“Do not murder.” Exodus 20:13 Murder goes deeper than the death of a human being by the hand of another human being. Murder is the crime of unlawfully killing a person—especially with malice or forethought. Murder, therefore, is distinguished from killing by the issue of motive. Jesus identified...
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Genesis 9:6 Whoso sheddeth man's blood, by man shall his blood be shed: for in the image of God made he man.
Exodus 20:13 Thou shalt not kill.
Is there a conflict between these two scriptures, no.
Murder is the crime of unlawfully killing a person especially with malice or forethought. Murder, therefore, is distinguished from killing by the issue of motive.
Jesus identified that motive behind murder as anger in Matthew 5:21, 22. Christ goes to the root of the behavior and sees the anger behind the action. The act of murder is still subject to the punishement in Genesis 9:6.
In Exodus 20:13 God forbids murder as He emphasizes the value of human life because we are all made in His image, but God also shows us that killing doesn't always fall under the category of murder.
Situations where killing is not murder as in accidental death or in self-defense where one is allowed to protect themself, Exodus 22:2, 3; Deuteronomy 19; Nehemiah 4:11-14. Exodus 22:2, 3. If a thief breaks into your house at night time and is struck that he would die there is no blood guilt on the who causes the thief to die. But if it is during the daylight then the punishment of Genesis 9:6 would apply as the thief life was valued . So even after the command in Exodus 20:13 God permits the taking of a life if one's own life is in potential danger. While reasonable self-defense is recognized in scripture, value for human life is the rule.
Capital Punishment
Genesis 9:6 God established capital punishement even before giving the law of "Thou shall not kill" to Moses. The punishment in Genesis 9:6 speaks to the severity of the crime. The taking of a life warrants a punishment as in a death for a death. It's not given for vengeance, but for justice and the role of justice is carried out by one specific office, Romans 13:1-6.
Just Wars
In the OT we read that at times God commands battles between nations. These wars were God's hand of justice against the wicked. There is a difference between the act of murder and a death in battle. In the NT the Church is not a nation that goes to war anymore as the kingdom of God is not of this world, John 18:36. We no longer fight for territory or possessions, but the wicked of even today will be punished according to the law God established in Genesis 9:6.
Deuteronomy 32:39 See now that I, even I, am he, and there is no god with me: I kill, and I make alive; I wound, and I heal: neither is there any that can deliver out of my hand. 40 For I lift up my hand to heaven, and say, I live for ever. 41 If I whet my glittering sword, and mine hand take hold on judgment; I will render vengeance to mine enemies, and will reward them that hate me.