I was adding sample sentences to my flash cards when I noticed that 取り消す means withdraw.
前言を取り消す
withdraw [retract] one's statement
This reminded of a sample sentence for 取り下げる
告訴を取り下げる
retract an accusation
It's clear to me how 取る and 消す contribute to the meaning "to withdraw, take back" but I don't know what the role or the "semantic contribution" of 下げる is in this case. 下げる means to lower, right? Also, how do these two compound verbs differ in terms of nuance?
取り下げる is used with an accusation, a bill (law), an academic article, a statement of opinion, etc. Its use is limited to withdrawing things related to someone's claim or opinion. 取り消す is simply "to cancel", and it can be used with a wider variety of things. You can use 取り消す with an order, a reservation, etc. 発言を取り下げる and 発言を取り消す are interchangeable but the former sounds slightly more formal or legal.
what the role or the "semantic contribution" of 下げる is
We can say 取り上げる ("to bring up (a topic)"), so I think 取り下げる can be understood as the opposite of it, i.e., asking others to forget.
