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In FET, 'level' and 'flat' are presented as synonyms.

I guess that's the problem. They aren't the same thing.  A table top can be flat without being level.  If you want to say that it's level, you have to answer the question level compared to what?  Most people understand that to mean level with the floor.

If water always finds its own level, what determines what water's "level" is?