Whether the supposed peer is imagined to participate in His actions or not, and whether that partner is conceived as identical or dissimilar, the ruling is the same; a full exposition of this appears elsewhere.
One compelling proof that the two kinds of knowledge cannot be identical is that the Lord is All-Knowing of everything—whether one says He knows by a single, all-embracing knowledge or by an infinite number of knowledges. No such option exists for the servant; both alternatives are impossible for him. Indeed, were someone to claim that God’s knowledge of a particular thing equals the servant’s knowledge of it, the claim would be absurd, for God’s knowledge surrounds the matter completely, whereas the servant’s does not encompass it.
Moreover, we know self-evidently that God is more knowing and more powerful than His creatures, as the Exalted says:
“Have they not seen that Allah, who created them, is mightier than they are in strength?” (Qur’an 41:15).
And He says:
“He knows you best when He produced you from the earth and when you were embryos in the wombs of your mothers … He knows best who is truly mindful of Him.” (Qur’an 53:32).
And He says:
“Allah knows, and you do not know.” (Qur’an 24:19).
And He says:
“You have been given of knowledge only a little.” (Qur’an 17:85).
These proofs, transmitted and rational alike, are too manifest to require further evidence. How, then, could equality be imagined when superiority is decisively established?
I have raised this point because some Muʿtazilite “affirmers of attributes,” who affirm the seven essential attributes yet deny the so-called report-based attributes—claiming that such affirmation would be impermissible anthropomorphism—were confronted with this argument during a controversy that erupted between the affirmers and the deniers. The Chief Judge at the time declared (or it was said on his behalf): “Rather, we too affirm these attributes while denying any likeness, just as you have affirmed those other attributes.”