Can we use "not" without helping verb?

Question

We form negative declarative clauses with not after be (she is not talking), after modal verbs (they must not go) and after auxiliary verbs do and have (we did not like it; they have not eaten). Cambridge Dictionary

And I found the following sentence in Oxford Dictionary:

perhaps not surprisingly, he was cautious about committing himself.

But perhaps is not a helping verb. So, Can we use "not" without helping verb?

Update:

The Negation Rule: In English, in order to claim that something is not true, you form a negative sentence by adding the word not after the first auxiliary verb in the positive sentence. If there is no auxiliary verb in the positive sentence, as in the Present Simple and Past Simple tenses, then you add one (in both these cases, the auxiliary verb do). White Smoke

We make negatives by putting not after the first part of the verb. British Council

Another example of using not without an auxiliary verb:

I can think of a hundred reasons not to come.

is the above negative clauses? if yes, What is the rule to use not without auxiliary verb? if no, what is the part of speech of not in the above sentence?

Answer 1

If not is negating a finite verb, i.e. one that is connected to and inflected by a subject, then not should come after a helping verb, meaning verb to be, modals and auxiliary verbs be, do and have, for example:

I am not well today.

I have not finished my assignment yet.

Don't you have better things to do?

She was not paying attention.

This is what is normally called negative clause

However, if the verb being negated is nonfinite, which means infinitives with and without to, participles, except for perfect tenses, and -ing gerunds, except for progressive tenses, then not normally comes before the verb it negates:

It is common not to tip severs in some parts of Europe.

The problem was solved by not using the defective part in further projects.

"The Road Not Taken" is a poem by Robert Frost.

I can think of a hundred reasons not to come.

Likewise, it is possible to negate words and phrases other than verbs, normally by placing not right before the word or phrase one wishes to negate. Your first example falls into this category.

Perhaps not surprisingly, he was cautious about committing himself.

He won not only the championship, but also the hearts of thousands of fans.

Answer 2

The short answer to your question is yes, you can do this. It is grammatically correct although normally in this situation you would use "unsurprisingly" instead of "not surprisingly".

Answer 3

The primary definition of a word in the dictionary provides with its unique meaning, which granted it its entry.

Using words in their primary definition will construct a sentence in plain English, and eliminate any outlets of interpretation from its intended meaning.

Nonetheless, the amount of words to choose from can be puzzling, and there are so many words with multiple meanings, to easily leave the reader puzzled, if we don't pay attention.

Yet, there are not so many sentences which will tell exactly what we mean, or mean exactly what we wish to tell.

Although the primary usage of ' not ' is to form a negation, the meaning of a sentence using 'not' is not always in the negative sense.

Plain text is rather monotonous, but ensures it to be understood.

Whereas, on one hand, using 'not' in a positive sense or other embellishing metaphors to make reading more exciting is entirely exploitable, on the other hand, making sense, when we speak, is still a requisite.

It depends on how much we need to get our point across. Sometimes, writings are just meant to be confusing.

However we do it, we pick the words we need, as what counts, at the end, is not only what we mean but also to be understood.