What does "beg the question" mean? It means to assume what you are trying to prove as part of the argument in your proof.
He's is saying that this "Plymouth Brother" is so deeply ensconced in his religion that every part of his belief is used to prove some other part, and vice versa and all the way around.
You will find many native speakers use this phrase, incorrectly, to mean that something "raises a question." It's incorrect and should be avoided. For example: "It was snowing so hard today it begs the question why they didn't cancel school." This is an incorrect use of the phrase.
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