I just reread your question and according to grammar borrow would be the only acceptable verb to put into that sentence. But the question is very unclear, in the way that you have written it.

Engage is the best fit of the choices given. The second sentence describes how the tanks or springs interact with ideas. In this way the first sentence is used to give a reason for this description. "Take" does not work as it implies a specific type of interaction; one that " 'Springs' adopt them" directly prevents. Borrow also implies a too specific, though opposite to take, interaction, equally prevented by " 'tanks' just take over ideas". Assume can mean to "take on" a role or quality "She assumed the role of chairman". It can mean the way someone views a statement with a lack of evidence "I assume John was not late today". Sometime it can be used similarly to the previous way as a warning or request "I assume you wont eat the last of my candy". One does not occupy an idea but is rather occupied by it. The sentence is a little awkward sounding given the way the question is phrased. Personally. I would write the sentence thus: In an unusual analogy Coleridge described people as " tanks " or " springs " according to the way they engage with the ideas of others: " tanks " just take over ideas and store them like water; " springs " adopt them, producing a stream of water and so making them their own. I hope this helps!

I would say this depends on the meaning you are trying to convey. "Take" implies that the "tank or spring" does not have permission to use the idea. "Engage" doesn't really fit the sentence, but could be used if you mean that the "tanks or springs" help a person to make their own ideas happen. "Borrow" implies that the "tank or spring" has permission to use the idea. "Assume" is similar to "take". "Occupy" doesn't really work at all.

I don't see the question that you want me to answer, so I can't help.