind of truth has been the focus of much investigation. The question

of how it is that we might know a statement to be true without checking the facts

of the world has been discussed by many philosophers

and various distinctions of

truth have been made. For example, we started out by characterizing this type of

truth in epistemological terms, that is in terms of what the speaker knows (or needs

to know before making a judgment about truth). From this perspective, truth that

92 Semantic Description

is known before or without experience has traditionally been called apriori. This

aprioritruth is contrasted with a posteriori truth: truth which, as in our examples

4.17 and 4.18 earlier, can only be known on the basis of empirical testing.

Another related concept is Leibniz’s distinction between necessary truths, which

cannot be denied without forcing a contradiction, for example the arithmetical state-

ment Twoandtwomakefour,andcontingent truths which can be contradicted,

depending on the facts, for example the sentence The dodo is extinct.Ifsomeoneunex-

pectedly found a dodo in a forest on Mauritius, this latter sentence would become

false. It is difcult, on the other hand, to imagine circumstances in which Two a n d

two make four would unexpectedly become false. This is similar to our apriori/apos-

teriori distinction but comes at truth from another viewpoint: not in terms of what

the speaker knows but in terms of what the world is like. We can say that it is hard to

think how our sentence about two and two making four could not be true without

changing our view of the present facts of the world.

From this perspective a sentence

like 4.40 is also necessarily true and a contradiction like 4.41 is necessarily false.

In another, related terminology tautologies like 4.39 are analytic while a sentence

like My father is a sailor is synthetic. Analytic statements are those where the truth

follows from the meaning relations within the sentence, regardless of any relationship

with the world, while a synthetically true statement is true because it accords with

the facts of the world.

Thus we have three related distinctions of truth: between aprioriand a poster i-

ori, necessary and contingent, and analytic and synthetic. These notions are closely

linked, yet not quite identical. As noted by Kripke (1980), part of their difference

comes from the concerns of the analyst: the apriori/a posteriori distinction is an epis-

temological one: it concerns the source of what the speaker knows. If just knowing

a language is enough to know the truth of a proposition then it is apriori.Ifthe

knowledge has to be based on experience of the world it is a posteriori. The neces-

sary/contingent distinction on the other hand is really a metaphysical one, where we

are philosophically questioning the nature of reality. We can hypothesize that it is the

nature of reality that ensures that a sentence like Two and two make four is a neces-

sary truth. Finally, the analytic/synthetic distinction is semantic in orientation. The

traditional claim has been that analytic sentences are true because of the meaning of

the words within them: for example, the meaning of the predicate might somehow

be included in the meaning of the subject: it might not add anything new.

This

certainly seems to be true of our tautology My father is my father.

We can see that the three notions are related because under the kind of denitions

we have introduced so far, our example sentence My father is my father is an apriori

truth, it is necessarily true and it is analytic. As we have mentioned, this classication

of truth has been the subject of much debate in the philosophical literature and it

has been argued by some philosophers, for example Kripke (1980), that the terms

do not characterize exactly the same set of statements, for example that a statement

might be a necessary truth but not an aprioritruth. To parallel a standard example,

a statement of identity like Mogadishu is Hamar is necessarily true because these are

two names for the same city, the capital of Somalia. Clearly, though, it is possible

for a person not to know this, and therefore for this person our sentence is not an

aprioritruth. The person might have to ask people or look it up in a book, making

the knowledge a posteriori.

This sketch is enough for our present purposes. In our discussion we will infor-

mally use necessary truth and analytic truth as synonymous terms to describe

Sentence Relations and Truth 93

sentences which are true by virtue of their meaning, and which therefore are known

to be true by a speaker of the language without any checking of the facts. See Grayling

(1982) for further discussion of the relations of these notions.

We can provide further examples of sentences that are analytic or necessarily true

in this sense if we imagine logically minded sports fans looking forward to the next

World Cup Final and saying the following:

4.42

a. Either Germany will win the World Cup or Germany won’t win the

Wor l d C u p.

b. If Germany are champions and Brazil are runners-up then Germany

are champions.

c. All teams who win are teams.

d. If Germany beat Brazil then Brazil lose to Germany.

Sentences like 4.42 a–c above have been important in the development of logic.

