In sentences such as I think not, the word not is a proform standing in for a negated subordinate clause. It is not negating the verb think. Rather it is the complement of that verb. We use not in the same places where we use so to represent positive subordinate clauses.
- Has Bob eaten yet?
- I think [Bob hasn't eaten yet].
- I think [not].
- I think [Bob has eaten].
- I think [so].
Because not represents a subordinate clause here, it does not make the larger sentence negative.
1. Verbal negation in finite clauses:
The word not is often used to negate clauses. When occurring in finite clauses, it occurs after the auxiliary verb (apart from in some types of question, where the auxiliary moves to the front of the clause leaving the word not in situ).
If there is no auxiliary verb, we need to insert the dummy auxiliary, do:
- The elephants are swimming.
- The elephants are not swimming.
- My elephants swim.
- My elephants do not swim.
- *My elephants not swim. (ungrammatical).
We can show that the word not belongs with the auxiliary here by 'contracting' not with the auxiliary verb:
- The elephants aren't swimming.
The reason that we can use not in the Original Poster's sentence We need not tell the police is that the verb need is an auxiliary verb here. We can show this by using a contraction:
- We needn't tell the police.
Notice that this whole sentence is therefore negative. We can show this by using a question tag. Negative sentences always take positive tags:
- We needn't tell the police, need we?
- *We needn't tell the police, needn't we? (ungrammatical)
We often use proforms in English to refer back to a previously mentioned phrase or clause (what's really happening of course, is that we're referring back to a previously mentioned entity or idea). For example, we often use pronouns to refer back to a previously mentioned noun phrase, where the pronoun replaces the whole noun phrase , not just the noun:
- See that man in the red t-shirt? He is my Maths teacher.
In the example above the pronoun he is standing in for the previously mentioned phrase that man in the red t-shirt. We also have proforms, such as the word there, for example, which stand in for whole preposition phrases:
- We were at the bottom of the valley. It was very beautiful there.
In the example above the proform there is standing in for the at-preposition phrase at the bottom of the valley.
If we want to use a proform for a whole clause, we often use the proform so.
- Has Bob finished his work?
- Well, he said so.
- Well, he said he has finished his work.
In the examples above we can see that the word so is replacing a clause as the complement of the verb said. The clause that has been replaced means something like he has finished his work.
Notice however, that so can't replace a negative clause. If we want to replace a negative clause with a proform, we have to use the proform not, which stands in for negative clauses:
- He didn't eat it, did he?
- I think so. (= "I think he ate it")
- I think not. (= "I think he didn't eat it)
Notice that although not represents a negative subordinate clause here, it doesn't make the larger sentence negative. We can show this by putting a negative tag at the end of the sentence:
- You think not, don't you?
In the Original Poster's sentence, I think not, the word not is a pro-clause item standing in for a negative clause. It represents a subordinate clause functioning as the complement of the verb think. It does not negate the verb think or make the larger sentence negative. We can use not or
so as a proform with many other verbs that take subordinate clauses.
Below is an excerpt on pro-form so and not from The Cambridge Grammar of the English Language (Huddleston & Pullum, 2002 p.849).
Excerpt from the Cambridge Grammar of the English Language: