Grammar notes: 才and 就

I have to admit that most of the grammar in my current textbook isn’t highly challenging, at least not until I start asking strange questions about whether I can do x, y, and z with it. But this one made my head hurt a little. My book says 就 means something happened earlier than expected, and 才means something happened later than expected. So far, so good. Except that these words also have a bazillion other uses in Chinese, and they keep throwing me off–I keep thinking 就 is later than expected. But setting that aside, here is how it works. Let’s just suppose that the average age a child learns to speak is 2. If I say

她	两	岁	会	说话	了。
tā	liǎng	suì	huì	shuōhuà	le。
she	two	years of age	able to	speak	le。

It means she knew how to speak when she was 2. If I say

她	一	岁	就	会	说话	了。
tā	yī	suì	jiù	huì	shuōhuà	le。
she	one	years of age	jiu	able to	speak	le。

it means that she learned to talk when she was one, and that was earlier than expected. The sentence “She had already learned to talk when she was one.” is almost equivalent. If I say

她	三	岁	才	会	说话.
tā	sān	suì	cái	huì	shuōhuà.
she	three	years of age	cai	able to	speak

it means she learned to speak when she was three, and that was later than expected. I think the English sentence “She didn’t learn to speak until she was three.” is equivalent.

But here’s the confusing bit. The observant reader will notice a difference between these sentences: If I use 就(jiù)，I have to use 了(le). If I use 才(cái), I can’t use 了(le). (If you don’t know what 了(le) is, it’s way too complicated to explain here. It often indicates that something is completed or that a change of state has happened.)

When I asked my teacher why, she didn’t have an explanation. It’s just our habit, she told me. (This is why linguists have jobs. Most people can’t explain why their own language does what it does.) So I thought about it more, and here’s my first theory about the reason.

Our boring sentence just tells us about one time, like this:

. . . . Learn to speak (2) . . . .

However, our other sentences are actually about two times: the explicitly mentioned age when the child learned to speak and the age the child is expected to learn to speak, which is not explicitly mentioned. Our 就 (jiù) sentence tells us this:

. . . . Learned to speak (1) . . . . Expected age of learning (2) . . . .

Our 才 (cái) sentence tells us this:

. . . . Expected age of learning (2) . . . . Learned to speak (3) . . . .

So our 就(jiù) sentence tells us that the event of learning was completed at the explicitly mentioned time, before the expected time. Our 才(cái) sentence, on the other hand, tells us that the event was completed at the explicitly mentioned time, but at the expected time, the event hadn’t been completed yet. So the 了(le) in this construction is about completion– but not with respect to the explicitly mentioned time. Our 就(jiù) sentence requires a 了(le) because the event is completed before the expected time arrives. Our 才(cái) sentence forbids a了(le) because the event isn’t completed before the expected time arrives.

For added fun, my teacher tells me that if I want to really emphasize that an event happened earlier than expected, I can add 才(cái) to a 就(jiù) sentence. This is just like the 就(jiù) sentence given above, except 才(cái) is added in before the time phrase. For this one, however, I have no explanations at all.