By Jon Cogburn
[Update: Please see Nick Stang's "Did Kant Conflate the the Necessary and the A Priori." Stang argues against one of my key claims, but (in addition to advancing it) his paper shows really well what the debate is in the secondary literature.]
I'm not a historian of philosophy and I only know a tiny bit of the enormous literature on Kant. For all I know, someone has already made the principal claim I am suggesting here, that when Kant talks about the synthetic a priori he's really talking about what we would nowadays call necessary a posteriori. Or there might be obvious reasons why this is a clearly false hypothesis. I'd be very, very interested in references to articles or books relevant to either confirming or disconfirming the hypothesis.
I am more confident that the hypothesis is non-trivial. In addition to articulating why it might be plausible, below I put enough on the table to show why it's important. In what follows I first present a little bit of the standard Whig history of analytic philosophy to explain why most of us interpret Kant the way we do on the analytic/synthetic and a priori/a posteriori distinctions. Then I show why I think this is mistaken and conclude with why I think this is actually something worth getting right.
Alberto Coffa's To the Vienna Station in part recounts how the linguistic turn and development of modern logic allowed early analytic philosophers to understand the analytic/synthetic division as a semantic one, concerning meaning. Analytic truths are those true solely in virtue of meaning while synthetic ones are those true also in virtue of the way the world is. This then leads us to think of the a priori/aposteriori distinction as an epistemic one, solely concerned with the justification of claims. There are two ways this can be cashed out. One can say a claim is a priori if it can be justified without recourse to sensory experience, or one can say that a claim is a priori if it cannot be justified by sensory experience. In Naming and Necessity, Kripke (to me somewhat inexplicably) makes fun of people who use the second notion. Not much hinges on this because the defender of each way of cashing out the distinction can easily characterize the distinction as made by the other person. If one accepts that the really philosophically interesting claims are those that can't be justified by experience but yet can be justified, such claims will be a priori in both senses. It's just that the Kripkean has to append "and they are also not a posteriori."
From this perspective a synthetic a priori claim is one that is true in virtue of the way the world is, yet such that (following the non-Kripkean) our sensory experience cannot justify it.
By understanding Kant to have been talking about this all along, you can piggyback on Kant's own self conception and tell a wonderful Whig history of philosophy, from Plato to Kant and beyond. Plato noticed that our sensory experience of a finite, and in many other ways wretched, world could not justify the geometric knowledge that we used in making sense of sensory experience. So he postulated a separate realm of forms that are the real object of geometric knowledge. Geometry is then synthetic because it is true of the realm of forms. It is a priori because our sensory experience doesn't justify it. And other problem areas such as ethics are explained by Platonists in the same way. Then, the history of philosophy is a series of footnotes to this move. Trying to account for problem areas of knowledge without appeal to the forms, which are unsatisfying for all sorts of reason. Kant's innovation, according to this story, was to explain the synthetic nature of such knowledge in terms of the humans being the part of the world that render them true.
This is a great Whig history. It set a major part of the program of analytic philosophy. Initially, via the positivists, we just need to explain how science and math can still work once we've gotten rid of the synthetic a priori propositions. With the new logic, we could understand math and geometry as analytic a priori and (pace Kant) natural science as all being synthetic a priori. Ethics? Well. . . ethics schmethics.
Of course these days we philosophize in the ruins of positivism. Luckily, there are still rich treasures to be found by those of us willing to do a little bit of excavation and new building (cf. the churches built with bricks from Roman ruins).
On this story, the metaphilosophical importance of Kripke is that he was part of a narrative of what we can do in the ruins. The positivists tried to explain all necessary truths in terms of their being analytic a priori. For various reasons, this doesn't at all work. But Kripke's approach to completeness proofs for modal logics via an accessibility relation on the space of possible worlds, plus his reflections on his own achievements, plus David Lewis' work on possible worlds, blessedly allow us to realize that necessity didn't need the logical positivists and return us to a pre-Kantian era of dogmatic metaphysics.
A New History Suggested by Kripke and Gödel:
One of the many interesting things coming out of Kripke's Naming and Necessity is the defense that there are necessary a posteriori claims. Given what analytic philosophers mean by these terms, these would be claims that are such that they can be justified by sensory experience, and not otherwise justifiable, yet such that it is not possible that they be false. For Kripke, since they are necessary they are true at all possible worlds accessible from the actual world. I am not going to get into the weeds of rigid designation here to explain his arguments (I think it's misleading anyhow, because once one realizes that Kripke and Kant are talking about the same thing, then one sees that most such cases don't involve rigid designation). Let us just note that a canonical example that Kripke gives is that water is H2O. We learn that it is true by empirical means, yet it is true in all possible worlds accessible from this one. A world where we might think it would be false would really be a world where there is just wet stuff that resembles water.
