For Christian love I look to the teachings of Jesus, as written in the Gospels, with a little help from Paul (because he elaborates on some important teachings). It's important to note that Christ, like the Buddha, didn't write down his teachings; we could call this "mysticism," the idea that the Truth or Way must be lived and experienced, not written, to make sense.
Christian love is as simple as Buddhist love; it goes like this: love everyone, without qualification. (Buddha sometimes goes further by saying love every living thing).
Like Buddhist loving kindness, love is foundational. There are many ways that love is expressed as the greatest. Paul says “the only thing that counts is faith expressing itself through love” and “if I have a faith that can move mountains, but have not love, I am nothing” and “do everything in love.” And, of course, the famous wedding passage--"love is patient, love is kind"--which ends: “And now these three remain: faith, hope and love. But the greatest of these is love.” But people people usually don’t hear the beginning of this famous passage, which says “and now I will show you the most excellent way.”
Love is the Golden Rule and the greatest commandment:
“Love the Lord your God with all your heart and with all your soul and with all your mind and with all your strength. The second is this: love your neighbor as yourself. There is no commandment greater than these.”
This is constantly restated, and Paul interprets it as one law: “The entire law is summed up in a single command: love your neighbor as yourself.” (later he says “honor one another above yourselves.”)
Who is our neighbor? In the good samaritan story (Lk 10:30), Jesus says that everyone in need of help is our neighbor.
Love your enemies
But, as we saw in Aurelius and Buddha, there is an extension to the golden rule, an even higher commandment (request?) that Jesus gives as well:
“You have heard that it was said, ‘love your neighbor and hate your enemy.’ But I tell you: Love your enemies and pray for those who persecute you, that you may be sons of your Father in heaven…Be perfect, therefore, as your heavenly Father is perfect.” (A perfect God, then, does not hate enemies, but loves them.)
This is added to elsewhere with “do good to those who hate you, bless those who curse you” and (even!) “lend to them without expecting to get anything back. Then your reward will be great.” A more practical, or rational reason (think Aurelius) to love enemies is to be better than sinners: “If you [only] love those who love you, what credit is that to you? Even sinners love those who love them.” Very much like Buddha, Christ and Paul do not think this love-your-enemies stuff is just wishful thinking; they think that love can drive out, extinguish, and get rid of hatred and evil:
“Live in harmony with each other…Do not repay evil for evil…live at peace with everyone. Do not be overcome by evil, but overcome evil with good.” And 1 John adds “perfect love drives out fear.” Buddha (who said "this is an old rule") and Gandhi would agree with this.
How does love act?
First, by obeying moral principles:
“If anyone loves me, he will obey my teaching.”
Second, by forgiving. Paul makes this clear when he gives Corinth instructions on how to treat someone who has (apparently) done something bad:
“The punishment inflicted on him by the majority is sufficient…now instead, you ought to forgive and comfort him…reaffirm your love for him.”
Third, through sacrifice:
“Greater love has no one than this, that he lay down his life for his friends. You are my friends if you do what I command…this is my command: Love each other.”
Paul adds to this: “Very rarely will anyone die for a righteous man…But God demonstrates his own love for us in this: While we were still sinners, Christ died for us.”
Jesus sees his mission as to transfer God’s love to people: “I have made you known to them, and will continue to make you known in order that the love you have for me may be in them and that I myself may be in them.” And Jesus shows the “full extent” of his love for his disciples when he washes their feet: “Now that I, your Lord and Teacher, have washed your feet, you also should wash one another’s feet…no servant is greater than his master, nor is a messenger greater than the one who sent him.”
Love Part 1: Platonic Love
Love Part 2: Aristotle
Love Part 3: Epictetus and stoic love
Love Part 4: Marcus Aurelius
Love Part 5: Plotinus
Love Part 6: the Buddha
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