The principle that the meaning of a sentence determines its truth conditions (i.e., the kinds of situations in which the proposition it expresses would be true) is the foundation for most of what we talk about in this book, including word meanings. A proposition is judged to be true if it corresponds to the situation about which a claim is made.
A major goal of semantic analysis is to explain how a sentence gets its meaning, that is, why a given form has the particular meaning that it does. In this chapter we have mentioned a few benchmarks for success, things that we would expect an adequate analysis of sentence meanings to provide for us. These benchmarks include explaining why certain sentences are analytic (always true) or contradictions (never true); and predicting which pairs of sentences will be synonymous (always having the same truth value in every possible situation), incompatible (cannot both be true), etc.
In this chapter we have introduced two very important types of inference, entailment and presupposition, which we will refer to in many future chapters. Entailment is strictly a semantic relation, whereas presupposition has to do with pragmatic issues such as managing the common ground and appropriateness of use. However, we have suggested that presupposition failure can sometimes block the assignment of truth values as well.
Further reading
Good basic introductions to the study of logic are presented in Allwood et al. (1977: ch. 3) and Gamut (1991a: ch. 1). The literature dealing with presupposition is enormous. Helpful overviews of the subject are presented in Levinson (1983: ch. 4), Geurts & Beaver (2011), Zimmermann & Sternefeld (2013: ch. 9), and Birner (2012/2013: ch. 5). Potts (2015) also provides a good summary, including a comparison of presuppositions with conventional implicatures (which we will discuss in chapters 8 and 11). Von Fintel & Matthewson (2008: §4.1) discuss cross-linguistic issues.
Discussion exercises
A: Classifying propositions. State whether the propositions expressed by the following sentences are analytic, synthetic, or contradictions:
- My sister is a happily married bachelor.
- Even numbers are divisible by two.
- All dogs are brown.
- All dogs are animals.
- The earth revolves around the sun.
- The sun does not shine at night.
- CO2 becomes a solid when it boils.
B: Relationships between propositions. Identify the relationship between the following pairs of propositions (entailment, paraphrase, contrary, contradictory, independent):
(1) a. John killed the wasp.
b. The wasp died.
(2) a. John killed the wasp.
b. The wasp did not die.
(3) a. The wasp is alive.
b. The wasp is dead.
(4) a. The wasp is no longer alive.
b. The wasp is dead.
(5) a. Fido is a dog.
b. Fido is a cat.
(6) a. Fido is a dog.
b. Fido has four legs.
C: Presuppositions. Identify the presuppositions and presupposition triggers in the following examples:
- John’s children are very well-behaved.
- Susan has become a vegan.
- Bill forgot to call his uncle.
- After he won the lottery, John had to get an unlisted phone number.
- George is sorry that he broke your Ming dynasty jar.
D: Presuppositions vs. entailments. Show how you could use the negation and/or question tests to decide whether the (a) sentence entails or presupposes the (b) sentence. Evaluate the two sentences if spoken by the same speaker at the same time and place.a
(1) a. Dave knows that Jim crashed the car.
b. Jim crashed the car.
Model answer
The statement Dave knows that Jim crashed the car, its negation Dave doesn’t know that Jim crashed the car, and the corresponding question Does Dave know that Jim crashed the car? all lead the hearer to infer that Jim crashed the car. This suggests that the inference is a presupposition.
(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.
a Adapted from Saeed (2009: 114, ex. 4.8)
Homework exercises
A: Classifying propositions. Classify the following sentences as analytic, synthetic, or contradictions.
1. If it rains, we’ll get wet.
Model answer:
Sentence 1. is synthetic, since we can imagine some contexts in which the sentence will be true, and other contexts in which it will be false (e.g., if I carry an umbrella).
2. If that snake is not dead then it is alive.
3. Shanghai is the capital of China.
4. My brother is an only child.
5. Abraham Lincoln was the 16th president of the United States.
B: Relationships between propositions. Identify the relationship between the following pairs of propositions (entailment, paraphrase, contrary, contradictory, independent):
(1) a. Michael is my advisor.
b. I am Michael’s advisee.
(2) a. Stewball was a race horse.
b. Stewball was a mammal.
(3) a. Elvis died of cardiac arrhythmia.
b. Elvis is alive.
C: Identifying entailments. For each pair of sentences, decide whether sentence (a) entails sentence (b). The two sentences should be evaluated as if spoken by the same speaker at the same time and place; so, for example, repeated names and definite NPs refer to the same individuals.
(1) a. Olivia passed her driving test.
b. Olivia didn’t fail her driving test.
Model answer:
If a is true, b must be true; if b is false, a must be false; this follows from the meanings of the sentences, and does not depend on context. So a entails b.
(2) a. Fido is a dog.
b. Fido has four legs.
(3) a. That boy is my son.
b. I am that boy’s parent.
(4) a. Not all of our students will graduate.
b. Some of our students will graduate.
D: Presuppositions vs. entailments. Show how you could use the negation test to decide whether the (a) sentence entails or presupposes the (b) sentence. Again, evaluate the two sentences as being spoken by the same speaker at the same time and place.
(1) a. The boss realized that Jim was lying.
b. Jim was lying.
Model answer:
Both The boss realized that Jim was lying and The boss didn’t realize that Jim was lying lead the hearer to infer that Jim was lying. This suggests that the inference is a presupposition.
(2) a. Singapore is south of Kuala Lumpur.
b. Kuala Lumpur is north of Singapore.
(3) a. I am sorry that Arthur was fired.
b. Arthur was fired.
(4) a. Nobody is perfect.
b. Everybody is imperfect.
(5) a. Leif Erikson returned to Greenland.
b. Leif Erikson had previously visited Greenland.
