The end game for this philosophical discussion begins by Demea's re-affirmation of his original worry about the a posteriori character of Cleanthes's argument. In its place he proposes "that simple and sublime argument a priori" as avoiding all the embarrassments into which Cleanthes had been led by Philo at the end of Part VIII. Cleanthes points out that it's pointless to extol the advantages of an argument unless you've shown that it works, so Demea is forced to clarify what he means by the "argument a priori". It is, he says, "the common one":
Whatever exists must have a cause or reason of its existence; it being absolutely impossible for any thing to produce itself, or be the cause of its own existence. In mounting up, therefore, from effects to causes, we must either go on in tracing an infinite succession, without any ultimate cause at all; or must at last have recourse to some ultimate cause, that is necessarily existent: now, that the first supposition is absurd, may be thus proved. In the infinite chain or succession of causes and effects, each single effect is determined to exist by the power and efficacy of that cause which immediately preceded; but the whole eternal chain or succession, taken together, is not determined or caused by any thing; and yet it is evident that it requires a cause or reason, as much as any particular object which begins to exist in time. The question is still reasonable, why this particular succession of causes existed from eternity, and not any other succession, or no succession at all. If there be no necessarily existent being, any supposition which can be formed is equally possible; nor is there any more absurdity in Nothing's having existed from eternity, than there is in that succession of causes which constitutes the universe. What was it, then, which determined Something to exist rather than Nothing, and bestowed being on a particular possibility, exclusive of the rest? External causes, there are supposed to be none. Chance is a word without a meaning. Was it Nothing? But that can never produce any thing. We must, therefore, have recourse to a necessarily existent Being, who carries the REASON of his existence in himself, and who cannot be supposed not to exist, without an express contradiction. There is, consequently, such a Being; that is, there is a Deity.
This argument has given no end of trouble to casual readers of the Dialogues. Demea certainly has not stated it in the clearest form. But there is a particular historical argument in mind here, namely, Clarke's argument in his Demonstration of the Being and Attributes of God. This argument was very well known in the period, being widely read and studied; it is usually called the 'a priori argument' (to give just one example). Further, Cleanthes later will quote part of Clarke's argument on a particular point. And if this were not clear enough there are even clear verbal similarities between Demea's argument and Clarke's. Compare Clarke's with Demea's above:
Either there has always existed some one unchangeable and independent being, from which all other beings have received their original; or else there has been an infinite succession of changeable and dependent beings, produced one from another, in an endless progression, without any original 13cause at all. According to this latter supposition, there is nothing in the universe self-existent or necessarily-existing: and, if so, then it was originally equally possible, that from eternity there should never have existed any thing at all, as that there should from eternity have existed a succession of changeable and dependent beings: which being supposed, then, what is it that has from eternity determined such a succession of beings to exist, rather than that from eternity there should never have existed any thing at all? Necessity it was not; because it was equally possible, in this supposition, that they should not have existed at all. Chance is nothing but a mere word, without any signification: And other being it is supposed there was none, to determine the existence of these. Their existence, therefore, was determined by nothing; neither by any necessity in the nature of the things themselves, because it is supposed that none of them are self-existent; nor by any other being, because no other is supposed to exist.
It is very significant that it is not Philo but Cleanthes who responds to this argument. Cleanthes, you will recall, has committed himself to the claim that there is only one legitimate argument for God's existence, his own. It therefore naturally falls to him to argue that Demea's alternative is untenable. He identifies five problems for the Demea-Clarke argument:
(1) Matters of fact cannot be demonstrated at all, much less be proven a priori. Things are demonstrable only if their contrary implies a contradiction; nothing distinctly conceivable implies a contradiction; whatever we conceive of as existing we can conceive of as not existing. Thus there is no being whose existence is strictly demonstrable. Cleanthes is extraordinarily confident of this: "I propose this argument as entirely decisive, and am willing to rest the whole controversy upon it."
(2) The argument claims that God is necessarily existent, and that this means that if we knew His whole nature, we would recognize the impossibility of his not existing. But since we cannot do this with our present faculties, the words 'necessary existence' are, for all practical purposes, meaningless.
(3) Even if this were not so, we could just as easily say that the material universe itself is the necessary being, and explain this necessary existence in the same way.
(4) Causation implies priority in time, and thus it is absurd to ask for the cause of a succession that has nothing prior to it (like an eternal one).
