Summary
In Books I and II Hobbes argued that in order to achieve peace, which is man's natural inclination, one should obey the civil laws of a commonwealth. The project of Book III is to reconcile this obedience with obedience to the divine laws of God, namely, the divine laws handed down to man through revelation and prophets. As Hobbes will eventually show, not only is there no tension between the civil and divine laws, but also obedience to a sovereign is a necessary component of obedience to God himself.
The main reason for the perceived tension between obeying divine and natural laws is the mistaken belief that during a man's life he lives both within a natural kingdom, or Kingdom of Man, and the Kingdom of God. Obviously if one lives within two kingdoms than one has two kings or sovereigns to obey. Yet Hobbes shows through careful Biblical interpretation that man no longer lives within the Kingdom of God during their natural lives. During the time of Adam and Eve, and later Noah and Abraham, God ruled directly over man; and in fact, God made a direct covenant with the Israelis to rule over them through the prophet of Moses and his successors. Eventually, the Israelis asked for a human King to rule over then, to which God consented, and the Kingdom of God left the earth, not to return until the end of the natural world.
The belief that humans still live in the Kingdom of God where he still hands down laws and decrees through revelation and prophecy is destructive to the authority of the commonwealth. While Hobbes does not discount the possibility of God handing down divine laws through such means - God is, after all, omnipotent - Hobbes urges the reader to take caution when being showed any so-called miracles or prophecies. Any prophet must show somehow that they are a true prophet, which is shown mainly through performing miracles, or events that have no cause in the natural world; and every man "is bound to make use of his natural reason...to apply to all prophecy those Rules which God has given us, to discern the true from the false." In the absence of a miracle or sufficient proof of a miracle, no one is obliged to believe or obey the so-called prophet, and man should direct their obligations to the sovereign, "who has the only legislative power."
Additionally, when miracles are performed or prophecies unveiled, one should take careful note that these are the direct actions of God, and do not, then, have anything to do with the person performing the miracle or witnessing the revelation. A prophet is just a vessel of communication through which God acts through and has no special divine powers himself. To believe otherwise, and to worship a prophet as if he has God-like powers, is to worship a false idol.
Hobbes also argues that the mistaken belief that the Kingdom of God exists at present, combined with ignorance about the true nature of heaven and hell, is yet another way people use religion instrumentally and for their own gain. Through the use of scripture Hobbes argues that the concept of eternal damnation and paradise are used metaphorically, and that the afterlife, or heaven, is being relieved from the burdens of natural life (of the "Kingdom of Darkness" Hobbes returns to in Book IV). Using his philosophy of the natural world, Hobbes also argues that it is illogical to conceive of a place where man feels pain and pleasure for all eternity. After all, pain and pleasure are concepts relating to the material and corporeal world, so how can an immaterial and incorporeal soul - what leaves the body and conceivably is sent to heaven or hell after death - experience such qualities?
In essence, many of the problems arising from this mistaken belief in the present Kingdom of God comes from a conflict of scriptural interpretation. Having a sovereign person or body that interprets scripture, in addition to a civil sovereign, results in two competing authorities, and thus, instability and civil war. Again drawing on scripture, Hobbes argues that since the time of Constantine civil and religious authority have been combined in one sovereign.
The argument for having a separate religious authority not answerable to the sovereign seems to presuppose that this authority somehow has unique insight into the Kingdom of God, and gives the only proper interpretation for how to obey God. Yet as Hobbes argues, since "the Kingdome of Christ is not of this world; therefore neither can his ministers (unless they be Kings) require obedience in his name. For if the Supreme King, have not his Real Power in this world, by what authority can obedience be required to his offices." Hence, sovereign of a commonwealth should be the sole authority on matters both civil and religious. The sovereign may appoint ministers and pastors, but just as they do with regard to civil matters, their authority extends only as far as the sovereign allows.
It is important to note that Hobbes is not arguing that since God is not omnipresent in the natural world man has no obligation to him. Rather, Hobbes believes that to obey civil laws is to obey God himself:
Seeing then our Saviour hath denyed, his Kingdome to be in this world, seeing he hath said, he came not to judge, but to save the world, he hath not subjected us to other Laws than those of the Common-wealth ...the observing whereof, both he himselfe, and his Apostles have in their teaching recommended to us, as a necessary condition of being admitted by him in the last day into his eternall Kingdome, wherein shall be Protection, and Life everlasting.
In the case that the sovereign is areligious or even anti-religious, and one believes that obeying a civil law jeopardizes one's chance of entering into the Kingdom of Heaven, Hobbes argues that no words spoken or actions undertaken for these reasons risks one's chance at redemption. What is required for salvation is obedience to laws and "faith in Christ," the latter of which is an entirely subjective and personal matter.
Analysis
Methodologically, Book III is a radical departure from Hobbes' first two parts. That he uses close scriptural interpretation, or exegesis, to justify much of his argument might seem to contradict some of his earlier statements that something is not true just because posterity says so, and that we should carefully scrutinize and apply our own reason to arguments in order to justify its logic. But one needs to take into account both the subject matter Hobbes is dealing with and the audience he has in mind.
Man's rational capacities are only one source of discovering the divine laws, and the other two sources, revelation and prophecy, are recorded in scripture. For men like Hobbes who live after these original prophets, the Bible is the only authentic historical record of these other two sources. Taking a more pessimistic view of Hobbes' opinion of religion, Hobbes lived in a time far more religious than our own, so backing up his conclusions with scripture could have been one way he hoped to reach a wider audience. Regardless, in Book III Hobbes does not entirely do away with his geometric-style of proof; he always begins by establishing definitions. Oftentimes he uses both reason and exegesis.
Another question one might have while reading Book III - and one which Hobbes' contemporaries surely had as well - is whether Hobbes was actually advancing an argument for atheism. Although he repeatedly distances himself from atheists, there is debate as to whether his whole treatment of religion is ironic, and is actually a subversive way of arguing against religion. As Edwin Curley notes, Hobbes could be employing some kind of rhetorical device (one Curley calls "suggestions by disavowal") where Hobbes innocently argues for something but does so in a way that makes the conclusion seem almost ludicrous. For example, in his treatment of miracles Hobbes urges the reader to investigate possible causes of the miracle, to be wary of false prophets performing miracles, and even notes how true miracles have not occurred for some time before going on to show their place in his philosophic system. Are we to take Hobbes at his words here, or is he up to something more cunning and subversive?
Additionally, from Hobbes' claim that the Kingdom of God no longer exists in the natural world one might believe that Hobbes is advancing an argument for deism. Deism, the belief that God created the world and essentially abandoned it to its inhabitants, would also seem to follow from Hobbes' insistence on scientific reason and urging for skepticism concerning miracles and prophets. On the other hand, Hobbes does not deny that God has, or could again, communicate directly with the world through revelations and prophets. He also explicitly says that God is honored and worshiped not because he is the first cause of the universe, but because of his sheer omnipotence. Again, it is up to the reader to decide whether or not to read Hobbes literally.