Omniscience

They made kings, but not through me. They set up princes, but without my knowledge.

Omniscience is a state of possessing all knowledge. It is the complete understanding of anything and everything. Typically, it is attributed to deities (for the sake of esteeming deities). But, it can, alternately, be taken simply as the sum of all knowledge known to all knowers in all of time.

From the intuition that knowledge is consistent with itself, omniscience does not include 'knowing that' 2+2=5. So, unlike omnipotence, omniscience is not easily construed in such a way as to entail a contradiction. On the other hand, the cardinality of the set of interesting natural numbers is at least aleph-naught. Thus the total number of independent statements of facts in any catalog of number theoretical information is infinite. "Kurt Godel proved for any computable axiomatic system that is powerful enough to describe the arithmetic of the natural numbers (e.g., the Zermelo–Fraenkel set theory with the axiom of choice), that: If a (logical or axiomatic formal) system is consistent, it cannot be complete." With respect to any finite number of entities containing only computable knowledge, this means there must be something they don't know.

Omniscience is often, though not always, a prerequisite for deities. The God of the Abrahamic religions is considered to be omniscient. Oddly, the Abrahamic God does not often display his omniscience. For instance, God asked Cain where his brother, Abel, was and the Hebrews' needing to mark their doors with lamb's blood to keep their firstborn male children from being killed.

Apparently God's omniscience does not extend to the consequences of his own actions, because in Genesis 6:7 he said, "I will blot out man whom I have created from the face of the land, from man to animals to creeping things and to birds of the sky; for I am sorry that I have made them." There is clearly a question of whether, if he’s omniscient, determinism is true — i.e. whether there’s any way for him to know ahead if schedule how others will choose to think and/or act. Further i.e. whether the future yet exists to be known/be in the omni-.

The Bible and omniscience
Most people who believe in the omniscience of the Bible's God (Yahweh) rarely pay attention to the verses which clearly demonstrate the opposite. When they do, however, they state that the verse is being written from man's point of view, or that the verses involving God asking humans questions was God merely testing them. This is a good example of the desperate fundamentalist's clutching for straws. In, the meaning implied by the verse is clear. God is saying that in order for him to know man's heart, he must search it first, even though in other verses God is stated as being the one who created man in the first place. and basically repeats the words of the former verse. So according to the Bible, Yahweh is not omniscient. After all, the New Testament states that not even Jesus knows when the end times will arrive, which only makes one wonder what else Jesus doesn't know. The usual explanation for this is that Jesus gave up some of his divine attributes during his time as a human being, or that the other members of the trinity kept the knowledge from him. The latter situation is no different than the Greek Pantheon keeping secrets from each other, constantly fighting and bickering. The former makes no sense, Jesus could still do everything else, so it would mean that he was definitely not against showing partiality.

Psalm 139:1-4 is often cited as proof of God's omniscience (or omnipresence), but a closer inspection reveals inconsistencies in this reading. The verse was written by David, Yahweh's anointed king over Israel. This verse isn't declaring his supreme knowledge, rather it is emphasizing the intimate relationship between Yahweh and David. Rather than recognizing that Psalm 139 focuses on David and Yahweh, and applied universally, the believer and God, most have interpreted as either meaning just the latter or referring to God and mankind. The emphasis on the closeness in their relationship is maintained consistently throughout the Book of Psalms, and to ignore it in this verse but not the others reveals the confirmation bias present in many Christian interpretations of the Bible.

Fun things to do with deities' omniscience
If When entities like Answers in Genesis are insisting that their version of God knows everything, a fun thing is to ask them the method to get God to reveal additional knowledge, such as:
 * Methods of treating drug-resistant bacteria, and prevent them from developing additional resistances.
 * Alternatively, methods of preventing infection of such drug-resistant bacteria or viruses once an arbitrary amount of them get in your body.
 * Methods of in vivo regeneration of lost arbitrary body parts, including but not limited to organs and limbs.
 * Better yet, methods of in vivo regeneration of additional arbitrary body parts of arbitrary function that may be useful later NOW.
 * Methods of faster-than-light travel of matter and information.
 * Effective lossless compression methods for completely random data.
 * The formula that predicts how a protein folds.
 * It's completely necessary to know the math if you want to intelligently design a bacterial flagellum.
 * A testable theory that unifies quantum mechanics and general relativity.

The problem with omniscience
An irreconcilable problem with being 'all-knowing', is that you cannot know whether or not you know everything, simply because you may not know what you don't know. For example, if one was to be omniscient, and therefore 'knows' that they were the one that knows the most about quantum physics, they would have no source to check against as to whether or not they truly know everything about that subject because some of the topics they "know" about aren't discovered yet and likewise they don't know what hasn't be discovered that they might not know about. As a result, the only tangible knowledge that you have as an omniscient being would be true appreciation of your ignorance, as you would have no higher knowledge to check your facts with. Although if you were the one that created everything, there'd be nothing you weren't aware of...

In mathematical speak, this is a known consequence of, more specifically the lemma by that there cannot exist a set of all truths.

If all of this is too above your head, then consider the 'Divine Liar Paradox:

(DLP): "God will not believe this statement is true."

If the statement is true, then God must not believe a true statement, but then there is a true statement God can be said not to know, and so can't be said to know all truths. If it's false, on the other hand, it's false that God doesn't believe it. It must then be true that he believes it. God, therefore, believes a falsehood.