play one's part是一习语

有人问到这样一句话:

(1)In Australia—where an aging population, life-extending technology and changing community attitudes have all played their part—some states are going to consider making a law to deal with euthanasia.

have all played their part在此何义? 为何用单数名词part而不用复数名词parts?

play one's part, do one's part, act one's part皆意为“起其作用”或“尽其本职”。have all played their part在此可看作相当于“都产生了影响”。这里用part而不用parts乃是由于play one's part是一习语,part已抽象化,意为“作用”,故不可改动。这种情况并不罕见,再如:

(2)They can't put their finger on what's wrong. (put one's finger on something是一成语,故their finger不改为their fingers)

(3)They know when to speak and when to hold their tongue. (hold one's tongue是一成语,故their tongue不可改为their tongues)

然而,也不可一概而论,如:

(4)They have turned their backs on us. (这里则用复数名词backs)