(5) In such a chain, each part is caused by what preceded it, so every part of the chain has a cause. What more could one want? Demea has asked for a cause of the whole, but taking these as a whole is simply an arbitrary act of the mind. If I have a collection of twenty particles, and give a cause for each particle's being in the collection, it would be absurd then to ask for a cause for the whole twenty; you've sufficiently explained it by explaining its parts.
It's somewhat difficult to evaluate how we should take these objections in the whole context of the Dialogues. Hume himself would certainly agree with (1) and (4), and possibly with (5); we don't know where he would stand on (2) and (3). (1) , whether right or wrong, is usually taken as begging the question against Demea and Clarke; (2) and (3) interestingly put Cleanthes in the company of the atheists, since d'Holbach, for instance, makes the same objections to Clarke's argument; (4) requires a view of causation that would be considered controversial; and Clarke, for instance, would have a response to (5). Presumably Hume thinks these are adequate reasons for rejecting Demea's argument, but the discussion is so quick and undeveloped that it hardly makes for a thorough refutation of one of the most popular and closely developed arguments of that era. This puzzling character of the refutation goes with a general puzzle people tend to have about Book IX: most readers read the Dialogues in such a way that they can't help but view Book IX as virtually just thrown into the discussion, not having much to do with its surroundings. I would suggest, however, that this underestimates Hume's skill as a writer.
In particular, I would suggest that Demea is not the primary interest here. While there were defenders of Clarke's argument, most of Hume's contemporaries would not have been convinced by it. They would have agreed, if not with all the details, at least with the general tenor of Cleanthes's dismissal. It is not necessary for Hume to look at the argument in detail. Why does he bring it in at all? There is a twofold literary value in doing so.
First, since Demea has been so wary of the a posteriori character of Cleanthes's argument, considering the a priori argument is a good way to begin preparing for Demea's being knocked out of the 'game'. Up to this point, Philo and Demea have been allies; at this point they begin to diverge, although Demea does not realize it.
Second, and more immediately, Philo himself barely devotes any consideration to Demea's a priori argument. Rather, he uses Demea's argument and Cleanthes's response to it to suggest a line of attack against Cleanthes's a posteriori argument. This, I would suggest, is the primary reason for this apparent detour. Cleanthes is committed to his argument being the only legitimate one for God's existence; but his response to Demea's argument suggests a further problem for his own argument, and Philo's development of this problem provides some subtle indications of how to interpret the position we will find Philo accepting in Part XII.
To see the value of Cleanthes's response for Philo, let's look more closely at Philo's argument. We find in mathematics a number of examples of wonderful regularity. For instance, every product of 9 is such that by adding the digits of that number you can get 9. Thus 9 x 2 is 18, and 1 + 8 is 9; 9 x 3 is 27, and 2 + 7 is 9. And so forth. A naive discoverer of this fact might assign it to chance or to design; but a mathematician can show it to be necessary. Thus, says Philo,
Is it not probable, I ask, that the whole economy of the universe is conducted by a like necessity, though no human algebra can furnish a key which solves the difficulty? And instead of admiring the order of natural beings, may it not happen, that, could we penetrate into the intimate nature of bodies, we should clearly see why it was absolutely impossible they could ever admit of any other disposition? So dangerous is it to introduce this idea of necessity into the present question! and so naturally does it afford an inference directly opposite to the religious hypothesis!
Note that Philo's argument doesn't really affect Demea, whose argument does not depend on the economy of the universe or the order of natural beings; it does, however, affect Cleanthes. If Cleanthes can respond to Demea's argument that matter might be the necessary being explaining why there is something rather than nothing, so too can somebody suggest that matter might be such that the design Cleanthes attributes to matter might well be due to necessity and not a designer. While Cleanthes rejects the coherence of the notion of necessary existence, this doesn't affect the notion of necessary order -- we have examples of necessary order in mathematics, for instance.
This, I would suggest, is important for understanding Philo's supposed concession to Cleanthes in Part XII. But for the moment Philo drops the subject, and simply goes on to note that most people don't find the a priori argument very convincing. This will allow Demea at the beginning of Part X to give Philo a starting point for both driving the argument to a point Demea cannot accept, and building a massive argument against Cleanthes, who had in Part VIII fatally committed his argument to certain claims about how good the order of nature is.