> English syntax is not mathematical logic
Open any book or paper on semantics (the linguistics kind, not the philosophy or the early-20th-century pseudoscience kind) and you might be surprised :) It’s just that the logic is not that straightforward to get out, and of course there’s semantics (the literal meaning, where “Can you pass the salt?” is a question about ability) and then there’s pragmatics (the thing one is actually trying to communicate, where “Can you pass the salt?” is a request with certain degrees of respect and formality attached to it).
> “I Can’t Get No Satisfaction”
This is probably not a very good example as it’s just (AFAIU) not strictly “standard English” in that it exhibits negative concord absent from the standard grammar (for dramatic effect, although “We Don’t Need No Education” is probably a better case). That is to say, this is a phrase in a language (which is very similar to standard English but not quite the same) where the grammar requires dummy negations on complements of negative verbs—a purely syntactic thing that doesn’t even reach the layer of semantics / logic.
But then many other varieties of English do that (I remember reading somewhere that the dialect that gave rise to the current standard is actually somewhat unusual among other dialects in that respect), so does my native Russian (and other Slavic languages, and some but not all Romance ones), and Japanese actually requires you to negate the adjective when using the adverb meaning “hardly, not very”[1] while at the same time using some double negations as polite affirmations[2].
[1] https://japanese.stackexchange.com/q/18006
[2] https://www.nhk.or.jp/lesson/english/teacher/36.html