In this section, Demea challenges Philo's skepticism with a priori arguments, which, if they are valid, offer infallible demonstration of religious truths, instead of probabilistic proofs. In addition, a priori arguments can accomplish all of the things that Philo has shown the argument from design to be incapable of: they can prove that God is infinite, perfect, and simple (that is, not made up of more than one part).
The particular a priori argument that Demea has in mind is a version of the ontological argument. His version of the argument goes as follows: (1) Whatever exists must have a cause or reason for its existence. (2) If something exists, either there is an infinite chain of causes with no end, or else there is some thing which carries the reason of its own existence within itself—a necessarily existing thing. (3) It cannot be the case that there is an infinite chain of causes because then, though each particular link in the chain will have a cause, there will be no cause for the existence of the entire chain. In other words, there will be no reason why this chain of causes exists rather than some other chain of causes, or rather than no chain of causes at all. (4) Therefore, there must be a self-causing being, that is, God.
Cleanthes argues against the ontological argument. First, he claims that the very project is flawed because it is impossible to prove matters of fact with a priori arguments. The reason for this claim goes as follows: (1) If something is demonstrable (i.e. able to be proved a priori) then its contrary implies a contradiction. (2) Nothing that is distinctly conceivable implies a contradiction. (3) Whatever we conceive of as existing we could also conceive of as not existing. (4) So there is no being whose non-existence implies a contradiction. (5) Therefore, there is no being whose existence is demonstrable.
Second, even if the argument were legitimate it would not prove enough. All that the argument proves is that there is some necessarily existing being. But why believe that this necessarily existing being is God? The necessarily existing being could just as easily be the material universe. Cleanthes argues that in either case (whether the necessarily existing thing is God or the material universe) we have no idea how and why this necessary existence works. One or the other of these, according to the argument, would have to possess some mysterious qualities we know nothing about. There is no reason to assume that it is God who has these mysterious qualities rather than the material universe.
Third, you cannot coherently talk about a first cause of an eternal succession of events. Something eternal cannot have a cause because the concept of cause essentially involves priority in time and a beginning of existence.
Finally, even if we overlook the contentions that it is impossible to establish matters of fact with a priori arguments, that the argument does not prove God's existence, and that it is incoherent to speak about the cause of something eternal, the argument still fails: the whole thing turns on a faulty premise. There could be an infinite chain of causes without there being a cause for the chain. As long as each link in the chain is sufficiently explained by the link before, it would not matter that there was no cause acting as the reason of the whole. There does not need to be a reason for the whole, separate from each individual reason among the parts, because there is no such thing as the whole, for at no time does the chain exist (except as an abstract construct in our minds), instead at any given moment what exists is a link in the chain.
Philo is basically satisfied with Cleanthes' objections, but he has one of his own to add. Demea says that either there must be an infinite chain of causes or else there must be some self-causing being, but Philo can think of another alternative: there might be a principle of necessity in the material world, some law governing nature that acts as the final explanation. He likens this type of necessity to the necessity found in mathematics: to someone who did not know algebra, he points out, certain arithmetical patterns might seem very mysterious. Someone would did not know math might feel the need to posit chance or design to account for these patterns. But anyone who knows algebra understands that these patterns arise because of mathematical necessity. The same might be true of the universe. Philo concludes the chapter by remarking that no one who was not already convinced of God's existence was ever convinced by this version of the ontological argument.
The ontological argument has a long and illustrious history in philosophy. The first known version of the argument was presented by the medieval thinker St. Anselm. This version of the argument appealed to the fact that our idea of God is an idea of a perfect being. (1) God is that of which nothing greater can be conceived. (2) That which exists is greater than that which does not exist. (3) Therefore, if God does not exist then we can think of something more perfect than Him, in which case He would not be God. (4) Therefore, denying the existence of God involves a contradiction.
