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Can anyone explain the difference between cannot and can’t is?

Is the only difference that cannot is more formal than can’t is?

tchrist
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    When a mother wants to get the point across,she uses a child's full name. "Mary Weatherspoon Smith, you get to bed this minute!" Similarly the full form has more strength than the corresponding contraction. I suspect that everything I have said is true in other languages, and I hope that the lurking linguists will set me straight if I am wrong. – Airymouse Jan 16 '17 at 14:23
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    I'd like to point out that whatever the difference, it's the same difference there is between other pairs of contracted vs uncontracted negations (like is not vs isn't). The peculiarity with cannot is that it's not written as two separate words, but that's really just a spelling detail. However, it's worth noting that can not is also valid but normally means something else! "Right now I cannot think" means that I'm presently unable to think; "Right now I can not think" means that I am currently able to avoid thinking (an unusual sentence, but there are more idiomatic examples). – LjL Jan 16 '17 at 15:09

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There is no difference in meaning.

There is a mild difference in use:

  • Contractions like can't have until recently been strongly deprecated in the most formal writing, and it will usually be avoided in legal/bureaucratic contexts. But the academic dialect (at least in the humanities) is creeping closer to the colloquial style, and using can't will not usually be regarded as an error (though your editor may change it).

  • By the same token, in ordinary conversation cannot will usually impart some air of formality; but the effect is slight, and will probably not be noticed unless it accompanies a general 'rise' in your diction toward the written dialect.

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    Sometimes cannot feels more in the deontic mode than can’t does, becoming more like must not in sense. – tchrist Jan 16 '17 at 14:02
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    @tchrist mmm ... I'd be inclined to say that deontic cannot tends to be somewhat severer than deontic can't, and that that's a result of its marked formality. – StoneyB on hiatus Jan 16 '17 at 14:46