This term is generally used when two or perhaps a few more people debate something so obscure, or perhaps simply uninteresting to the general public, that they are the only people on the planet who know about the subject, and therefore know so much more about this specific subject than everyone else that they can only be deemed "scholars" on the subject.
Ex. 1

Scholarly debater 1:
"The other day my friend from Finland and I got in an argument over whether or not it was proper for Miklos Spanyi to use a piano forte rather than a period instrument such as the harpsichord in his recent recordings of Carl Philipp Emanuel Bach's keyboard concertos. We thought it would be on the news.. but it wasn't."
(sadly this is for the most part a true story)

Normal person: "The fuck are you talking about??"

Ex. 2

Scholarly debater 2
"More recent lab studies on Rhesus monkeys have suggested that old studies showing that cannabis damages the hippocampus were based on unsound and dishonest methods (not surprising since they were government sponsored) and that even at 100 times the amount that would get you high, there is actually a total lack of any long term effects on the hippscampus region of the brain."

Normal Person: "Hippo what?? fuck this, I'm going to go smoke a bowl."
by Max Senalger August 23, 2011
Get the Scholarly debate mug.