What does ‘even’ mean in ‘NEGATIVE X or even Y’?
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Now over thirty years old, he had never dated or even associated with women.
What does ‘even’ mean in this idiom “NEGATIVE X or even Y”? Which of the following senses appertain here? ‘the original sense was "level" or "alike.”’
Modern adverbial sense (introducing an extreme case of something more generally implied) seems to have arisen 16c. from use of the word to emphasize identity ("Who, me?" "Even you").
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In this case, your X is a subset of Y. Y is easier to achieve than X.
The "even" in "or even" emphasizes that not only was X not achieved, but the easier and necessary Y was not achieved either.
This construct is a means of pointing out how far away the achievement of X is, being that the simpler and easier Y has not been achieved.

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