This is just defining terms to not be contradictory. Define essence. Define Person.
Is Jesus God? Is the HS God? Is the Father God?
Well that's at least a start, you accept that the explanation doesn't violate the law of non-contradiction. You just need clarification now upon what Christianity means my essence, and by person.
If we accept that by definition God is a Maximally Great Being (MGB), that is, whatever attributes God possesses, He must necessarily possess them to their maximum, then if we are to say that the Father, Son, and Spirit are one in essence and three in person, then it must be true that each of them, in person, possess all the same attributes of God, or else one person wouldn't be God.
Now, I don't want to get sidetracked into what "ingredients" makeup the MGB, so hopefully we can for the sake of discussion simply accept some basic Christian attributes assigned to God. So let's assume that it is more maximally great for a being to be all powerful (omnipotent) than limited in power. Let's also assume that being eternal is more maximally great than being created. For a being to be God, He must be maximally great, and possess all the attributes of a MGB to their fullest. For example, if God wasn't omnipotent, and another being was omnipotent, then that other being would actually be God.
So for the sake of discussion, let's accept that part of being MGB means the being possesses the following: omnipotence, omniscience, eternality, immutable in character, and goodness.
Therefore, any being that is God must necessarily possess each of those attributes to their maximum. Therefore, if we say that each person of the Trinity is God, then each person of the Trinity must possess all attributes of God to their maximum.
If this is the case (and I think it is), then in essence all three person's of the Trinity are one. They would never disagree, they would not act differently, they would never think differently, they would be in perfect unison, in perfect relationship at all times, with the same will, purpose, and goals. For there could be no disagreement if each person of the Trinity possessed in equal measure all the attributes of the MGB.
Thus, while they may have different roles, their essence is the same, because they are God. One God, three persons.
Also, while I want to give you the benefit of the doubt, I highly doubt you followed any of the previous links I provided and looked at the material, so I'll just copy/paste some of it here for your benefit.
Essence and Person
Essence. What does essence mean? As I said earlier, it means the same thing as being. God’s essence is his being. To be even more precise, essence is what you are. At the risk of sounding too physical, essence can be understood as the “stuff” that you “consist of.” Of course we are speaking by analogy here, for we cannot understand this in a physical way about God. “God is spirit” (
John 4:24). Further, we clearly should not think of God as “consisting of” anything other than divinity. The “substance” of God is God, not a bunch of “ingredients” that taken together yield deity.
Person. In regards to the Trinity, we use the term “Person” differently than we generally use it in everyday life. Therefore it is often difficult to have a concrete definition of Person as we use it in regards to the Trinity. What we do not mean by Person is an “independent individual” in the sense that both I and another human are separate, independent individuals who can exist apart from one another.
What we do mean by Person is something that regards himself as “I” and others as “You.” So the Father, for example, is a different Person from the Son because he regards the Son as a “You,” even though he regards himself as “I.” Thus, in regards to the Trinity, we can say that “Person” means a distinct subject which regards himself as an “I” and the other two as a “You.” These distinct subjects are not a division within the being of God, but “a form of personal existence other than a difference in being” (Grudem, 255; I believe that this is a helpful definition, but it should be recognized that Grudem himself is offering this as more of an explanation than definition of Person).
How do they relate? The relationship between essence and Person, then, is as follows. Within God’s one, undivided being is an “unfolding” into three personal distinctions. These personal distinctions are modes of existence within the divine being, but are not divisions of the divine being. They are personal forms of existence other than a difference in being. The late theologian Herman Bavinck has stated something very helpful at this point: “The persons are modes of existence within the being; accordingly, the Persons differ among themselves as the one mode of existence differs from the other, and — using a common illustration — as the open palm differs from a closed fist” (Bavinck,
The Doctrine of God [Banner of Truth Trust, 1991], page 303).
Because each of these “forms of existence” are relational (and thus are Persons), they are each a distinct center of consciousness, with each center of consciousness regarding himself as “I” and the others as “you.” Nonetheless, these three Persons all “consist of” the same “stuff” (that is, the same “what” or essence). As theologian and apologist Norman Geisler has explained it, while essence is what you are, person is who you are. So God is one “what” but three “who’s.”
The divine essence is thus not something that exists “above” or “separate from” the three Persons, but the divine essence is the being of the three Persons. Neither should we think of the Persons as being defined by attributes added on to the being of God. Wayne Grudem explains,
But if each person is fully God and has all of God’s being, then we also should not think that the personal distinctions are any kind of additional attributes added on to the being of God. . . . Rather, each person of the Trinity has all of the attributes of God, and no one Person has any attributes that are not possessed by the others. On the other hand, we must say that the Persons are real, that they are not just different ways of looking at the one being of God . . . the only way it seems possible to do this is to say that the distinction between the persons is not a difference of ‘being’ but a difference of ‘relationships.’ This is something far removed from our human experience, where every different human ‘person’ is a different being as well. Somehow God’s being is so much greater than ours that within his one undivided being there can be an unfolding into interpersonal relationships, so that there can be three distinct persons. (253–254)
What Is the Doctrine of the Trinity?