Well, just to clarify, the term 'professor' usually means having a faculty appointment in a university or other academic institution. But, setting that aside,

Well, just to clarify, the term 'professor' usually means having a faculty appointment in a university or other academic institution. But, setting that aside, you definitely do not need an affiliation with a university to pursue a life of the mind. If you want to be a person of letters, a scholar, even a public intellectual, then go for it!