Whitehead suggests that Western Philosophy has been mistaken with its metaphysical view that the world is made up of concrete beings. Instead, he suggests that everything in the world ("entities") is in a constant state of change, of becoming. Each actual entity exists only during that in which it is experiencing (other entities) and being experienced. God is the entity that functions as the fountain of all possibilities for every other entity's unwritten future, and provides a sense of coercion, keeping the world in some sort of order. The world has a sense of connectivity, as each entity feels/experiences others.
The philosophy of Whitehead is novel and profoundly creative (no pun intended with either word). His thought is a helpful reminder that the world is not just merely a cold collection of static objects. Reading it brought afresh Bonhoeffer's distinction between Being-Towards-Adam and Being-Towards-Christ (which could easily be restated Becoming-Adam / Becoming-Christ, both in a federal sense), although Whitehead certainly saw the world differently than Bonhoeffer did. I also enjoyed considering the ontological (or, anti-ontological; perhaps metaphysical is more appropriate here) connectivity between people. Here I contemplated Saint Paul (and Pascal) on the body of Christ.
However, there are a number of problems that emerge from his philosophy. First, the underlying notion of evolutionary progress is uncritical (also consider Bergson here). Even with the acknowledgment of biological evolution, there is no reason to believe that this can be applied outside the sphere of biological sciences. A brief look at history--or a person's unkept back yard--will reveal a picture quite contrary to progress evolution. Second, in all of Whitehead's metaphysics, he ignores the "elephant in the room." If everything is becoming, it had to initially (be)come. So here, Whitehead faces the same problem as agnostic/atheist naturalist scientists, but \has all the more reason to discuss such issues by writing a metaphysics. Whitehead's "God" is, like Decartes', a logical necessity. Yet, it is not a God who could bring the world into existence. Instead, we are faced with absurd questions: e.g., who/what caused God? a bigger God? If so, is that God merely becoming as well? if so, who/what caused THAT God?, et cetera. Third, it is still unclear to me how conscious organisms have one unified experience. If every electron in our body is prehending, there seems to lack any clear explanation for "meta-prehension" for the entire organism.
Hartshorne was an interesting read in that he writes very clearly and has many suggestive arguments. I appreciated his focus on relativity in the sense that God is indeed relational. His thought is similar to Whitehead's (and thus the same critiques mostly apply), but with a much greater emphasis on the religious aspect in who God is. Here I would first question his notion that an orthodox, traditional view of God is a tyrant. As illustrated by Plato in his Republic, it is not necessarily the case that an authoritarian ruler is bad. Rather, the only truly perfect ruler would be one who held absolute power and was absolutely good and perfect. Classical Christian theism portrays a God who rules justly and perfectly with love and holiness--that is a "tyrant" that ought to be welcomed! To acknowledge God's relational qualities (that Hartshorne argues for), "God showed His love for us in this, that while we were still sinners, Christ died for us." If God is a tyrant, meant in the worst sense of the word, it would be absurd for Him to send His son to die for those he ruled over, those who rebelled against His authority.
I would also question Hartshorne's critique of the classical properties attributed to God, most specifically his immutability. First, God is triune, and therefore has always been relational. So, creation was not adding a new dimension (relativity) to God. Secondly, as we have briefly discussed, the suggestion that God is immutable by creating the universe is a misunderstanding based on time and eternity. If God were operating within a temporal structure, then the process critique would be sound. However, God is the author of time. If God is a timeless totality (not to detract from His personal attributes), then it does not seem an uncritical jump to attribute "all that was, and is, and is to come" to God's being. If the process philosopher or theologian were to here offer critique that God's eternity makes God impersonal or non-relational, the response must be a resounding reminder that the Word became flesh and dwelt among us. This is the very tension that lay on the Word's lips in the Lord's prayer--our Father (personal) in Heaven (transcendent other).
Cobb's process theology attempts to take the God as suggested by the process philosophers (most notably, the two discussed above) and reconcile it with the bible. Yet, however much he attempts to do so, this is hardly a Christian theology in any broad traditional sense. In his doctrine of God, I would appeal to arguments made above, such as that in Christ's humiliation and exaltation, God is proven not to be passionless. Not only is sending Christ incomprehensibly loving, but during his ministry, Christ showed this love. When Jesus the man wept, the second person of the trinity was actually weeping in and through the man. Cobb also misunderstands time and eternity, which results in building much of his theology around the problem of evil. While it is naive to not take time to provide adequate answers to the problem of evil, if we understand God is eternal, and that real judgment is coming (for the righteous and unrighteous), we begin to see a different picture emerge. Rather than being a God who is concerned with "extrinsic rewards and punishments" (Process Theology, p. 54), he is the God who made loving covenant with humanity---e.g., he brought Israel out of slavery before giving them the law. God's ultimate plan, then, is redemption, not enjoyment of His creatures. This does not mean that God does not want us to have enjoyment, but rather that we will only find enjoyment in Him alone.
Finally, Cobb vastly misunderstands the person of Jesus. Most importantly, He does not accept his divinity. Instead, he believes Jesus to be the Christ in that he is the ultimate source of creative transformation. However, the notion of creative transformation seems to be nothing more than Hegelian synthesis. It is somewhat perplexing how the idea of creative transformation as Christ can be considered Biblical, in that the authors of the four Gospels make repeated reference to his divinity (especially in light of the Son of Man in the book of Daniel, etc). To paraphrase C.S. Lewis, Jesus must be either a liar, as crazy as the man who believes he is a poached egg, or God--he does not leave any other alternative open to us. As a result of Cobb's misunderstanding of who Jesus was, he also fails to understand his ministry, calling his teaching "irrelevant and impractical" (p 96) to the Roman empire. However, Jesus was talking about a much different Kingdom, that of His Father. For broader arguments on Cobb, such as his doctrine of God, the arguments discussed for Whitehead and Hartshorne are largely applicable to Cobb as well.