All 4 Uses

nevertheless
in
To the Lighthouse
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But nevertheless, the fact remained, it was impossible to dislike any one if one looked at them.†
Part 1 *

nevertheless = despite that (used to connect contrasting ideas)
Perhaps it is bad French; French may not contain the words that express the speaker's thoughts; nevertheless speaking French imposes some order, some uniformity.†
Part 1
But, he added, there is considerable merit in some of the plays nevertheless, and Mrs. Ramsay saw that it would be all right for the moment anyhow; he would laugh at Minta, and she, Mrs. Ramsay saw, realising his extreme anxiety about himself, would, in her own way, see that he was taken care of, and praise him, somehow or other.†
Part 1
They had nothing to say, but something seemed, nevertheless, to go from him to her.†
Part 1

Definitions:

(1) (nevertheless)
despite that

Based on idea 1 we might not expect idea 2, but this is a way of saying that even though idea 1 was just stated, we still have idea 2. Synonyms include in spite of that, despite that, nevertheless, nonetheless, on the other hand, in contrast and but.
(2) (meaning too rare to warrant focus)