Semantics teaches that we can differentiate between the extension and the intension of a term. The extension is also known as the denotation and the intension is known as the connotation.
The current Prime Minister of Canada is Stephen Harper. Since Canada became a nation in 1867, it has had a number of prime ministers starting with John A. MacDonald. The prime minister is the leader of the government of Canada, the person whose party has the most seats in the House of Commons. This is known as the intension of "prime minister". It can also be called the denotation.
However, when people speak about the prime minister, it is likely that they speak about a specific individual. If they speak about the current prime minister, they speak about Stephen Harper. This is known as the extension of "prime minister". This can also be called the connotation.
This distinction between extension and intension can be applied to many situations. For example, "fastest land animal in the world", "president of Mexico", "capital of Brazil", "Olympic city" and "King of France" have different intensions and extensions.
The fastest land animal in the world is the animal which can run faster than any other. This is the intension of "fastest land animal". The extension is the cheetah.
The president of Mexico is the person who is the head of the Mexican government. This is the intension. The extension is the current Mexican president, Felipe Calderon.
The capital of Brazil is the city which is the seat of the Brazilian government. At one time, this was Rio de Janeiro. However, the current capital of Brazil is Brasilia. This is an example which illustrates that the extension of a term can change for not only people but also cities.
The term "Olympic city" refers to a city which hosts either the Summer or Winter Games. Many cities have been Olympic cities. The last city to host the Summer Games was Beijing and the last city to hold the Winter Games was Turin. To know the extension of Olympic City, it is necessary to specify the Olympic year.
The King of France is the French head of state. However, France no longer has a king because the French monarchy ended with the French Revolution of 1789.
Thus, this term can refer to past kings of France such as Louis XIV but cannot refer to any present king because France no longer has any. If referring to the present, we must say that the extension is null because at present France has a present as head of state and not a king.
It is useful to differentiate between the extension and intension of a term. When people speak, they may refer to either the extension or the intension. In some cases, they may even refer to both.