The meaning of Love in the Bible
(From Easton's Bible Dictionary)

This word seems to require explanation only in the case of its use by our Lord in his interview with "Simon, the son of Jonas," after his resurrection (John 21:16,17). When our Lord says, "Lovest thou me?" he uses the Greek word agapas ; and when Simon answers, he uses the Greek word philo , i.e., "I love." This is the usage in the first and second questions put by our Lord; but in the third our Lord uses Simon's word. The distinction between these two Greek words is thus fitly described by Trench:, " Agapan has more of judgment and deliberate choice; philein has more of attachment and peculiar personal affection. Thus the 'Lovest thou' (Gr. agapas) on the lips of the Lord seems to Peter at this moment too cold a word, as though his Lord were keeping him at a distance, or at least not inviting him to draw near, as in the passionate yearning of his heart he desired now to do. Therefore he puts by the word and substitutes his own stronger 'I love' (Gr. philo) in its room. A second time he does the same. And now he has conquered; for when the Lord demands a third time whether he loves him, he does it in the word which alone will satisfy Peter ('Lovest thou,' Gr. phileis), which alone claims from him that personal attachment and affection with which indeed he knows that his heart is full."

See more on the meaning of Love in the Bible:
Love {International Standard Bible Encyclopedia}

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