Philosophers traditionally distinguish between analyticand synthetic propositions. An analytic proposition is one that is true or false by virtue of the relations between its constituent concepts. A stock example is “All bachelors are unmarried,” which is true because the concept of being unmarried is included in the concept of being a bachelor. A synthetic proposition is true by virtue of something beyond the relations between its constituent concepts. For example, the proposition “Some bachelors are lonely” is true by virtue of a contingent empirical relation between being a bachelor and being lonely, rather than a necessary conceptual relation between them.
A second traditional distinction is that between propositions knowable a priori and those knowable a posteriori. A priori propositions are those knowable independently of sensory experience. A stock example would be an arithmetical proposition like 2 + 2 = 4. An a posteriori proposition is one that is known through sensory experience. An example would be “There are two cars in the parking lot.”
Kant noted that combining these notions yields four putative classes of proposition:
1. Analytic a priori
2. Analytic a posteriori
3. Synthetic a priori
4. Synthetic a posteriori
Classes 1 and 4 are relatively unremarkable. The analytic proposition “All bachelors are unmarried” is knowable a priori precisely because we know that the concept of being unmarried is included in the concept of being a bachelor. You don’t need to rely on observation in order to determine that it is true, but merely need to understand the concepts. “Some bachelors are lonely” is known a posteriori precisely because it is only the observable facts that reveal to us its truth. Understanding the concepts is not enough.
Class 3, the synthetic a priori, is of course the one that Kant was famously concerned about. Such a proposition would be one which is not true merely by virtue of the relations between its constituent concepts, but nevertheless can be known without relying on experience. Kant held both that it is difficult to see how there could be such propositions, but also that there must be if knowledge of the natural order is to be possible.
The reasons had to do with the implications of Hume’s empiricism. For example, Hume seemed to have shown that necessary causal connections between things could not be known a posteriori, since we have no impression (in Hume’s sense of the term) of any force or power in a cause that necessitates its effect. But he also seemed to have shown that such causal connections are not analytic either, insofar as causes and effects are “loose and separate” and in principle any effect or none might follow upon any cause. Hence to be knowable, causal connections would have to synthetic a priori. Explaining how there could be such knowledge is the starting point of Kant’s system.
Naturally, as a Scholastic Aristotelian I don’t agree with the whole way Hume, Kant, and the other early moderns frame these issues, much less with their conclusions. But that’s not my topic here. My topic has to do with something else Kant says, which is that in fact there cannot be such a thing as class 2 or analytic a posteriori propositions. For analytic propositions are necessary, and what is necessary, Kant thinks, is knowable a priori.
But knowable to whom? Consider the proposition “God exists” as understood by classical theists like Augustine, Anselm, and Aquinas. Addressing the question whether this is a self-evident proposition, Aquinas writes:
A thing can be self-evident in either of two ways: on the one hand, self-evident in itself, though not to us; on the other, self-evident in itself, and to us. A proposition is self-evident because the predicate is included in the essence of the subject, as “Man is an animal,” for animal is contained in the essence of man. If, therefore the essence of the predicate and subject be known to all, the proposition will be self-evident to all… If, however, there are some to whom the essence of the predicate and subject is unknown, the proposition will be self-evident in itself, but not to those who do not know the meaning of the predicate and subject of the proposition… Therefore I say that this proposition, “God exists,” of itself is self-evident, for the predicate is the same as the subject, because God is His own existence... Now because we do not know the essence of God, the proposition is not self-evident to us; but needs to be demonstrated by things that are more known to us, though less known in their nature – namely, by effects. (Summa TheologiaeI.2.1)
The demonstrations Aquinas refers to in the last sentence are arguments like the proof of a first cause in De Ente et Essentia, which argues that anything the essence of which is distinct from its existence must have a cause the essence of which is identical to its existence. (This is “the Thomistic proof” that I defend in Five Proofs of the Existence of God.) The proof shows that the ultimate cause of things cannot be something which merely has being in a derivative way, but must be something which just is subsistent being itself.
Now, because God just is being itself, to know the essence of God would entail knowing that God exists. In that sense, the proposition “God exists” has in itself the self-evidence of an analytic proposition. But we know this only because we’ve reasoned from the existence of the things of our experience to an ultimate cause having this essence. So we’ve arrived at it in an a posteriori way. And that’s the only way we can arrive at it. Because of the limitations of our intellects, our conceptualization of God is too imperfect to enable us to “cut to the chase” and get to knowledge of his existence directly, merely from a grasp of the concept of God. (You might say: The ontological argument works, but not for intellects as limited as ours.)
In the same article from which I just quoted, Aquinas cites the proposition “that incorporeal substances are not in space” as an example of something “self-evident only to the learned.” You need a certain amount of sophistication to grasp the constituent concepts well enough to know it a priori. Someone who is not learned could still know it on the basis of the authority of someone who is. But the unlearned person could also at least in principle come to know it a priori himself, once he acquires sufficient knowledge. That possibility might make Kant reluctant to concede that an example like this is a genuine case of an analytic a posteriori proposition.
But the proposition “God exists” differs from this example, in Aquinas’s view, insofar as failing to know it a priori is not merely a consequence of lacking sufficient learning. No amount of learning would make it knowable a priori for the human intellect left just to its natural capacities. We human beings can reason a posteriori to the conclusion that God exists and that his essence must be such that to know it perfectly would suffice all by itself to afford us knowledge of his existence. So we know that the proposition “God exists” must be analytically true and knowable a priori for anyone with a sufficiently penetrating grasp of the constituent concepts. But we don’t have such a grasp, and so we don’t know the proposition in that manner. Hence, we have in this case an example of a proposition that is in a clear sense analytic a posteriori, at least for us.
This particular example comes from natural theology, that body of knowledge about God’s existence and nature that is available to us via purely philosophical arguments and apart from special divine revelation. But other examples would come from revealed theology, which includes propositions about the divine nature that could not in principle have been arrived at through purely philosophical means and are knowable only if specially revealed by God. The doctrine of the Trinity is an example. If we had a perfect grasp of the divine essence, we would see that the claim that God is three Persons in one divine nature is as necessary and self-evident as “All bachelors are unmarried.” But in fact our grasp is so imperfect that we cannot arrive at knowledge of this claim even through indirect natural means, through philosophical arguments, as we can with “God exists.” We need supernatural assistance.
This assistance comes via a divine revelation backed by miracles, and in particular via the teaching of Christ. And that is something we know about only a posteriori. So, once again we have an example of a proposition that is in a clear sense analytic a posteriori.