I also want to add that a scholar is a very broad term. You could be a scholar that specializes in Abrahamic religions, or ancient Greece of certain periods. A historian of certain empires… A scholar in Greek usage, or Chinese. I mean, there are hundreds of categories to study that would make you a scholar.
Then you have recognized scholars - they paid money to an institution, studied what they were told to study, using the course work that the professor specified. If these people stay largely within orthodoxy of the given school, they may be accepted into a PhD program and press on to be another disciple of that school of thought.
Then there are independent scholars who may not have any credentials, and yet may actually be more knowledgeable in a wide range of topics, and may see the “bigger picture” better. Or they may be frauds…
In regards to arrogance, it is very typical for a PhD scholar, on a given position, to mock someone else based on their lack of credentials. I mean, I understand that credentials are indeed a way to tell someone “I should be knowledgeable in this area” and yet, just from my experience in my field (non-academic, IT) I see people with many certificates that state they are capable, and yet they lack some very basic reasoning skills. Their deductive reasoning, ability to think outside the box, non existent. They can’t analyze, and they make for poor IT people. Yet, most of them are schooled, at least formally, much greater than I am, but they can’t solve the complex problems and struggle with intermediate ones. On paper, these guys should Trump me, but it doesn’t happen. Additionally, lest I come off as arrogant, it is more confidence. It isn’t that I think I am the best, but I definitely rank myself as one of the best in my field, at least in the IT generalist administrator role and am capable of specializing in certains area if needed, on the fly. IMO, the ability to self teach Trumps formal education. Of course, they are not mutually exclusive - you can have both! But both are not required.
On my phone all week, and it capitalizes stuff and makes a lot of typos. Just an FYI.