This is because their truth can be predicted from their logical form. Take 4.42a for

example: if, as before, we replace each clause by an arbitrary letter, we produce a

logical form, for example:

4.43 Either p or not-p

This formula will be true for any clause, as long as each clause is the same, repre-

sented above by using the same letter. For example:

4.44 Either we’ll make it on time, or we won’t make it on time.

Similarly, sentence 4.42b above can be given the logical form:

4.45 If p and q then p

Once again whatever clauses we use for p and q the formula will be true, for example:

4.46 If the house is sold and we aren’t there, the house is sold.

Sentence 4.42c is also necessarily true because of its logical form, but in this case

the truth behavior is caused by the presence within the clause of the quantier all.

To nd its logical form we have to go inside the clause and replace the subject and

predicate by variables, for example:

4.47 All X’s that Y are X’s.

Again, this form will be true whatever subject and predicate we insert for X and Y,

for example:

4.48 All birds that y are birds.

The study of the truth behavior of such sentences with quantiers like all, every,

each, some, one gave rise to a second type of logic usually called predicate logic.

Once again, good introductions to this logic can be found in Allwood et al.

94 Semantic Description

(1977). We will come back to both propositional and predicate logic again in

chapter 10.

The important point here is that, as we have seen, there are certain words like

the connectors and, or, if . . . then,thenegativewordnot, and quantiers like all,

some, one, which inuence the truth behavior of sentences. For this reason these

are sometimes called logical words. So the sentences 4.42a–c are necessarily true

because of the presence of logical words, which means that their truth behavior is

predictable from their logical form.

The truth of sentence 4.42d (If Germany beat Brazil then Brazil lose to Germany),

however, depends on the meaning of individual words like beat and lose,andnotany

logical form we might give the sentence, like 4.49:

4.49 If GXBthen BYG.

We can see this because, if we replace the verbs with other verbs, we cannot predict

that the resulting sentence will also be analytically true, for example:

4.50 If Germany attack Brazil then Brazil outscore Germany.

This sentence might be true, or not: we cannot tell just from the sentence. It seems

that sentence 4.42d is necessarily true because of the semantic relationship in English

between the verbs beat and lose. This kind of necessary truth has not traditionally

been a concern of logicians, because its effects cannot easily be reduced to general

rules or schemas: it relies on the very varied and individual lexical relations we looked

at in chapter 3. Thus such necessarily true sentences can derive from synonymy as

in 4.51a below; from simple antonymy as in 4.51b; from converse pairs as in 4.51c;

or hyponymy as in 4.51d:

4.51

a. My bachelor brother is an unmarried man.

b. If Elvis is dead then he is not alive.

c. If she’s his sister then he’s her brother.

d. A cat is an animal.

So our examples have shown us that sentences can be analytically true because of

the behavior of logical words (connectors, quantiers) or because of the meaning of

individual nouns and verbs. In each case we know that the sentences are true without

having to check any facts about the world.

4.4 Entailment

Using this special meaning of “truth” that we have been looking at, some semanticists

have claimed that the meaning relations discussed in section 4.1 can be given a more

rigorous denition. The claim is that there are xed truth relations between sen-

tences which hold regardless of the empirical truth of the sentences. We can examine

this claim by looking at the semantic relation of entailment. Let’s take as an exam-

ple the relationship between sentences 4.52a and b below, where a is said to entail b:

4.52

a. The anarchist assassinated the emperor.

b. Theemperordied.

Sentence Relations and Truth 95

Assuming as usual that the same individual is denoted by the emperor here, there

are a number of ways of informally describing this relationship. We could say that

if somebody tells us 4.52a and we believe it, then we know 4.52b without being

told any more. Or we could say that it is impossible for somebody to assert 4.52a

but deny b. What such denitions have to try to capture is that entailment is not

an inference in the normal sense: we do not have to reason to get from 4.52a to b,

we just know it instantaneously because of our knowledge of English. A truth-based

denition of entailment might allow us to state the relationship more clearly and

would be something like 4.53 below:

4.53 Entailment dened by truth:

Asentencep entails a sentence q when the truth of the rst (p) guarantees

the truth of the second (q), and the falsity of the second (q) guarantees the

falsity of the rst (p).

We can see how this would work for our examples:

4.54 Step 1: If p (The anarchist assassinated the emperor) is true, is q (The

emperor died) automatically true? Yes.

Step 2: If q (The emperor died) is false, is p (The anarchist assassinated

the emperor) also false? Yes.

Step 3: Then p entails q. Note if p is false then we can’t say anything about

q; it can be either true or false.

