ENTAILMENT (Ms Phung)

We will start with the relation of entailment. Entailment may be defined in a number of equivalent ways. Here are three:

(i) X entails Y

- whenever Y is true, X must be true.

- a situation describable by X must also be a situation describable by Y

- X and not Y is contradictory (can't be true in any situation)

Take proposition (ii). This entails all the propositions in (iii):

(ii) The constables drove the fast cars.

(iii) The constables drove.

The constables drove something.

Some law enforcement officers drove the fast cars.

Someone drove fast cars.

Some fast cars were driven by someone.

The fast cars were driven by someone.

The constables existed.

The constables did something.

The constables drove automobiles.

Some police officers drove automobiles.

Some people did something to automobiles.

These sentences all meet the criteria in (i): they are true whenever “The constables drove the fast cars” is true; if we can describe a situation with (ii), we can also describe it with any of the sentences in (iii) (although the informativeness of the different formulations is not equivalent); and the conjunction of (ii) and the negation of any of the propositions in (iii) is contradictory (e.g. The constables drove fast cars and the constables did not drive). Note that entailment has nothing to do with truth in a particular situation: whether or not (ii) is true in a given situation, it has the entailments listed in (iii).

Sentence (ii) does not entail any of the sentences in (iv):

(iv) Not everyone drove fast cars. Some people drove slow cars.

The constables drove fast.

Fast cars are dangerous.

The constables wanted to drive fast cars.

The constables drove Ferraris. The probationary constables drove fast cars.

The constables drove fast police cars.

The constables were in uniform.

Any of these additional statements might be true, but none of them is entailed by (ii): we could imagine a world where (ii) was true but where the sentences in (iv) were not.

As demonstrated by (ii) and (iii), the range of a proposition's entailments is related to the lexical relations of the proposition's elements. Thus, we can substitute a hyperonym of constable (police officer, law enforcement officer, person), but we cannot substitute a hyponym (probationary constable in (iv).