they are often incomprehensible (or at least illogical) to people learning English! Which does it do? Burn up or burn down?

They're idiomatic (in the sense that you have to learn their meaning because it is not immediately apparent from the various parts)) and they're phrasal verbs, and as goofy and I have pointed out, they're something that goes back (beyond) the earliest recorded English. All language is incomprehensible to people just learning it. The solution is you have to memorize their meaning along with the verb. I am constantly confounded by idiomatic phrases in Japanese, so much so that I bought a dictionary of idioms.

That being said, if you study the verbal particles (and I own a whole bunch of monographs and books on them, going back to the late 19th century) in English can can see that they are systematic at least.

Ceci n'est pas un seing.