We can try to show this relation in an accessible form if we take the logician’s truth

tables, seen earlier, and adapt them somewhat. We can continue to use the symbols p

and q for our two sentences, and T and F for true and false, as in normal truth tables,

but we will add arrows (→ and ←) to show the direction of a relation “when … then.”

So the rst line of 4.55 below is to be read “When p is true, q is true,” and the last

line is to be read “when q is true, p can be either true or false.” By taking these

liberties with traditional truth tables, we can show the truth relations of entailment

in 4.55, a composite truth table:

4.55 Composite truth table for entailment

T → T

F → TorF

F ← F

TorF ← T

When this set of relations hold between p and q, p entails q. From this table we can

see that only the truth of the entailing sentence or the falsity of the entailed sentence

has consequences for the other sentence. When p is false, q canbeeithertrueor

false: if all we were told was that the anarchist didn’t assassinate the emperor, we

wouldn’t know whether the emperor was dead or alive. When q is true, p can be

either true of false: if we just know that the emperor is dead, that doesn’t tell us

anything about whether the anarchist assassinated him or not.

96 Semantic Description

We have said that an entailment relation is given to us by linguistic structure: we

do not have to check any fact in the world to deduce the entailed sentence from the

entailing sentence. The source may be lexical or syntactic. In our example above it

is clearly lexical: the relationship of entailment between 4.52a and b derives from

the lexical relationship between assassinate and die. In some sense the meaning of

assassinate contains the meaning of die. In chapter 3 we called a similar relationship

of meaning hyponymy; and indeed hyponymy between lexical items is a regular

source for entailment between sentences. For example, the noun dog is a hyponym

of animal, so it follows that sentence 4.56 below entails sentence 4.57:

4.56 I bought a dog today.

4.57 I bought an animal today.

Other sources for entailment are syntactic: for example, active and passive versions

of the same sentence will entail one another. Sentence 4.58 below entails 4.59, and

vice versa:

4.58 The Etruscans built this tomb.

4.59 This tomb was built by Etruscans.

In fact, the relationship of entailment allows us to dene paraphrase. Paraphrases,

like 4.58 and 4.59, are sentences which have the same set of entailments, or, to put

it another way, mutually entail each other.

This truth-based denition does seem to capture our basic intuitions about entail-

ment and semanticists have gone on to characterize other semantic relations in terms

of truth relations. For example, we could very simply characterize synonymy with

the table:

4.60 Composite truth table for synonymy

T → T

F → F

T ← T

F ← F

This table simply says, of course, that p and q always have the same truth-value,

that is, if p describes a situation so will q, and vice versa; while if either incorrectly

describes a situation so will the other. We can see this is true for examples like:

4.61 Alice owns this book.

4.62 This book belongs to Alice.

where again we observe the convention that it is the same Alice and the same book

in the two sentences.

Sentence Relations and Truth 97

The opposite of this relation of synonymy would be contradiction, with the truth

table below:

4.63 Contradiction

T → F

F → T

T ← F

F ← T

where the simplest examples involve negation, as below:

4.64 Mr Jones stole my car.

4.65 Mr Jones did not steal my car.

but other examples might also include the lexical relation of simple or binary

antonymy, as in our earlier examples with beat/lose to.

So thus far it seems that recasting semantic relations as truth relations allows us

to describe neatly the relations we listed in section 4.1 as being the focus of our

investigations. In the next section, however, we look at one of these relations, pre-

supposition, which seems to lend itself less well to a truth-based description.

4.5 Presupposition

4.5.1 Introduction

In ordinary language, of course, to presuppose something means to assume it, and

the narrower technical use in semantics is related to this. In the following examples

the a sentence is said to presuppose the b sentence:

4.66

a. He’s stopped turning into a werewolf every full moon.

b. He used to turn into a werewolf every full moon.

4.67

a. Her husband is a fool.

b. She has a husband.

4.68

a. I don’t regret leaving London.

b. I left London.

4.69

a. The Prime Minister of Malaysia is in Dublin this week.

b. Malaysia has a prime minister.

4.70

a. I do regret leaving London.

b. I left London.

