Is there always a difference between 'is the' and 'is a'?

Question

For instance, 'every dog owner is the friend of a dog owner' vs 'every dog owner is a friend of a dog owner'.

For me, the former seems to imply that every dog owner is the friend of a particular dog owner. Where the latter seems to imply that every dog owner is the friend of just any other dog owner, not a specific one.

Now of course, the actual differences doesn't (usually) matter when conversing with another person, due to human context, though I am studying logic where such a difference is crucial.

Thanks :)

Answer 1

The definite article on the complement of a universal implies that it is the 'only' one, so dog owners only have one friend! Both ways will be understood correctly (the brain can't store the definite article - it has to either choose an instance or the universal), but the indefinite is literally correct (the brain chooses the universal, which implies any members).

Every son is the child of a mother. (understandable, but could imply that mothers can only have one child)

Every son is a child of a mother. (better)

Answer 2

I know this is an old question, but...

Some scenarios in which "the" works, but "a" doesn't:

• He's the best potato eater! He eats all the potatoes all the time. The greatest thing about him is the smile on his face once he sees the potatoes on the dining room table.

However, scenarios in which "a" works would work with "the," too. Just replace it in your head:

• I have a great plan. To break into a bank, we need a map of the city and a screwdriver. Don't forget that we also need to have a good time while stealing a heap of money.

Also, "a" can connote a different tone. For example, you can say, "Obama's the president," which sounds regular and casual. Yet, if you say, "Obama's a president," it sounds pretty derogatory somehow. It sounds like you mean Obama isn't special and he's just one of the many presidents in this world.

"The" sounds more specific, as if you're thinking about a certain item when you say it. The house sounds very confident: a house could be any one in the world.

Fun thing to talk about. Hope this helped!