For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
This is a very interesting question, John! I think it is an attribute of God alone. It is the quality of having all knowledge (Is.aiah 40:14: "Whom did he consult, and who made him understand? Who taught him the path of justice, and taught him knowledge, and showed him the way of understanding?").
Omnipotence, Omnipresence, and Omniscience represent the nature of God concerning His relation to the creation.
—Source unknown
Also, John, see 1 John 3:20, New International Version:
20 If our hearts condemn us, we know that God is greater than our hearts, and he knows everything.