Presupposition has been an important topic in semantics: the 1970s in particular

saw lively debates in the literature. Books devoted largely to the subject include

98 Semantic Description

Kempson (1975), D. Wilson (1975), Boer and Lycan (1976), Gazdar (1979) and Oh

and Dinneen (1979); and important papers include J. D. Fodor (1979) and Wilson

and Sperber (1979). In retrospect this interest in presupposition can be seen as coin-

ciding with the development of pragmatics as a subdiscipline. The basic idea, men-

tioned in chapter 1, is that semantics would deal with conventional meaning, those

aspects which do not seem to vary too much from context to context, while prag-

matics would deal with aspects of individual usage and context-dependent meaning.

The importance of presupposition to the pragmatics debate is that, as we shall see,

it seems to lie at the borderline of such a division. In some respects presupposition

seems like entailment: a fairly automatic relationship, involving no reasoning, which

seems free of contextual effects. In other respects though, presupposition seems sen-

sitive to facts about the context of utterance. We will look at this sensitivity to context

in section 4.5.5.

For now we can begin by identifying two possible types of approach to presuppo-

sition, arising from different ways of viewing language.

4.5.2 Two approaches to presupposition

In the rst approach, rather in the philosophical tradition, sentences are viewed as

external objects: we don’t worry too much about the process of producing them,

or the individuality of the speaker or writer and their audience. Meaning is seen

as an attribute of sentences rather than something constructed by the participants.

Semantics then consists of relating a sentence-object to other sentence-objects and

to the world. When in the last section we characterized sentence relations in terms

of truth relations we adopted this perspective. The second approach views sentences

as the utterances of individuals engaged in a communication act. The aim here is

about modeling the strategies that speakers and hearers use to communicate with

one another. So we might look at communication from the speaker’s viewpoint and

talk about presupposition as part of the task of packaging an utterance; or adopt the

listener’s viewpoint and see presupposition as one of a number of inferences that the

listener might make on the basis of what the speaker has just said. The rst approach

is essentially semantic and the second pragmatic.

Let’s use 4.71 below and its presupposition 4.72 as an example to show these

different views.

4.71 John’s brother has just got back from Texas.

4.72 John has a brother.

We can adopt the sentences-as-external-objects approach and try to identify a

semantic relationship between these two sentences. One obvious way is to cast this

as a truth relation, as we did for entailment and other relations in the last section.

To do this we might reason as in 4.73, to set up the partial truth table in 4.74:

4.73 Presupposition as a truth relation.

Step 1: If p (the presupposing sentence) is true then q (the presupposed

sentence) is true.

Step 2: If p is false, then q is still true.

Step 3: If q is true, p couldbeeithertrueorfalse.

Sentence Relations and Truth 99

4.74 A rst composite truth table for presupposition

T → T

F → T

TorF ← T

At the risk of being longwinded, we can work through 4.73. If it is true that John’s

brother has come back from Texas, it must be true that John has a brother. Similarly,

if it is false that John’s brother has come back from Texas (if he is still there, for

example), the presupposition that John has a brother still survives. Finally, if is true

that John has a brother, it doesn’t tell us anything about whether he has come back

from Texas or not: we just don’t know.

So viewing presupposition as a truth relation allows us to set up a truth table like

4.74, and allows us to capture an important difference between entailment and pre-

supposition. If we negate an entailing sentence, then the entailment fails; but negat-

ing a presupposing sentence allows the presupposition to survive. Take for example

the entailment pair in 4.75:

4.75

a. I saw my father today.

b. I saw someone today.

If we negate 4.75a to form 4.76a then it no longer entails 4.75b, repeated as 4.76b:

4.76

a. I didn’t see my father today.

b. I saw someone today.

Now 4.76b no longer automatically follows from the preceding sentence: again it

might be true, we just don’t know. Compare this with the presupposition pair:

4.77

a. The mayor of Liverpool is in town.

b. There is a mayor of Liverpool.

If we negate 4.77a to form 4.78a the resulting sentence still has the presupposition,

shown as 4.78b:

4.78

a. The mayor of Liverpool isn’t in town today.

b. There is a mayor of Liverpool.

So negating the presupposing sentence does not affect the presupposition, whereas,

as we saw, negating an entailing sentence destroys the entailment. So it seems that

viewing presupposition as a truth relation allows us to capture one interesting dif-

ference between the behavior of presupposition and entailment under negation.

