The second part of Wolff's Theologia naturalis appeared just a year after the first part. While the first part had given an empirical proof of God's existence and his attributes by using a cosmological argument that moves from the existence of worldly things to the existence of their creator, the second part should begin with an a priori proof of these very same matters. Of course, it seems unclear why the first proof was required, if an a priori proof was already going to be written. Yet, one should remember that for Wolff, a priori meant simply all deduction of propositions, no matter whether the premises of the deductions contained some empirical statements. Indeed, we shall see that the second deduction is essentially based on the ideas of first deduction and cannot work without it.
What we should do, for now, is to forget all Kantian thoughts about the impossibility of ontological proof. We should ignore the idea that existence is not a true predicate, but positing of something. We should not say that e.g. possibility requires coherence with all the presuppositions of experience and generally forget all Kantian ways to understand modalities. All these concerns are anachronistic, and as we shall see, Wolffian proof has weak points, even when evaluated by its own standards.
Let us then summarise Wolff's proof. Wolff starts from the Leibnizian idea that when you just admit the possibility of God or perfect being that has all compossible realities and also accept that such a being would also have necessity as its property, then, because necessity just means something that exists, if it just is possible, then God would definitely exist. We might figuratively say that all possibilities reside in some shadowy world of potentialities, all waiting for some external push to move themselves to the actuality – all except one, that is, the being that pushes itself to actuality with its own power. Wolffian God is then like baron Münchhausen, who could get himself out of a mire just by pulling his own hair.
Wolff's proof has then three crucial points. Firstly, we may at first ask what this whole discourse of realities and their compossibilities actually means. Secondly, we may question whether such a perfect being would be possible. Finally, we should consider how we can be sure that necessity is one of these compossible realities.
Starting with the question of realities we find a bit of a problem. Although we would expect the word ”reality” to be explained in all its details in Wolff's ontology, it is actually something that Wolff just mentions briefly in passing. What little we can see from this mention is that reality is connected somehow with the concept of res or thing. Now, one should remember that for Wolff thing means something that is at least a possibility and that might well actually be a mere possibility. Reality is then that which makes something res or thing. Note that reality has nothing to do with actuality – actualities are not said to be more ”thinglike” than possibilities. Instead, by reality Wolff appears to refer to what makes something as perfect as it can be: all restrictions and limitations limit also the ”thingness” of something.
Now, each individual reality itself must be something possible, that is, it must be a feature of some possible thing. This doesn't mean that putting two realities together would make another possible thing: if squareness and circularity were both realities, they surely could not belong to a single possible thing. Thus, it makes sense to speak of compossibles, that is, realities that together can make up a possible thing. Thus, it makes some sense to ask whether there could not be several sets of compossible realities, but we may assume for the sake of argument that Wolff could somehow describe the set defining God in more detail and in such a manner that it would refer only to him and to nothing else.
Is then such a combination of realities possible? We know that the realities themselves are by definition possible. Because we are not yet trying to determine what these realities are, we need not prove individually of any of them that they are possibilities and thus realities. Combining the realities or possibilities should also produce something possible, because once again by definition, the realities are meant to be compossibilities. So, we may conclude that the notion of perfect being is always a possibility – there just isn't yet any guarantee what actual features this supposedly perfect being would have (for all we know, it might be something really mundane, like a shiny coin).
The most important part then lies in proving that necessity is one of these realities. What we should then do is to show that necessity is a possibility: because necessity would then clearly be more unlimited than contingency or impossibility, we could then suppose it is also a reality. Problem is that there seems to be no straightforward way to prove the possibility of anything – we could know something as possible, if we knew it was or at least had been actual or if we could infer the possibility of something from the actuality of something else.
Wolff solves this problem rather straightforwardly. A necessary being exists, therefore necessity is a possibility. And how do we know some necessary being is actual then? Why that is simple – it has been proven in the first part of Wolff's natural theology. We know that God exists, because world requires some final explanation, and we know that God is necessary, so surely we know that necessity is also a possibility.
The audacity of Wolff's argument cannot fail to be noticed. The supposed a priori proof of God's existence requires the assumption of God's possibility, which Wolff then sets out to do by invoking an a posteriori proof of God's existence. Firstly, it must be noted that Wolff really cannot have done otherwise. Ultimately, the only justification of possibility in Wolff's philosophy can only be through actuality – we know some actual red things, so we know redness is a possible feature of things, or we know actual things that require some other type of things for their existence, so we know that these other type of things must also be possible.
Secondly, we have to remember what a priori knowledge means in Wolffian philosophy – it is merely any type of knowledge based on proofs, no matter what the premisses of these proofs are. Thus, it matters not so much if Wolff's a priori proof of God's existence is based on some previous a posteriori proof.
It is still strange that Wolff decided to use such a circuitous reasoning – after all, if we do know God's existence, why bother proving it a second time, if we have to use God's existence as a premiss of the proof? I suspect the case is a bit similar as with the relation of rational to empirical psychology – rational psychology adds in a sense nothing new to empirical psychology about the activities of human consciousness, but merely explains the data of empirical psychology through a reasonable hypothesis. Similarly, the a priori proof of God's existence does not note anything new about its apparent topic, but it does open a new perspective by highlighting the role of God as the perfect being - no wonder then that Wolff uses many chapters to show that all of the God's attributes proved in the first book reflect actually God's absolute perfection.