Today, "Rabbi" is a title which generally means that the person has studied particular areas of Jewish law and has been tested and found competent by another rabbi. It is a "degree" in the sense that it is the end goal of particlar study and in some schools, there is a program of classes which must be taken. In the past, people also used the term for anyone who was a teacher or who helped to lead a community, regardless of the specifics of his education.
It is also the subject of much argumentation. I wrote an essay about it a while ago (dealing with the question of a woman's place in the rabbinate)
In case you don't know it, I am a rabbi. Strange but true. A number of years ago, I, realizing my own weakness in my understanding of Juda...
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