By comparison, we can sketch an idea of how an alternative, interactional view

of presupposition might work for our original example; John’s brother has just got

back from Texas. This approach views presupposition as one aspect of a speaker’s

strategy of organizing information for maximum clarity for the listener. Let us say

roughly that the speaker wants to inform the listener that a particular individual has

returned from Texas. The way she does this will depend on what she estimates about

100 Semantic Description

her listener’s knowledge. If she thinks he knows John but not his brother, we can see

in her use of 4.64 an ordering of the assertions in 4.79–80:

4.79 Assertion 1: John has a brother X.

4.80 Assertion 2: X has come back from Texas.

In our example 4.71 the rst assertion is downgraded or backgrounded by being

placed in a noun phrase [John’s brother] while the second assertion is highlighted or

foregrounded by being given the main verb. Why foreground one assertion rather

than another? The answer must depend on the speaker’s intentions and her guesses

about the knowledge held by the participants. For example the speaker might judge

that the listener knows 4.79 but that 4.80 is new information, and therefore needs

to be foregrounded. Here we could speculate that the speaker decides to include

the old information 4.79 to help the listener to identify the individual that the new

information is about. Note too that a speaker can use 4.71 even if the listener does

not know John has a brother. In such a case both assertions are new but the speaker

has decided to rank them in a particular order.

4.5.3 Presupposition failure

One phenomenon which has traditionally caused problems for a truth relations

approach but may be less problematic in an interactional approach is presuppo-

sition failure. It has been observed that using a name or a denite description to

refer presupposes the existence of the named or described entity:

so the a sentences

below presuppose the b sentences:

4.81

a. Ronald is a vegetarian.

b. Ronald exists.

4.82

a. The King of France is bald.

b. There is a King of France.

Example 4.82 is of course the subject of Bertrand Russell’s discussion of the prob-

lem (Russell 1905), and is by now one of the most discussed examples in this liter-

ature. The problem arises when there exists no referent for the nominal. If there’s

no Ronald or King of France, that is if the b sentences above are false, what is the

status of the a sentences? Are they false, or are they in a gray area, neither true nor

false? In a truth-based approach, on a gray-area analysis, we need to add a line to

our truth table, but what does the line look like?

4.83 A second truth table for presupposition

T → T

F → T

TorF ← T

?(T or F) ← F

Sentence Relations and Truth 101

What this table tries to show is that if q is false, the status of p is dubious, possi-

bly neither true nor false. This is a problem for truth-based theories, known as a

truth-value gap. If a statement can be neither true nor false, it opens a nasty can

of worms. How many degrees in between are possible? A good deal of the attractive

simplicity of the truth-based approach seems in danger of being lost. It is a problem

that has generated a number of solutions in the philosophical literature; see McCul-

loch (1989) for discussion, and for a solution in the linguistics literature, J. D. Fodor

(1979). Russell’s famous solution was to analyze denite descriptions as complex

expressions roughly equivalent to 4.84 (adapted from McCulloch 1989: 47):

4.84 The King of France is bald is true if and only if:

a. at least one thing is the king

b. at most one thing is the king

c. whatever is the king is bald.

From 4.84, it follows that sentence 4.82a is false if there is no king of France, and that

there is no gray area between true and false, no truth-value gap. The cost however is

a large discrepancy between the surface language and the semantic representation.

Do we really want to say that a name is underlyingly a cluster of three statements?

For an interactional approach, there is less of a problem. Such an approach would

claim that a speaker’s use of denite NPs like names and denite descriptions to refer

is governed by conventions about the accessibility of the referents to the listener. In

some obvious way, I have made a communication error if I say to you:

4.85 Heronymous is bringing us a crate of champagne.

if you don’t know any person called Heronymous. Your most likely response would

be to ask “Who’s Heronymous?,” thus signaling the failure. So we can hypothesize

that there is an interactional condition on referring: a speaker’s use of a name or

denite description to refer usually carries a guarantee that the listener can identify

the referent.

So in an interactional approach the issue of presuppositional failure shifts attention

from the narrow question of the truth-value of statements about non-existent entities

to the more general question of what conventions license a speaker’s referring use of

denite nominals.

4.5.4 Presupposition triggers

We have seen that the use of a name or denite description gives rise to a presuppo-

sition of existence. Other types of presupposition are produced by particular words

or constructions, which together are sometimes called presupposition triggers.

