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In English, is saying "It is normal for me to not want 'blank'" correct, or would it be "It is normal for me not to want 'blank'"?

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    The negative to-infinitive is normally "not to do" as in Hamlet's to be or not to be. Occasionally you can find "to not do". – rogermue Feb 29 '16 at 18:13
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I think the main question is that if "not want" is a valid action distinct from just not "want". This may sound silly, but where that "to" goes definitely changes the meaning in a subtle way.

Let's start with "She decided not to go" versus "She decided to not go". The latter is a little more clumsy, but implies that "not go" is what she decided to do, more than she decided not "to go". It is a slightly stronger decision. That is, she didn't just decide not to do something, but she decided to "not do" something (if there is an opposite of that something, then you are getting very close to saying you are doing that; how close is dependent on how purely opposite the pairing is). So, three ways of saying nearly the same meaning can be seen as a continuum from passive to active:

  • She decided not to go
  • She decided to not go
  • She decided to stay

Now, is "to go" the exact opposite of "to stay"? Depends on the specific context, but usually there is an implied "where". For instance, if we were talking about school, "She decided not to go [to school]" is not really the same as "She decided to stay [home]" because the latter is more specific. If there is difference between the two, then the negated-infinitive-inversion form lies somewhere between: she decided to "not go", which includes she is not going to school, but adds more force to the decision, yet doesn't specify any substitute action.

Going back to "to want", we have the same difference in emphasis. There "to want" may be seen as somewhat opposite of "to have", or perhaps "to be content". So, the trio of meanings is:

  • It is normal for me not to want
  • It is normal for me to not want
  • It is normal for me to be content / It is normal for me to have

Arguably, the second is distinct enough from the third to allow the slight clumsiness of phrasing, and even if not for the distinctness might be used to give literate variety. It is one of those practices which will quickly grow tiresome if overused, but can add spice if used very infrequently (in my opinion of course).

  • In either location "not" is negating the VP "want x", so no difference in meaning in the OP's example. – BillJ Feb 29 '16 at 19:51
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It is normal [for me VPinf]

comes via Extraposition from

[For me VPinf] is normal

i.e, both of the following are also grammatical

  • For me not to VPinf is normal
    and
  • For me to not VPinf is normal

The question of where the negative can go in an infinitive clause is full of zombie rules.
The actual rule is that not can be put

either

  • immediately before the infinitive verb phrase:
    [For me [to not [VPinf]]]

or

  • immediately before any constituent containing the infinitive verb phrase:
    [For me not [to [VPinf]]]

Both are fine, both are common, both mean the same thing.
Like many other phenomena in English grammar, this is speakers' choice.

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'Not to want', in some languages you can put 'not' anywhere you want but in english it usually goes up front. And 'to do', 'to want' is something you don't divide, it's like a whole phrase.

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