BPJ, you're wife has a point. The partitive corresponds to the indefinite as a rule of thumb. This works pretty well both ways in language learning. Partitive is used as the reference case for nouns in plural, but not in singular. This is because partitive also has a role as a plural marker. 

But in the big picture Finnish does not have a case that corresponds to Swedish/English definiteness. This is because partitive and nominative are cases (there's also the accusative but in current linguistics it's not considered a case which causes further confusion). 

When you use the word in a different case, you won't be able to have it in PAR or NOM anymore, so you'll have to express definiteness with word order, the subject representing something that is already known (definite) and the object expressing new information (indefinite). 

But then again, if both the subject and the object are definite or if both are indefinite, it becomes impossible to express this with the word order. Instead, definiteness is understood in the context - by someone who is learning Finnish. I think some Finnish people don't really understand definiteness.

I'll give you a couple of easy examples:

talo (NOM-SG) = a house
taloja (PAR-PL) = houses

Corresponding to indefinite:

Mäellä on talo. (There's a house on the hill.)
Mäellä on taloja. (There are houses on the hill.)

These are (kind of) definite:

Talo on mäellä. (The house is on the hill.)
Talot ovat mäellä. (The houses are on the hill.)

I think the hill (mäki) is known - otherwise you would probably use the determiner 'eräs - eräällä' (some).

But there's also:

Taloja on mäellä. (It's on the hill that the houses are.)

Note that the above example is impersonal (Jyri might be able to explain this better). A word in the partitive cannot be a genuine subject:

*Taloa on punainen.
*Taloja ovat punaisia.

It must be:

Talo on punainen. (House-NOM is red-NOM.)
Talot ovat punaisia. (Houses-NOM are red-NOM-PL)

So we go back to the beginning.