Some of these triggers derive from syntactic structure, for example the cleft con-

struction in 4.86 and the pseudo-cleft in 4.87 share the presupposition in 4.88:

4.86 It was his behavior with frogs that disgusted me.

4.87 What disgusted me was his behavior with frogs.

4.88 Something disgusted me.

102 Semantic Description

Other forms of subordinate clauses may produce presuppositions, for example, time

adverbial clauses and comparative clauses. In the following sentences, the a sentence

has the presupposition in b:

4.89 a. I was riding motorcycles before you learned to walk.

b. You learned to walk.

4.90 a. He’s even more gullible than you are.

b. You are gullible.

Many presuppositions are produced by the presence of certain words. Many of

these lexical triggers are verbs. For example, there is a class of verbs like regret

and realize that are called factive verbs because they presuppose the truth of their

complement clause. Compare sentences 4.91 and 4.92 below: only the sentence

with the factive realize presupposes 4.93. There is no such presupposition with the

non-factive verb think.

4.91 Sean realized that Miranda had dandruff.

4.92 Sean thought that Miranda had dandruff.

4.93 Miranda had dandruff.

Similarly compare 4.94–6:

4.94 Sheila regretted eating the banana.

4.95 Sheila considered eating the banana.

4.96 Sheila ate the banana.

Some verbs of judgment produce presuppositions. Compare 4.97–9 below:

4.97 John accused me of telling her.

4.98 John blamed me for telling her.

4.99 I told her.

Once again one verb, blame, produces the presupposition in 4.99, while another,

accuse, does not.

For a nal example of lexical triggers, consider so-called aspectual verbs, like

start, begin, stop. These verbs have a kind of switch presupposition: the new situ-

ation is both described and is presupposed not to have held prior to the change;

see for example 4.100–1 below, where again the a sentences presuppose the b

sentences:

4.100

a. Judy started smoking cigars.

b. Judy used not to smoke cigars.

Sentence Relations and Truth 103

4.101

a. Michelle stopped seeing werewolves.

b. Michelle used to see werewolves.

4.5.5 Presuppositions and context

As mentioned earlier, one problem for a simple truth-based account of presupposi-

tion is that often the presuppositional behavior seems sensitive to context. While a

given sentence always produces the same set of entailments, it seems that this is not

true of presuppositions. Levinson (1983) gives as an example the type of presuppo-

sition usually triggered by time adverbial clauses, for instance 4.102a presupposing

4.102b below:

4.102

a. She cried before she nished her thesis.

b. She nished her thesis.

However, if we change the verb, as in 4.103a below, the presupposition 4.103b is no

longer produced:

4.103

a. She died before she nished her thesis.

b. She nished her thesis.

Why is this? It is argued that in 4.103 the presupposition is blocked or canceled

by our general knowledge of the world: quite simply we know that dead people do

not normally complete unnished theses. This characteristic is sometimes known

as defeasibility, that is the canceling of presuppositions. If presuppositions arise or

not depending on the context of knowledge, this suggests that we need an account

of them that can make reference to what the participants know, as in an interactional

approach, rather than an account limited to formal relations between sentences.

Another example of context sensitivity, pointed out by Strawson (1950), occurs

with sentences like 4.104 and 4.105 below:

4.104 It was Harry who Alice loved.

4.105 It was Alice who loved Harry.

These sentences seem to describe the same essential situation of Alice loving Harry;

or, to put it another way, we might say that they embody the same proposition. The

difference between them is that they belong to different conversational contexts:

whether the participants have been discussing Harry or Alice. As Strawson points

out, they seem to give rise to different presuppositions, with 4.104 producing 4.106

and 4.105 producing 4.107:

4.106 Alice loved someone.

4.107 Someone loved Harry.

The same phenomenon is found with intonation in English, where stressing differ-

ent parts of the sentence can produce different presuppositions. Using capitals to

104 Semantic Description

show the position of this stress, we can produce the presupposition in 4.106 above

with 4.108 below, and 4.107 above with 4.109 below:

4.108 Alice loved HARRY.

4.109 ALICE loved Harry.

Such phenomena are discussed by Jackendoff (1972) and Allan (1986) among oth-

ers. So these examples seem to provide another case where presuppositional behavior

is related to context: in this case the context of the discourse.

Another, narrower, contextual feature is traditionally called the projection prob-

lem, and is discussed by a number of writers, including Gazdar (1979), Karttunen

and Peters (1979), Levinson (1983), Soames (1989), and Heim (1992). Sometimes

the presupposition produced by a simple clause does not survive when the clause

is incorporated into a complex sentence. Levinson (1983: 191ff) gives the example

of conditional clauses. Sentence 4.110a contains the factive verb regret and would

normally produce the presupposition in 4.110b:

4.110

a. John will regret doing linguistics.

b. John is doing/will do linguistics.

