- Humans have got to know their limitations.
(Let's get away from mankind and his, OK? They're just distractions)
does have several senses, but they wouldn't all be pronounced the same, nor in the same place.
Have got to know is already ambiguous in British and American usage. In this particular case, the sense of 'have come to know' that many UK speakers and others will get is unavailable to American speakers. For that sense, Americans would say
- Humans have gotten to know their limitations.
instead of using got, because this is an inchoative 'change of state; come to be' usage of Perfect get, and the American past participle of that verb is gotten, not got, as it is elsewhere.
The other two senses of have got to know are the two modal senses that virtually every modal has, in this case the periphrastic modal have got to, often pronounced 'gotta', which does mean must:
- The Epistemic (logical necessity) sense, as in
This has to be/has got to be/must be the place he was talking about,
He has to be/has got to be/must know that this place is a dump.
- The Deontic (social obligation) sense, as in
You have to be/have got to be/must be back home by midnight,
He has to be/has got to be/must know all the verb paradigms to pass the test.