Analytic and A Priori
Take any ordinary analytic statement and prefix it with “It’s analytic that”: is the result analytic? Is “It’s analytic that bachelors are unmarried males” analytic? The answer would appear to be yes, since the meanings of the embedded sentence and the word “analytic” entail its truth. You don’t need to look outside the meanings of these words in order to know that the sentence is true. It’s not like saying that the sentence “Bachelors are unmarried males” was once uttered by W.V. Quine, which is a synthetic statement requiring knowledge of extra-semantic facts. What about synthetic sentences: if you prefix one of these with “It’s synthetic that”, do you get an analytic truth or a synthetic truth? You get something true, obviously, since the embedded sentence is synthetic (say, “Quine taught at Harvard”), but is the complex sentence itself synthetic? The answer would appear to be no, since the meaning of the embedded sentence requires that the world has to make a contribution to determining truth-value. It follows from what the sentence means that it is synthetic, so given the meaning of “synthetic” the complex sentence will be true in virtue of meaning, i.e. it will be analytic. More strictly, the sentence “It’s a synthetic truth that Quine taught at Harvard” will be analytically true, given that Quine actually taught at Harvard: that is, if Quine taught at Harvard, then it’s analytic that it’s synthetic that Quine taught at Harvard. It follows from the meaning of the embedded sentence that its conditional truth is synthetic, so this is an analytic proposition: the proposition is analytically synthetic. You can tell just from its meaning that its truth depends on the world, so it is analytically true that it is a synthetic proposition. We know just by philosophical reflection that synthetic propositions are synthetic, because this status depends on their meaning alone: the meaning of the corresponding sentence entails that it is synthetic, so it is analytic that this is a synthetic sentence. It is analytic that this is the type of sentence that is synthetic. So both analytic sentences and synthetic sentences are analytically of the type they are. (Compare the fact that we can necessitate both necessity and possibility: “Necessarily p” implies “Necessarily necessarily p” but also “Possibly p” implies “Necessarily possibly p”).
Now we get an interesting result: for every true proposition we can derive an analytically true proposition. That is clearly correct for analytically true propositions, since it is analytic that they are analytic; but it is also true for synthetically true propositions, since the statement that they are synthetically true is true analytically. Thus no one could claim that there are only synthetically true propositions: for every synthetic truth can provide the basis for a corresponding analytic truth, i.e. one saying that it is synthetic. It follows from the meaning of every synthetic truth that it is synthetic, i.e. requires the contribution of the world, so this fact is an analytic truth. It couldn’t be that every true sentence is synthetically true, since synthetic truths themselves generate analytic truths. If we announce that every sentence faces the tribunal of experience, we forget that this is not true for the sentence that says that it faces the tribunal of experience, because this is a fact about its meaning. Also, there are more analytic truths than synthetic truths, since every synthetic truth has a corresponding analytic truth, but not every analytic truth has such a corresponding synthetic truth. Someone might see in this asymmetry a reason for saying that analytic truth is more basic or primary, because all language requires the existence of analytic truths, even if they are limited to affirmations of syntheticity.
Turning to the a priori, we get a parallel result (not surprisingly). If a proposition (or piece of knowledge) is a priori, is it a priori that it’s a priori? Evidently yes, since we know without empirical investigation that it’s a priori. Mathematical knowledge is a priori, but so is the knowledge that it is a priori. We don’t need to do an empirical investigation of mathematical knowledge; we know it by philosophical reflection. That is, if it is a priori, then our philosophical knowledge that it is so is also a priori. We don’t find this out from empirical psychologists. But now what about a posteriori knowledge: is it a priori or a posteriori that a given piece of knowledge is a posteriori? Clearly it is a priori: philosophers know that empirical propositions are empirical by a priori means. We know that “Quine taught at Harvard” is an empirical sentence just by understanding it, so we know this fact a priori. We can just see that it requires a posteriori investigation by knowing what the proposition is, so this knowledge is a priori. So every a posteriori proposition has a corresponding a priori proposition—the proposition that it is a posteriori. It would therefore we wrong to say that all propositions are (or could be) a posteriori: some have to be a priori. Someone might see in this a reason for thinking that a priori knowledge is more basic or primary than a posterioriknowledge. For every piece of a posteriori knowledge, there is a piece of a priori knowledge to the effect it is a posteriori. We can say the same about certainty and doubt: if it is certain that p, it is certain that it is certain that p(e.g. the Cogito); but also if it is doubtful that p, it is certain that it is doubtful that p. If the external world is doubtful, this fact is a certainty—it isn’t itself doubtful. I know for sure that the existence of the external world can be doubted. So again, certainty exists wherever there is doubt, even if it just concerns what is doubtful. Certainty thus has a claim to being more basic and primary than doubtfulness. We can therefore conclude that certainty, the a priori, and the analytic are everywhere, lurking in the background of the doubtful, the a posteriori, and the synthetic. We just need to go up a step and they loom into view.
Once we have these points clear we can ask complicated questions about how the relevant concepts interact. Is it a priori that it’s analytic that it’s synthetic that p? Is it analytic that it’s necessary that p? Is it certain that it’s a posteriori and synthetic that p? I won’t go into these questions, but I think the answer is yes to each of them for suitable choices of p. People have tended to investigate the relevant concepts in isolation, but they interact in complex ways that tax comprehension. It is interesting to see how the semantic, epistemic, and modal line up, with the concepts that are often deemed secondary or dubious assuming a position of centrality. The certain, the analytic, the a priori, and the necessary all emerge as pervasive and tightly connected, as in hackneyed examples like “Bachelors are unmarried males”, which exhibits all four properties. This is actually a remarkable convergence once we take the measure of each concept (they are not at all identical or mutually entailing): it doesn’t seem necessary or analytic or certain or a priori that anything would exhibit all four properties together, and they can clearly come apart in certain cases. Yet here they all are crowded together into a single sentence! Finding them stuck together is the surprising thing, not finding them apart.
 Kripke showed in Naming and Necessity that they come apart in certain cases; post-Kripke we may wonder how they ever manage to join together. This is certainly a non-trivial fact: why should a single proposition be analytic and a priori and necessary and certain? Yet here they nestle together like members of the same family. We can imagine philosophers for whom this is a momentous discovery—not the discovery that they can be instantiated separately (that is a truism).