Double negatives

This has bugged me since I was a lad: most languages accept the double negative (as in "I never saw none of them") simply as a more emphatic negative; pedantic teachers of English insisted - perhaps still do - that "never seeing none" meant the speaker had at some time seen at least some of whatever was referred to. Speakers of everyday English, as opposed to commentators on the language, use the double (or triple, quadruple, even quintuple) negative as increasingly emphatic versions of the simple negative. Where I grew up, a speech such as "I ain't never seen ne'er a one of 'em, not never" would be accepted as a vigorous denial. It might also provoke suspicion that the speaker was protesting too much, but that's beside the (linguistic) point.