Swearing on a Bible is taken to mean that you will abide by the tenants taught in the Bible. Foremost among them is being truthful.
You are saying, "God, be my witness, I am telling the truth."
The Koran, and the teachings of Mohammed do NOT teach Moslems to be truthful when dealing with non-Moslems. Any Imam who says that it does is lying.
Ellison is saying, "Allah, be my witness, I will do what you want."
Bryan you asre exactly right, but sadly, our shameless society allows it unfortunately- howeverm even though they swear by Allah, God is watching and they are still swearin in His presence and are bound by His authority and law despite the fact that they might not beleive so. Originally we revered God enough to request that He be witness to our oaths- but sadly our culture ahs so disregarded Him that they no longer felt the need and made exceptions to the oath process to accomodate others- prefering man's opinion over God's- and quite frankly, man's opinion is worthless as we've seen by the continual breaking of oaths by members of Congress who repeatedly vow to attack the constitution by citing bogus 'interpretation differences' twisting the original to mean things it never was meant to.