Hi Weiyang Luo:
"Shilly-Shally" is a common expression which refers to the kind of imprecise, purposeless,
BACK---AND---FORTHING in human experience which accomplishes nothing.
Examples:
#1 A great many topics in the Italki "Discussion" forums consist of little more than a kind of
Shilly-Shallying around.
#2 "When you are done with this kind of Shilly-Shallying around, let me know, because I have work for you to do."
#3 "If all you can do is just Shilly-Shally around, then I want nothing to do with you.
I have business to conduct here."
#4: "Knock of the Shilly-Shally attitude and get to the point!"
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To Vacillate is to be indecisive. It can be used in the same sense as the
colloquialism or idiomatic expression Shilly-Shally, but it does not mean exactly the same thing.
Vacillate is a literalism. It means to be involved in some sort of decision-making process, in which one minute one might choose to do something, but the next minute, decide not to do anything at all.
Vacillation is not exactly " Shilly-Shallying around" but it could be.
Shilly-Shally refers to silly or foolish or wasteful activity. To Vacillate, is to have difficulty making up one's mind, as follows:
#1 I tend to vacillate about my financial choices. I cannot make up my mind to buy a new car now, or to wait another year.
#2 The Student vacillated between asking the Italki Teacher for lessons, or choosing to study English independent of a teacher.
#3 The Military Council had little time to vacillate. A serious decision had to be made about whether to take military action, or to use diplomacy.