The ontological argument played a big role in early modern philosophy. The rationalists, such as René Descartes, Baruch Spinoza, and G.W. Leibniz all used some version of the ontological argument in order to support their philosophical systems. This is because they believed that there is a reason for everything that happens in the world and that all of these reasons can be discovered just by thinking really hard. In other words, they thought that if we started with certain innate concepts (i.e. concepts they believed we were born with, such as the idea of God, the idea of infinity, the idea of matter and so on) we could use our faculty of reason to understand why everything in the world is the way it is. But in order for this to be the case, there must be some final cause that is its own reason for existence. If there is no such final cause then either there is an infinite chain of causes (in which case we can never understand everything, because we could never get to the end of this chain) or else there is some arbitrary end to the chain and so there is not really a reason for everything (i.e. there is no reason for the first link in the causal chain).
Hume, as an early modern empiricist, would not have been very sympathetic to the needs of the early modern rationalists. He would, in fact, have been very keen on showing that this argument does not work. However, the version of the ontological argument that Demea presents is not Descartes's influential proof, but a much weaker formulation. Also, despite the fact that Cleanthes does end up leveling very convincing arguments against this ontological argument, his most basic rebuttal is not very solid.
Cleanthes's argument for the claim that matters of existence cannot be proved a priori is worth examination. Cleanthes begins with the premise that all demonstrable truths (those that we can prove a priori) have a special property: to deny them involves a logical contradiction. For instance, consider the demonstrable truth "all bachelors are unmarried." If we try to deny this truth ("not all bachelors are unmarried") then we land ourselves in a contradiction. What it means to be a bachelor is to be unmarried, so you cannot logically maintain that not all bachelors are unmarried. Now consider another truth: "all men have a digestive system." If we deny this statement, we end up with a falsity, but not with a logical contradiction. There is nothing incoherent about claiming that some men lack a digestive system. The statement "all men have a digestive system" is true, but not demonstrably true; the only way to prove that it is true is to go out and look at human anatomy. One could, without a contradiction, imagine a man without a digestive system who survives by a miracle.
The relevant difference between this last truth and the previous truth about bachelors, according to Hume, is that the claim about men's digestive systems is a truth about the way the world is (a matter of fact) whereas the first truth are really just stating facts about our ideas or words (what we mean when we say "bachelor" is "unmarried man"). It is only this latter kind of truth (relations of ideas) that can be proved a priori. Since claims about existence are matters of fact and not relations of ideas, Hume does not think that such claims can be settled with a priori arguments. In his judgment, there can never be a contradiction in asserting the non-existence of anything (for instance, there is no contradiction in saying, 'the sun does not exist').
The next step in Cleanthes argument is to show that God's existence is not a demonstrable truth. Nothing that is distinctly conceivable, he tells us, involves a contradiction. This is reasonable, for it is impossible for us to imagine anything that involves a contradiction, such as a ball which is all one color and is blue and not-blue. Next, Cleanthes claims that whatever we conceive of as existing we could also conceive of as not existing. For instance, we can imagine that the sun does not exist, despite the fact that it does. Thus, any statement which denies the existence of anything will not involve a contradiction. Therefore, there is no being whose existence is demonstrable. Therefore, Cleanthes thinks that there can be no contradiction in the statement, "God does not exist."
However, St. Anselm argued that it is impossible to conceive of God as not existing, for existence is part of God's nature (whereas it is not part of the sun's nature to exist), because anything that exists is more perfect than anything which does not, and God is the most perfect thing that can be thought of, so God must exist. A denial of God's existence, according to St. Anselm, would go as follows, "God, who exists, does not exist," and this statement clearly does contain a contradiction. So for Cleanthes's first objection to hold, he must either deny that existence is a perfection or that God is not the most perfect being that can be thought of. Many philosophers, including Kant, believed that existence is not a perfection.
Cleanthes's second objection may be similarly vulnerable. He says that the material universe may be the necessarily existing being, but according to his own logic this seems impossible. For there is no contradiction (or at least no trivial contradiction) in the statement, "the universe does not exist," and so the existence of the universe does not seem to be necessary.
Cleanthes' third objection, that the chain of causes does not exist except as an abstraction of our mind, is the most convincing. However, it is possible that someone who wants to defend the ontological argument could say that even though the chain of causes does not exist at any one time, it certainly does exist.