- 世界睡著了；沒有人睡覺 公民為社會的進步而努力；每個人都自己出去他們拿著the繩；他們被領導了
"It is commonly believed, that ____. However, ____"
"It is a common misconception, that ____. In reality ____."
"Many believe it to be true, that ____, when in fact ____."
"You'd be forgiven for believing that ____ was what happened, as that was what we were told. The truth is that ____."
What you write depends on what you want to say, and who is saying it.
If your emphasis is on the second part, you don't need to explain the first part. You can use something like:
If you want to emphasize that there is a change from a prior state, the prior state must be clear. If it can be clear from the earlier setting, it might not take much.
If there is something about the character you are trying to expose, it may take a little more work:
If what you place in a character's mouth doesn't feel right to the character, just let them say it the way the want to. If you are saying more than you need, say less. If questions remain, that is good if the questions drive the reader's curiosity for what happens next. Remember that by inducing questions you have implicitly promised to answer them while they are still important. If the questions aren't important to move the story, answer them before they are asked through setting, character, or backstory. Confirmation builds belief. Unanswered questions create disappointed readers.
I like "It is received wisdom that …" though this can sound stuffy in many contexts. But it does apply to both conditions (X and Y) in that when used it connotes that the actual wisdom lies elsewhere.
There are as many ways to say "here is an idea" as there are words. The second part doesn't matter for now; it will naturally follow the first.
You are going to make a contrast, but first you are going to introduce an idea.
"People often say" is one brief way to introduce an idea that you are identifying as a common concept or belief.
But so is: "Among the philosophers and rulers of ancient Rome, the belief that the gods often directly intervened in human affairs was as certain as it was among the proletariat."
My point is that situation (plot), concept and character are everything. Is your character (or narrator) a scholar who would use academic phrasing, or a radio announcer who would use glib wordplay, or a teenager who uses slang to speak bluntly?
That's just one way of looking at the phrasing question.
"Many will say that..." or "Many have said that..."
In some cases it will work to simply negate X, and then state Y.
These might not be the best examples though.
Try simply eliminating the first part of your sentences or eliminating the "It is commonly said":