This question drew my attention to something that seems perfectly clear to native English speakers, but leaves English learners bewildered.

When you negate a sentence containing a modal or an auxiliary verb, the outcome varies depending on the modal or auxiliary. For example, when you negate a sentence containing must, the obligation remains but the action is inverted:

I must stay at home
I must not stay at home

With need, however, the obligation is cancelled (it becomes an option), and the action remains the same.

I need to stay at home
I need not stay at home

The original question referred just to these two cases, but the potential for confusion exists for all modals and auxiliary verbs. This is a canonical post that deals with the broader issue. Two questions, then:

  • Why is it so quirky?
  • Are there any rules to decide what effect negation will have?

The main issue with negation of sentences containing modals and auxiliary verbs is whether the negation affects the modal/auxiliary (for example, cancelling an obligation) or the main verb (inverting the action). In Medieval English, not affects the preceding verb. Here is an example:

Father, forgive them; for they know not what they do (Luke 23:34, King James Version, 1611)

In modern English, not goes between the modal/auxiliary and the main verb affects the following (main) verb. If there is no auxiliary, we also add do, as in this example:

Father, forgive them, for they do not know what they are doing (Luke 23:34, New International Version, 1978)

For the majority of modals and auxiliaries, not follows the modern usage and affects the verb that follows it, so the modal remains in force and the action is negated. Here are some examples:

I must [not stay at home]
I will [not stay at home]
I shall [not stay at home]
I would [not stay at home]
I may [not stay at home] - may - probability
I might [not stay at home] - might - probability
I should [not stay at home]
I prefer [not to stay at home]
I prefer to [not stay at home]
I want to [not stay at home]

There are exceptions, where not follows the old usage and affects the verb it follows (the modal/auxiliary), cancelling the modal and not negating the action. Here are two cases where it always happens:

I [may not] stay at home - may - permission
I [used not] to stay at home

have and need can be either a true modal (without to), or an auxiliary verb (with to). With have the meanings are different. For a modal, not cancels the modal: for an auxiliary verb, it negates the main verb

I [need not] stay at home - no obligation
I need to [not stay at home] - negated action
I [have not] stayed at home - no completion
I have to [not stay at home] - negated action

can, could and do work both ways. When written as separate words, they can be ambiguous. In speech, emphasis on the modal confirms the modal, and emphasis on not confirms the negated action. For these words, the difference between cancelled modal and negated action is not always large.

I [cannot] stay at home
I [can't] stay at home
I [can not] stay at home
I can [not stay at home]
I could [not stay at home]
I [couldn't] stay at home
I [could not] stay at home
I [don't] stay at home
I [do not] stay at home
I do [not stay at home]

We can cancel auxiliary verbs by adding do not in front of the auxiliary verb:

I do [not want] to stay at home
I do [not need] to stay at home

In other languages, it is permissible to negate a modal verb, but we cannot do this in English:

I do [not must] stay at home - incorrect

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