From the classic Bob Enyart vs Samuel Lamerson written debate:
Omniscience means that God knows everything, exhaustively, and without exception. Does Scripture really teach this, or is this another philosophical invention? Memories of perversion burden God, and nothing requires Him to retain pristine recollections of every filthy deed. “You have burdened Me with your sins, you have wearied Me with your iniquities” (Isa. 43:24). God wants to put these wicked things out of His mind because it is ugly to remember them. “I, even I, am He who blots out your transgressions for My own sake; and I will not remember your sins” (Isa. 43:25; etc.).
When God says to the wicked, “I, even I, will utterly forget you” (Jer. 23:39), we rightly constrain this as a figure of speech, not meaning that God will no longer even recall men like Esau or Judas, but that His mercy toward the wicked will not endure forever. So, when God says that memory of filth is a burden that He wants to blot out of His mind, we weigh that against our philosophical doctrine of omniscience. Settled View proponents prioritize the quantitative aspect of vast knowledge above the qualitative attributes of God as good and personal. The Settled View denies out-of-hand the possibility that God’s loathing of sin might bring Him to limit His recollection of lewd acts. A pornography video does not have to play eternally in God’s mind.
Passages of God’s desire to forget sin are far more literal and “exhaustive” than any strained “proof-texts” for omniscience. We know that because these passages flow from the goodness and righteousness of God, whereas the omniscience “proof-texts” deal with quantity rather than quality. Thus they exaggerate the superficial at the expense of the substantive. No one can impose vulgar duty on God. Such basic biblical teaching shows that the non-biblical term “omniscience” overstates the truth. What is the true doctrine of God’s knowledge? God knows everything knowable that He wants to know. God does not want to know everything! And yes, He knows how many hairs are on your head, but He doesn’t know how many hairs are on the boogeyman’s head, because there is no boogeyman. God can do that which is doable, and He can know that which is knowable. So He knows, or at least He can determine instantly if He wants to know, how many hairs are on your head. And if He wants to lengthen the life of sparrows, God can instantly locate and strengthen them all. There are beings who keep track of endless reams of meaningless data, but God is not a bureaucrat. Does God keep track of every molecule in every roll of toilet paper, to trace its path from tree to the mill, to the store, to your sewer pipe, and back again? Does this interest God? The LORD has a purpose for His knowledge. God created man in His likeness, able to intuitively dismiss infinite piles of data as unimportant and endless possibilities as meaningless. God’s ways are higher than our ways (Isa. 55:9), but they are not lower. He reveals that He has no desire to retain Memorex memories of endless sadism, sodomy, and rape, and He need not keep infinite charts analyzing the base bodily functions of all animals. So while the unbiblical concept of omniscience demeans God, the true doctrine of His knowledge exalts Him in wisdom. God knows everything knowable that He wants to know.
For full debate, click here.