I think what you mean is that he didn't have a traditional formal education. However, he was constantly surrounded by some of the greatest painters of his time. He attended Académie Royale des Beaux-Arts , the Hague School and the Academy of Fine Arts in Antwerp. He stayed at each place long enough to learn what he needed.
He also learned at the hands of such artists as Willem Roelofs and Anton Mauve, was mentored and supported by them. He lived among some of the greatest artists of his time and shared knowledge with them. His brother supported him and he lived and breathed nothing but art. If he wasn't painting he was studying the works of the masters. His entire life's work reflected the influences of his learning at some of the finest art schools in Europe.
He didn't teach himself a "certain tradition", he cherry-picked knowledge and studied everything that seemed relevant to his needs, and developed a style all his own. This is exactly what sets him apart from the majority of his contemporaries and a good part of the reason why he was unsuccessful in his time; his art was his own and not what was "traditional".
Regardless, a degree won't make you an artist. Highly developed skills, natural talent, a firm grasp of the many years of gathered wisdom and knowledge of your predecessors, and a large dose of creativity is what makes an artist.
Finally, and getting to the heart of your email discussion, van Gogh wasn't a folk artist because his work wasn't in the least unsophisticated. He painted for himself, for art's sake, works of aesthetic superiority (exemplified by his clear understanding of palette and his incredibly uniform brushstrokes) the very definition of fine art.
BTW, thanks for the art debate. It's always enjoyable.