Orwell complains - no, really - that the distinction between imply and infer seems to be in decline and beyond rescue. That was in the 1940s, so one can only assume that the patient, though still far from well, is proving remarkably hardy. But Bill Bryson notes this, in Troublesome Words:
The distinction is useful and, in careful writing nowadays, expected. However, it must be pointed out that there is not a great deal of historical basis for the distinction. Many great writers, among them Milton, Sir Thomas More, Jane Austen and Shakespeare, freely used infer where we would today insist on imply. Indeed, until as late as 1976, The Concise Oxford Dictionary treated the words as interchangeable.*
I am currently putting on a convincing, interminable impression of a 19th century consumptive, possibly Doc Holliday as portrayed by Dennis Quaid. My wife is trying to outdo me. It's like having a pair of howler monkeys in the house. While trying to track down causes on the internet, I came across the following word, used in medicine: idiopathic.
It's Greek for "we don't know".