However, in the context of a conditional clause like 4.111 below, the presupposition

4.110b disappears:

4.111 If John does linguistics, he’ll regret it.

The context here is the syntactic one provided by the adjoining clause.

So we can see that different levels of context can cause uctuations in presup-

positional behavior. At the most general level, the context provided by background

knowledge; then, the context provided by the topic of conversation; and nally, the

narrower linguistic context of the surrounding syntactic structures – all can affect

the production of presuppositions. Simply giving a truth table of xed relations

between presupposing and presupposed sentences cannot adequately describe this

complicated behavior. Some more sophisticated account is required which takes

account of how what participants know forms a background to the uttering of a

sentence.

4.5.6 Pragmatic theories of presupposition

There have been a number of responses in the semantics literature to the features

of presupposition we have outlined. Some writers (for example Leech 1981) have

divided presuppositions into two types: one, semantic presupposition, amenable

to a truth-relations approach; another, pragmatic presupposition, which requires

an interactional description. In contrast, Stalnaker (1974) argued that presupposi-

tion is essentially a pragmatic phenomenon: part of the set of assumptions made by

participants in a conversation, which he termed the common ground. This set of

assumptions shifts as new sentences are uttered. In this view a speaker’s next sen-

tence builds on this common ground and it is pragmatically odd to assert something

Sentence Relations and Truth 105

which does not t it. Presumably cases of presuppositional failure like The king of

France is bald would be explained in terms of the speaker assuming something (There

is a king of France) that is not in the common ground.

This type of approach can cope with cases where presuppositions are not neces-

sarily already known to the hearer, as when a speaker says My sister just got married

(with its presupposition I have a sister) to someone who didn’t know she had a sister.

To capture this ability Lewis (1979: 127) proposes a principle of accommodation,

where: “if at time t something is said that requires presupposition p to be accept-

able, and if p is not presupposed just before t then – ceteris paribus – presupposition

p comes into existence.” In other words presuppositions can be introduced as new

information.

A pragmatic view of presupposition is also proposed by Sperber and Wilson

(1995) who argue that presupposition is not an independent phenomenon but

one of a series of effects produced when the speaker employs syntactic structure

and intonation to show the hearer how the current sentence ts into the previ-

ous background. These writers integrate presupposition with other traditional dis-

course notions like given and new information, and focus. They propose (1995:

215) that the same principle of relevance to contextual assumptions covers both

presupposition and the choice of the different word orders and intonations in

4.112 below:

4.112

a. It rained on MONDAY.

b. On Monday it RAINED.

c. On MONDAY it rained.

These sentences belong to different contexts of use in a similar way to our pre-

supposition examples in 4.104–9, that is, the preceding context will naturally lead

a speaker to choose one of the sentences in 4.112 over another. In Sperber and

Wilson’s view a general theory of conversational cooperation will explain all such

cases. We will look at further examples of this in chapter 7.

4.6 Summary

In this chapter we have identied a number of semantic relations that hold

between sentences: synonymy, contradiction, entailment and presupposition;

and the sentential qualities of tautology and contradiction. We have reviewed

an approach which characterizes these in terms of truth relations, using a notion

of linguistic or analytic truth. We have seen that while this approach provides an

attractive account of a number of properties, including synonymy, contradiction,

tautology, and most importantly entailment, it fails to account for the full range

of presuppositional behavior, in particular presupposition’s sensitivity to contex-

tual features. We contrasted this purely semantic approach with accounts which

assume a pragmatic approach: describing presupposition in terms of a speaker’s

strategies to package her message against her estimate of what her audience knows.

We will come back to this idea of processes of packaging information again in

chapter 7.

106 Semantic Description

EXERCISES

4.1 Take three sentences, p, q, and r as follows:

p: The sun is shining.

q:Thedayiswarm.

r: The sun is shining and the day is warm.

Let’s make the working assumption that we can represent sentence r by

the logical formula p ∧ q. Use the truth table for ∧ givenin4.23inthis

chapter to show the truth-value of r in the three situations (S1–3) below:

S1. p is true; q is false

S2. p is true; q is true

S3. p is false; q is true

S4. p is false; q is false

4.2 In propositional logic is it assumed that p ∧ q and q ∧ p are logically

equivalent, that is the order of the elements is irrelevant. Discuss how the

following examples show that this is not true for the way that speakers use

English and.

a. He woke up and saw on TV that he had won the lottery.

b. Combine the egg yolks with water in a bowl and whisk the mixture

until foamy.

c. He made two false starts and was disqualied from the race.

d. Move and I’ll shoot!

