Adapted from another answer of mine
The Cambridge Grammar of the English Language have a subchapter covering the more general phenomenon laid out in the body of the question. It is titled "Increased specificity of negation". The rest of this post deals with cases such as those set out in the title.
I don't seem to have enough time.
I seem to not have enough time.
Some verbs that take clauses as complements create subordinate negation implicatures. This means that in a [verb] + [clause] combination, if we negate the verb, we imply the same meaning as if we had negated the complement clause. So, for example, the sentence "I do not want you to go" implies "I want you to not go". This means that we can, in most circumstances choose which part to negate when dealing with these types of verb. As a general rule of thumb, English speakers prefer to have the negation as early on in the sentence as possible. This makes the sentences far easier to process.
NEG-raising is a technical term which endeavours to explain how subordinate negation implicatures arise through a grammatical transformation.
It is a fact known to millions of hardworking English language students all over the world that native English speakers strongly prefer negating the verbs think, believe and want, amongst others, to negating the complement clauses that they license. So, for instance, all other things being equal, we prefer:
(1). I don’t believe that the Yeti exists.
(2). I believe that the Yeti doesn’t exist.
We also would tend to prefer:
- I don’t think I’m going to find it.
- I think I’m not going to find it.
and there is absolutely no doubt that:
is far more customary than the rather stilted:
Notice that what is implied by (1) is the same as what is literally encoded in (2). However, (1) does not in fact strictly semantically encode the same information as (2) at all. If we made no further pragmatic assumptions about what the speaker of (1) intended to convey, then the maximum we should be entitled to decode is that the speaker does not possess a positive creedal attitude about the existence of Yetis. It is entirely possible that the speaker may have no definite opinion about the existence or non-existence of Yetis, in which case they would not be able to truthfully commit to either a belief or disbelief in them. This might be due to an agnostic state of mind, or it may be merely because the speaker has never even thought about it. To commit the speaker of (1) to a belief in (2) is potentially doing them a great disservice.
Be that as it may, most listeners would understand (1) as conveying the same as (2), and they are indeed entitled to, because most speakers - unless they were wishing to be very explicitly technical about it - would prefer the former to the latter to convey the very same information. What is interesting here is that speakers are modifying the verb denoting the action of belief in order to manipulate the listener’s understanding of the object of the belief - the information in the complement clause. More specifically they are negating the verb denoting the believing, but implying a negation of the complement clause.
This phenomenon is known as SUBORDINATE NEGATION IMPLICATION. Verbs that tend to generate such implicatures seem to be verbs that denote states of intention, epistemic stance or opinion, or those which can be used performatively for advice. Dynamic verbs which denote actions, changes of mental states and so forth do not tend to generate these implicatures. Compare the following sentences with the dynamic verb say:
He didn't say that she danced.
He said that she didn't dance.
Here the two sentences do not convey the same information at all. We are not likely to infer the information in the second sentence when we read the first.
One more factor comes into play here. Verbs that generate subordinate negation implicatures, tend to be what are described in the CaGEL (The Cambridge Grammar of the English Language, Huddleston and Pullum, 2002) as medium strength verbs. They contrast for example 'stronger' know with 'medium strength' believe. The reason that these verbs tend to generate such implicatures is merely that, pragmatically, it does not seem very informative to tell somebody that you don't have a medium strength stance about something. We tacitly infer, on this basis, the more informative proposition that the speaker has a stance about a negative idea.
However, with so-called stronger verbs, on the other hand, it is informative to convey that your confidence in a stance is not 100%, or contrastingly with weak verbs to convey that that not even the slightest positive attitude is given to the proposition in the complement clause. The strong and weak usages of the following verbs do not, therefore, generate subordinate negation implicatures:
I don't know that she went. ≠ I know that she didn't go.
I don't suspect her of stealing. ≠ I suspect her of not stealing.
As to why speakers actually prefer to negate verbs such as want and believe rather than to negate their complement clauses, I do not believe that anybody knows (- by which I want you to infer that I believe that nobody knows).