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I have a question about "important". When we say <something> is important, that "<something>" is assumed to be positive/desirable.
But when we way something is NOT important, then that something could be either positive/desirable or negative/undesirable.
I have a feeling that #2 is weird. What do native speakers think?
Losing money is important is indeed a peculiar thing to say, though there's nothing wrong with the sentence's construction. It's simply extremely unusual for circumstances to arise where this would be a true statement.
However, I do have an example. This fiscal year, I had to reduce my tax burden by lowering my gross income below a certain level. The only way to do that was by incurring capital gains losses (i.e. making bad investments), so for a time, losing money was important to me.
Important means of great weight, rank, significance, or value; critical or pressing, and need not necessarily be emotionally positive. It's true that Hitler is an important figure in history, because his actions had a huge impact on the world, but it's also true that history (rightly) views him and his actions extremely negatively.
Earning money is important has positive (emotional) connotations because it's a positive (not negated) statement, and we generally view earning money as a good thing. Both not important examples express the idea that their subjects are not very desirable; one could take or leave earning money or losing money. There's no major positive or negative (in the emotional sense) connotation here. Often when we say something is not important, we mean that we don't have strong feelings either way about it.
I agree, #2 is weird.
It's hard to explain why, though — which makes this an interesting question. The best explanation I can come up with is that in #1 and #2, "is important" in the affirmative sense means "is important to do". In contrast in #3 and #4, "is not important" means "is not a significant concern".
"Losing money is important to do" doesn't make logical sense, so #2 is weird. (There would have to be some special circumstance — for example, if you were concocting a money-laundering scheme.)
On the other hand, "Losing money is not important" can make logical sense. (For example, "Losing money is not important. We just need to gain market share as quickly as possible.")
If we start assuming the meaning of important and not important without the context, I'm afraid, we may land on something perplexed.
It's simple as that - important generally means of great significance or value. Now it depends on you what do you think, in which circumstances do you think something is important or not.
Esoteric Screen Name gave good example of losing money which was important for him and on the other hand, for Richie Rich, losing money is not important but losing fame is.
In fact, at times, you see very confusing phrase too important to ignore where important should be understood carefully and without the context, it'll be difficult to know it.
