Can God love?

[SteveII]

Jesus had all the essential attributes of a human nature and all the essential attributes of a divine nature. There were some aspects of the divine nature that were set aside:  

Philippians 2:5-8 Paul says "Have this mind among yourselves, which is yours in Christ Jesus, who, though he was in the form of God, did not count equality with God a thing to be grasped, but emptied himself, taking the form of a servant, being born in the likeness of men. And being found in human form he humbled himself and became obedient unto death, even death on a cross."

Two natures in one person. Not a divided person.

It's not clear what specific meaning to attach to the passage you cite, as it's vague and speaks in metaphor.  It's also unclear what to make of it given that it appears to be contradicted by Colossians 2:9 which says: "For in him the whole fullness of deity dwells bodily..."  All it seems to indicate is that no one checked the bible for consistency.

Regardless, I'm not sure this formulation of yours is entirely helpful.  It seems to raise more questions than it answers.

Is it not an essential attribute of God that he is not composed of any parts?
Is it not an essential attribute of man that he consists of a body and a soul or spirit?
Is it not an essential attribute of God that he is a necessary being?
Is it not an essential attribute of man that he is a contingent being?
Is it not an essential attribute of God that he is immortal?
Is it not an essential attribute of man that he is mortal?

I don't think any of these pairs are problems. You have a new entity: God incarnate - with two natures:

1. The divine nature is immaterial, is a necessary being and is immortal
2. The human nature is physical, contingent, and mortal. 

Being combined does not need to effect the essential attributes of the other. I discuss how this might work below.

Google dictionary defines an essence as, "a property or group of properties of something without which it would not exist or be what it is."  Wikipedia for its part has this to say about essence:

In philosophy, essence is the property or set of properties that make an entity or substance what it fundamentally is, and which it has by necessity, and without which it loses its identity. Essence is contrasted with accident: a property that the entity or substance has contingently, without which the substance can still retain its identity. ... For Aristotle and his scholastic followers, the notion of essence is closely linked to that of definition (ὁρισμός horismos).

Wikipedia || Essence

So a thing's essence is that by which we are able to identify something as a specific kind of thing.  Thusly, a thing maintains a particular identity only in so far as it possesses all and only those essential properties which define that thing.  If you subtract essential properties from a thing, then it is no longer that thing.  This pertains to Christ if the supposed attributes he gave up are essential properties.  (Note that the trinity is defined as three persons who possess one essence.  If Jesus and God the Father possess different essential properties, you've entered the land of polytheism.)  So a thing is no longer that thing if it is without some of the essential properties which define that thing.  Likewise, if a thing possesses additional essential properties, it is no longer that thing, for the thing that it was is without essential properties which it has.  (This does not apply to accidental properties which you can add and subtract all day long.)  It's also worth noting that the essential attributes which define a man do so only with respect to the man, not necessarily with respect to Jesus, as they are not the sole essential properties which Jesus possesses.  If Jesus possesses both the essential properties of man and God, then he is neither man nor God, but something else entirely new.  (Which violates the doctrine that Christ is co-eternal with God the Father.)  In that case, Jesus would be 'a' god, perhaps, but not God with a capital 'G'.  The only way you can successfully identify Jesus as God is to treat the man-like properties as accidental properties, such that Jesus does possess all and only those essential properties which define him as God.  But then your contention that Jesus is both man and God is false because he no longer possesses the essential properties of a man.  It seems that the only way you can reach the conclusion that Jesus is both man and God, at least along this path, is by playing with essential properties in a way which is not valid, which undermines your entire argument.

Let me preface this answer by saying that the Bible does not tell us how this is done. We are left with trying to figure out an explanation that is not a logical mess, is true to the information that we are given, and is theologically sound (does not have unwanted conclusions). This is one such model:

First, you are right that if God the Son gave up any essential properties of being God in becoming Jesus, that would be problematic in a number of ways. So, I don't think that is how it worked. Jesus retained all divine attributes.

Second, we are made in the image of God. It seems that a large part of this is our mind/soul (same thing for this discussion) or personhood. So the commonality between humans and God is a mind/soul (albeit with infinitely different capacities). The mind/soul/personhood of Jesus was divine. The physical body and the brain are human--including desires, emotions, hunger, pain, and other human-specific states which inform the mind. Just like any regular man, he had both immaterial and material aspects in one entity (obviously I think that mind/body dualism is correct).

Thirdly, now what to do with all the divine attributes that Jesus didn't seem to have? Jesus as a boy "grew in wisdom, stature, and favor with God and man," there were things he did not know, or have complete control over, he was temporal, finite, limited, etc. I think Jesus' divine attributes were subconscious. Let me explain. 

A. Just like you have knowledge of something (like where you left your car keys) but cannot access it.
B. Just like a person can be hypnotized and there is a layer of knowledge that is there but not consciously accessible. On the other side of that coin, you can be hypnotized not so see things that are right in front of you. I am not saying Jesus was hypnotized, but the mind can be segmented.
C. That subliminal layer of knowledge can inform the conscious but you are not certain why-- for example, Jesus was not able to sin even as a young boy. 
D. I tend to think that Jesus did not do miracles using his own power. There is evidence that the Spirit was the one providing the power. 
E. How this limitation was imposed is an open question for which we will not get an answer.

With this understanding, Jesus's experienced human life much like we do--with many of the same struggles and limitations. This also illustrates more fully why your statement a few posts back was wrong about Jesus having all divine power and knowledge of the end result somehow takes away from the effect. 

In conclusion, I will say that this model might not be right. However, it is reasonable and consistent with basic theology and serves to protect the concept from charges of irrationality.