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.