Although I had originally wanted to post this song as a description of Hobbes's state of nature, I found Jay-Z had explicitly mentioned Plato and the Euthyphro dilemma! That being the case, these are the two philosophical ideas I thought were relevant in this song.
First, I'll discuss how this song relates to Hobbes's state of nature. The state of nature, as Hobbes describes it, is a hypothetical time before moral or legal rules. In this time period there is no such thing as immorality or injustice, and everyone is equal (e.g., those that are physically stronger than most people are still able to be defeated by those that are smarter). Given that everyone is equal, everyone is equally subjected to have their property taken, to be enslaved, killed, etc. As such, life in the state of nature is "solitary, poor, nasty, brutish, and short" for everyone (Leviathan, Chapters 11-14).
Since none of us want this kind of life, according to Hobbes, moral rules and/or legal rules were created as a result of individuals coming together and realizing it was in their best interest to form something like a contract with other individuals; all of whom found themselves in equally vulnerable circumstances.
Jay-Z and Kanye seem to share a similar sentiment about life without morals (or, life in the wild). Without rules, or some enforcement of rules, then there's no refuge (e.g., church) for any one. Jay-Z does a rather nice job describing the panic and visual spectacles that one could expect to see in a world without morals (e.g., the wild), and why someone would hope for something like a church in the wild. Kanye does a nice job of describing the personal struggles that one would face in the wild, as well as the self-destructive behavior in which most people would engage. My favorite line from Mr. West is the following:
"Two tattoos, one read "no apologies."
The other said, "love is cursed by monogamy."
That's something that the pastor don't preacher.
That's something that a teacher can't teach.
When we die the money we can't keep,
but we probably spend it all 'cause the pain ain't cheap.
I think the relationship between this song and Hobbes's state of nature is even more convincing if we replace 'wild' with 'state of nature' and replace 'church' with 'morals' (but I'll leave that for you to do).
Where Hov' and Yeezy differ from Hobbes seems to be in there idea of where morality came from and how everyone got out of the state of nature (or, the wild). So, while Hov' and Yeezy agree with Hobbes about the condition of life in a world without morality, they differ in how we escaped those conditions. This can be seen by looking at the chorus (sung by Frank Ocean):
"Human beings in a mob.
What's a mob to a king?
What's a king to a God?
What's a god to a non-believer who don't believe in anything?"
We see that there's an open question concerning what those who don't believe in god believe. It's hinted at in the song that if there's no belief in God, then we find ourselves in the wild (e.g., the state of nature) with no rules. This seems to reflect a quote from Fyodor Dostoyevsky's The Brothers Karamazov: "if there is no God, then everything is permitted." They seem to think that without a belief in a God that creates or enforces the rules there would be no morality. So for them the state of nature (or, again, the wild) is something like a world in which there is no God to create or enforce moral rules.
This leads us to the Euthyphro dilemma. Jay-Z explicitly cites this dilemma when he says:
"I’m wonderin’ if a thug’s prayers reach.
Is Pious pious cause God loves pious?
Socrates asks, “Whose bias do y’all seek?”
All for Plato, screech
I’m out here ballin’, I know ya’ll hear my sneaks.
Jesus was a carpenter; Yeezy laid beats.
Hova flow the Holy Ghost, get the hell up out your seats.
Plato raises this dilemma in his dialogue entitled, Euthyphro (hence it's being called the euthyphro dilemma). For simplicities sake, we'll replace 'pious' with 'good.' The dilemma arises for people who believe in God when we ask: "Is something good because God loves it? Or, does God love it because it's good? It's a dilemma because neither option seems appealing for the person that believes in God. (1) Either things are good because God loves them (which seems to allow that whatever is good could arbitrarily change at any moment). This option is a view known as Divine Command Theory. This is the view that God decides what is right or wrong, and this is the view I've attributed to Jay-Z and Kanye. Or, (2) good things exist independently of God, and one can do good things or be good without God.
So, either we can take the Jay-Z and Kanye route and say that whatever God loves is good, but we're then faced with the problems of (1) knowing what God loves, and (2) knowing when it changes and simply trusting that whatever God decides to love has now become good (e.g., if God suddenly decided that he loved to see humans eat babies then eating babies would be a good thing - I think most people that believe in God would have a hard time thinking that eating babies suddenly became a morally good thing); or we can take the second option which leaves us with the problem of explaining what makes something good if it's not God.
Who says rappers don't know philosophy :)