Negation of auxiliary

In He is not right, it is usually said that not negates the auxiliary is. But why not think of not as negating right instead?

Solution 1:

In He is not right, it is usually said that not negates the auxiliary is.
But why not think of not as negating right instead?

Congratulations. You have figured out that what "is usually said" about grammar in too many grammar books and too many English classes is not correct. Nor useful.

The answer to your question is:

This is indeed the way grammarians and logicians do in fact think of negation.
You should distrust any textbook or teacher who tells you that be is the main verb here.

Basically, negation is a monadic functor (that's a good phrase to use at a cocktail party, btw) which changes the truth value of a predicate from True to False or from False to True, depending on what it was originally.

The predicates are the meaningful part of the verb chain, so they are what gets negated. Furthermore, predicates are not always verbs. There are predicates that are adjective phrases (like right, tall, or very intelligent; these are sensibly called "predicate adjectives"), and also predicates that are nouns (like rice, beans, or a very good doctor; these are sensibly called "predicate nouns").
Predicate nouns that are singular and count require an indefinite article, as in She's a good doctor.

Predicate nouns and predicate adjectives carry the meaning, but they can't be inflected for tense, so they need an auxiliary be verb to carry the tense, and for use with other rules, like Negative Placement, which requires an auxiliary verb to precede not.

This turns out to be a good site for Contraction, too, so isn't, aren't, wasn't, weren't -- and he's not, they're not, I'm not, and you're not -- are pretty common with predicate adjectives and nouns.

Details on predicates, negation, and monadic functors in the Logic Study Guide.