4.3 Take three sentences, p, q, and r as follows:

p: Peter is drinking.

q: Aideen is driving home.

r: It is not the case that Peter is drinking or Aideen is driving home.

Let’s make the working assumption that sentence r is ambiguous: in one

reading the whole sentence is negated; in the other, just the rst disjunct

is negated. Thus the sentence may be given the two logical forms in a and

bbelow:

a. ¬ (p ∨ q)

b. ¬p ∨ q

Use the truth tables for ¬ given in 4.21 and ∨ in 4.24 in this chapter

to show the truth-values of a and b above in the four situations (S1–4)

below:

S1. p is true; q

is false

S2. p is true; q is true

S3. p is false; q is true

S4. p is false; q is false

4.4 To begin with, assume a general rule of disjunction reduction, by which

any phrasal or clausal disjunction is derived from the disjunction of full

Sentence Relations and Truth 107

sentences, that is, assume that a sentence like Yo u c a n s a y y e s o r n o is equiv-

alent to You can say yes or you can say no. For each of the sentences below,

decide whether the use of or corresponds to inclusive (∨) or exclusive

(

∨) disjunction. Discuss your reasoning. Do any of these sentences have

meanings that you feel are not captured by assuming disjunction reduc-

tion; or by the truth table characterization of the two logic connectors in

4.24 and 4.26 earlier?

a. We spend the afternoons swimming or sunbathing.

b. They can resuscitate him or allow him to die.

c. If the site is in a particularly sensitive area, or there are safety con-

siderations, we can refuse planning permission.

d. You can take this bus or wait till the next one.

e. Beffni is a man’s name or a woman’s name.

f. The base camp is ve or six days’ walk from here.

g. He doesn’t smoke or drink.

h. She suffers from agoraphobia, or fear of open places.

i. Stop or I’ll shoot!

4.5 Decide which of the following sentences are analytically true. Discuss

the reasons for your decision.

a. If it rains, we’ll get wet.

b. The train will either arrive or it won’t arrive.

c. Every doctor is a doctor.

d. If Albert killed a deer, then Albert killed an animal.

e. Madrid is the capital of Spain.

f. Every city has pollution problems.

4.6 Below are some paired sentences. Use the composite truth table for

entailment given in 4.55 in this chapter to decide whether the a sen-

tence entails its b partner. Note any cases of mutual entailment and the

difference in truth relations this involves. (As usual, assume that repeated

nouns, names and pronouns refer to the same entity twice, and that the

b sentences are uttered immediately after the a sentences.)

1 a. Olivia passed her driving test.

b. Olivia didn’t fail her driving test.

2 a. Cassidy inherited a farm.

b. Cassidy owned a farm.

3 a. Cassidy inherited a farm.

b. Cassidy owns a farm.

4 a. Arnold poisoned his wife.

b. Arnold killed his wife.

5 a. We brought this champagne.

b. This champagne was brought by us.

108 Semantic Description

6 a. Not everyone will like the show.

b. Someone will like the show.

4.7 We noted that factive predicates, like English regret, presuppose the truth

of their clausal complements, as in He regretted that he didn’t move to Mel-

bourne. Using your own examples, identify the factive predicates from the

following list: announce, assume, be aware, believe, be fearful, be glad, realize,

be sorry, be worried, know, reason, report.

4.8 Using the different behavior of entailment and presupposition under

negation as a test, decide whether the a sentences below entail or

presuppose their b counterparts. (Again, assume that repeated nouns,

names and pronouns refer to the same entity twice, and that the b sen-

tences are uttered immediately after the a sentences.)

1 a. Dave knows that Jim crashed the car..

b. Jim crashed the car.

2 a. Zaire is bigger than Alaska.

b. Alaska is smaller than Zaire.

3 a. The minister blames her secretary for leaking the memo to

the press.

b. The memo was leaked to the press.

4 a. Everyone passed the examination.

b. No-one failed the examination.

5 a. Mr Singleton has resumed his habit of drinking stout.

b. Mr Singleton had a habit of drinking stout.