Is there a rule for “wouldn't” used to mean “didn't want”?

Question

I have seen the sentences in books where wouldn't seems to have been used in the meaning of didn't want, and I wonder if such a rule exists. For instance,

I wanted to participate, but he wouldn't take me on.

What kind of rule is applied in the sentence above?

Answer 1

Would is a modal verb with several uses, of which one is to express past intention or willingness. As you suggested, in your example, it expresses willingness, or rather, because of the negative n’t, unwillingness. You could say but he didn’t want to take me on, but the use of wouldn’t makes the statement a little less explicit.

Answer 2

It doesn't state that "he" didn't want to "take me on", it says that this is a thing that he was not going to do.

It could be that "he" didn't want to, it could be that he didn't have time, there was a full roster of people participating and no more could be added, that as much as he really did want to include the speaker they lacked the prerequisite skill at the task in question, or anything else.

We're informed of the lack of action, not of the motivation.

We can sometimes infer that the reason someone wouldn't do something is that they don't want to, but not always, and not here (in the bare sentence at least, perhaps in the full passage we can).

Answer 3

Here "wouldn't" is the past tense of "won't".

If you take "I want to know but he won't tell me." and put it in the past, you get "I wanted to know but he wouldn't tell me."

So perhaps the question is "why do we use will here?"

That's a little harder to answer. I'll have to think about it (and probably look it up in a grammar book!)