The Christian has an answer to Euthyphro's Dilemma because the Christian God is absolute and transcendent. In addition, it is important to stress that ethical standards are related to God's character in a much more specific way than many Christians have argued. What I am referring to is the fact that the doctrine of the Trinity is the true source for specifically Christian ethics. The Christian answer to Euthyphro is found in an ethic of love specifically grounded in the fact of God's triunity.
First, according to Jesus, the very essence of the Christian ethic is found in the two great commandments that summarize the whole law of God. And one of them, a lawyer, asked Him a question, testing Him, "Teacher, which is the great commandment in the Law?" And He said to him, "'You shall love the Lord your God with all your heart, and with all your soul, and with all your mind.' This is the great and foremost commandment. The second is like it, ‘You shall love your neighbor as yourself.' On these two commandments depend the whole Law and the Prophets." (Mat. 22:35-40)
Second, this ethic of love is grounded in two important truths. The first is that God is a God of love. The second is that we have been created in His image. For us to do what is good is to conform to God. In so doing, we fulfill the meaning of our creation and become like God Himself.
Third, God is a Trinity. God is one Being in three eternal Persons. The Father, Son, and Spirit are a society bound in covenantal love. Each gives Himself wholly to the others. And all share in their love for the others — the Father and Son sharing together their love for the Spirit, the Spirit and Son sharing their love for the Father, and the Spirit and the Father sharing their love for the Son — so that the Trinity is a perfect fullness of love. It is clear that in this understanding of God, He could not be other than what He is, not only because it is ontologically inconceivable for God to be other than what He is, but also because of the fact that for the Persons of the Trinity to relate to one another any other way would mean the dissolution of the Trinity itself. The love which God commands is not arbitrary for it is grounded in the ontological and ethical necessities of His own being.
For a man to be ethically right means to do what pleases God. God is one. The Father, Son, and Spirit never disagree about what is good or right. Pleasing a sovereign Creator to whom we are responsible for our whole lives is something quite different from pleasing, or attempting to please, the gods of ancient Greece. All relationships with other persons as well as our stewardship over the non-personal creation are first of all and primarily to be understood in terms of our relationship with God. That is what it means for Him to be an absolute Creator and Lord.
At the same time, relationships with other persons are the second priority. We are to love others as we love ourselves. What that means exactly in the everyday affairs of men is spelled out in the law of Moses. Though the law of Moses was given to ancient Israel for her use in the land of Palestine until the coming of the Messiah, the ethical teachings of that law are still relevant for us today for they show us concretely the meaning of love.
Would Socrates have posed the same kind of questions about this kind of God? He certainly could not have referred to jealousy and strife between the Persons of the Trinity and questioned our ability to know what pleases God, as if what were pleasing to the Father might not be pleasing to the Son. If he understood the Christian notion of God, he would not have asked how God knows what is good.
God is love essentially and inescapably. When He commands what is right, we are to do it because it is pleasing to Him. Could He command us to do the opposite of what is loving? Not without ceasing to be Himself, for He is a God who subsists in three Persons who are equally ultimate, powerful, wise, and holy. What is right is what is loving and what is right and loving is what pleases the God of love who cannot be other than what He is. Euthyphro's Dilemma does not seem to be relevant. Though we still have questions about defining what is right and loving in a particular situation, the Christian answer is that God has revealed the way of love in His Word.
to be continue....