Ok, let me rephrase my answer to your post here:
Yes. But is it possible to imagine God without his personalities? In self-knowing, God the Father, self-knows himsself, so known person is God the father, not the son.
The Father knows the Son, but it is not self-knowing; because The Son, is another person.
The distinction between the Father and the Son (and the distinction between both and the Holy Ghost) are the only actual distinctions in God. All the attributes that are discoverable by reason alone, such as His existence, omnipotence, omniscience, and the fact that they (the attributes) are actually one and the same thing (ie Divine Simplicity), belong to the aspect of God that’s discoverable by reason alone. So, if a philosopher were to discover, through the natural powers of his intellect, that God has both Knower relation (God knowing) and Known relation (God as known by Himself), he would necessarily conclude that they’re not actually distinct due to Divine Simplicity. This I grant you.
But, since this same God had revealed, through supernatural means, that there’s an actual distinction between Him and His Knowledge of Himself, it’s no longer the case since then that we must necessarily conclude that these relations are actually one and the same.
This distinction, though, is not discoverable by human reason alone; it had to be supernaturally revealed by God Himself. So you have God-as-knowing-Himself relation and God-as-known-by-Himself relation that would have been thought to be one and the same if it were not for His Divine Revelation.
Why they are distinct, you may ask?
Because, according to this same Revelation, it wouldn’t make sense for the Knower to exist without the existence of the Known, which is distinct from the Knower relation
by definition, and vice versa (just as the giver relation and the receiver relation differs by definition, yet one cannot exist without the other by definition). God Himself supernaturally revealed that He Himself regards these two relations, the Knower and the Known, to be different, similarly as to how we regard these two exact relations to be different by definition.
To add to the giver-receiver analogy, these two relations can exist in one person (eg a man treats himself with snacks every Saturday, the giver being the man giving himself food and the receiver being the same man eating the food).
Please ask questions so that I may revise or clarify what I have posted here.