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What's the difference between the following sentences?

1 They came up with a new idea.

2 They dreamt up with a new idea.

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    Don't include the preposition with after to dream up. Also note that this generally a (casual / colloquial) disparaging turn of phrase (speaker doesn't think much of their new idea), whereas to come up with (also somewhat colloquial) is essentially "neutral" in and of itself (but can be used in contexts where it's either positive or negative). Also note that usually They introduced / formulated / conceived a new idea would be seen as positive / approving. Dec 17, 2020 at 17:42
  • I think dream up depends on the context too, it an be used very negatively (in the sense of imagining things, or having your head in the clouds) but it can also be a more evocative phrase that suggests they've come up with something special. Dec 17, 2020 at 17:53

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Dreamt up (or "dreamed up") can imply that the idea, according to the speaker, is unrealistic -- much like a dream can be bizarre and unrealistic because it is entirely imaginary, or possibly randomly or haphazardly inspired, a revelation, without much prior effort, planning or qualification -- so like your commenter said, it may be taken as disparaging or offensive, or imply that the speaker considers the idea to be self-indulgent. And does not use "with".

Though the phrase "dreaming up new ways to [do a thing]" may not be disparaging if the context is about a person whose job it is to invent new and fantastic things, such as an artist or rocket scientist.

We also borrow the German or Yiddish expression verkocht when we say cooked up an idea (or an excuse), which is to say that it is overcooked, and that is also usually disparaging because nobody likes overcooked food.

Similarly, concocted ("concocted a way to [accomplish something]") is a variation that can imply that the idea or solution is somewhat specious; it may work or succeed but the means or methods or explanation are not convincing or may only coincidentally achieve a desired result, like to literally throw some things together (in pot, a beaker, etc.) and the product be useful, even if the mechanism of the reaction are not well understood or explained.

Came up with implies that the idea took work to generate, or with some amount of intent and planning, and thus it is more like an invention. It doesn't assign a positive or negative opinion; it just describes that they have generated an idea.

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Both mean the same in this context as ideas don't come without some sort of work/process/plan. 'came up with' and 'dreamt up' are a bit informal, so you can use 'brought forth,' or 'discovered,' if you want to sound more formal.

By the way, 'they dreamt up with a new idea' should be 'they dreamt up a new idea.'

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Both can mean to invent, suggest or think of an idea.

However, dreaming up something implies using a lot of imagination, creativity, lateral thinking. Used negatively, it could be that the idea is a bit unrealistic, silly, half-baked, or too ambitious.

And it's more natural to leave out with:

They dreamt up a new idea.

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