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What is your definition of conscience?
Personally, (and just my opinion) I believe that there are 2 aspects to our conscience:
1) the GOD part that frequently is referred to as 'our heart" The part of us that abhors sin and wrongful doing, the part that consistently wants to do what is right in God's Eyes.
2) the other aspect of our conscience is our EGO. I think there is a constant battle within to KILL the Ego and replace it fully with "the heart".
Our conscience is part of our mind and the Bible tells us to put on "the MIND OF CHRIST".
I know it goes much deeper than this and would love to hear other's views.