shallyoudaoicibaDictYouDict[shall 词源字典]
shall: [OE] The etymological meaning of shall is ‘owe’. It goes back to a prehistoric Germanic base *skal-, *skul- which also produced German sollen ‘ought to’ and schuld ‘debt’. Its use in English as an auxiliary verb denoting future time evolved via the intermediate senses ‘ought to, must’ and ‘be to’. The notion of obligation survives in should, which originated as its past tense.
=> should[shall etymology, shall origin, 英语词源]
shall (v.)youdaoicibaDictYouDict
Old English sceal, Northumbrian scule "I owe/he owes, will have to, ought to, must" (infinitive sculan, past tense sceolde), a common Germanic preterite-present verb (along with can, may, will), from Proto-Germanic *skal- (cognates: Old Saxon sculan, Old Frisian skil, Old Norse and Swedish skola, Middle Dutch sullen, Old High German solan, German sollen, Gothic skulan "to owe, be under obligation;" related via past tense form to Old English scyld "guilt," German Schuld "guilt, debt;" also Old Norse Skuld, name of one of the Norns), from PIE root *skel- (2) "to be under an obligation."

Ground sense of the Germanic word probably is "I owe," hence "I ought." The sense shifted in Middle English from a notion of "obligation" to include "futurity." Its past tense form has become should (q.v.). Cognates outside Germanic are Lithuanian skeleti "to be guilty," skilti "to get into debt;" Old Prussian skallisnan "duty," skellants "guilty."