In order to question it, you need to present a basis for said questioning.
I did, oh he who thinks he understand things.
You said: "I see no eason to believe that it is impossible for someone, or something, to know everything, but be unaware that he actually knows it."
The unawareness you describe, is knowledge they don't know hence negating their all knowingness.
Prove it, oh he who thinks axioms are real.
Try again.
After you.
Edit to add: the computer's inability to supersede its programming and access its contents is an example of knowledge that it does not know. Plus, bad example because the "all knowledge" its set to collect would necessarily include the fact that it itself contains all knowledge - therefore, it KNOWS it knows everything - or else it hasn't COLLECTED all knowledge.
Yet, if it is unable to access the fact that it has all knowledge, my point still stands. You, on the other hand, are stuck with declaring you are right, and then proclaiming that anyone who doesn't recognize that fact, is stupid, all without providing any evidence beyond your belief in the existence of axioms.
Perhaps you should read some science fiction, you might discover how limited your understanding of thought is.
You have not presented an example of where the axiom could fail.
A computer that possesses all knowledge necessarily knows it possesses all knowledge. Its access to said knowledge is irrelevant to whether or not it possesses it and knows it possesses it, you example was horrendous.
You said it collects "all knowledge."
That it then possesses "All knowledge" becomes knowledge. Does it not collect that bit? Then it doesnt even possess all knowledge. Ya rick.