Back to Kant. For probably not surprising reasons, analytic philosophers have focused on Kant's two detailed characterizations of analyticity. Sometimes Kant uses a weird spatial metaphor, where an analytic claim is true if the predicate is somehow contained in the subject of the sentence. Sometimes analytic claims are presented as those such that it is logically contradictory to deny. The first view is too vague to be helpful. The latter view was made good on by analytic philosophers inventing modern logic, but the end result is either that almost nothing we thought was analytic ends up being analytic (since analytically true becomes "logically true" with our modern understanding of logic) or we lose our modern conception of logic. These failures end up being part of knocking down positivism.
Fine and good. But, weirdly, Kant's characterization of syntheticity is completely different from his characterization of analyticity. For Kant a claim is synthetic if one has to resort to intuition (empirical or pure) to justify the truth of the claim. His canonical discussion of 5 plus 7 in the Introduction to the Critique of Pure Reason makes this abundantly clear.
Remember that Kant is setting up the problem of synthetic a priori truths. So shouldn't we pay more attention to his characterization of syntheticity than his two characterizations of analyticity? But if we do this, then we see that by "synthetic" Kant just meant to be picking out what most of us today mean by "a posteriori."
This seems to cause a problem, because then Kant's discussion of what we call synthetic a priori propositions would be a discussion of a posteriori a priori propositions, which doesn't make any sense. Early analytic philosophers such as A.J. Ayer, for example in Language, Proof and Logic actually come pretty close to suggesting as such. But that interferes with the clarity of previous Whig history.
It's not a problem though. For if we turn to Kant's discussion of a priori truths in the very beginning of the Introduction to the Critique of Pure Reason, it is clear that what he's really concerned with their status as necessary truths. I'm not a Kant scholar, but as far as I can tell Kant took necessity to be both necessary and sufficient for a prioricity. And he interprets Hume showing that there is a problem with necessity, and motivates the book as an answer to this problem.
And this is why Kant wasn't talking about a posteriori a priori propositions. What Kant called "synthetic" is what we mean by a posteriori, but (at least for the purposes of his own project) what he called "a priori" is really what we mean by "necessary." So as long as we are using the locutions of analytic philosophers (and we should!) we should say that the Kantian problematic is the problem of necessary a posteriori truths. We should not say that he was concerned with synthetic a priori truths, because by the former we mean a semantic notion, where Kant meant an epistemic one, and by the latter we mean an epistemic notion, where Kant meant a logical/semantic one. Moreover the specific notions he meant much more closely track what we mean today by a posteriority and necessity.
What follows from this?
First, get off Kant's back about how logical positivists foundered on the analytic/synthetic distinction. It's not relevant. We all still talk about the a priori/a posteriori distinction, and necessity and possibility are in pretty good standing among analytic philosophers.
Second, Kant was right that many claims of natural science are synthetic a priori in his sense of "synthetic a priori." We learn about scientific laws and justify them via sensory experience. Nonetheless, they are necessary truths. This is what interested Kant and it's something still worth worrying about. Water = HsO gets you there, but it's a problem for any scientific law. One might claim that the water bit is metaphysically necessary and other scientific laws are necessary in some weaker sense (with respect to a more restricted set of possible worlds), but that doesn't negate Kant's basic insight.
Third, remember that, like all great philosophers, Kant himself constructed a Whig history leading up to him. Once we realize that he was concerned with the the necessary a posteriori we can adopt his Whig history in a similar way as classic analytic philosophy did. Remember that the null hypothesis Whig history sees Plato positing the forms because some claims (ethical, geometrical, etc.) are true of the world, yet such that our sensory experience of the world doesn't justify them. But perhaps Kant understood Plato differently. If the real issue concerns necessary a posteriori claims then Plato's problem was really we can only justify our knowledge of geometry and ethics and natural science via our experience of the world, yet our sensory experience doesn't justify the necessity of these claims. Plato then should be seen as extending what we sense, via our souls commingling with the forms in between earthly incarnations.
Fourth, I think, we can make much better sense of Kant's transcendental idealism in terms of the new Whig history. Kant's notion of "intuition" as discrete experience passively received can be understood as extending the notion of experience beyond the strictly sensory. Just as Plato posits the forms to explain how we could have a kind of quasi-sensory experience of mathematical and ethical reality which guarantee the necessity of such claims, Kant himself is helping us to have an experience of the constitution of our own minds, which guarantee the necessity of such claims. I should note that this understanding actually makes much better sense of Fichte's critique of Kant, because Fichte also viewed Kant in this way and in getting his students and readers to introspect he is simply extending what he took Kant to be doing. This also makes sense of why, early in the first Critique Kant argues that space and time are not only forms of intuitions but intuitions themselves. He's explaining how our judgments about space and time could be necessary a posteriori.
The debate between Descartes and Hobbes in the third set of objections to Descartes' Meditations circles around this very theme as well. Hobbes cannot make sense of Descartes' notion of an "idea" that includes sensory imagination as well as a kind of non-sensory mental perception of things like geometry. Descartes wrongly thinks this is just a semantic issue of how to use the word "idea." If we understand the problem of the first critique to be the problem of the necessary a posteriori, then it is clear that Kant is giving the response that Descartes should have given.
This leads to huge other issues with respect to the Bennett/Brandom claim that part of what is distinctive about Kant is that he characterizes concepts inferentially as opposed to the representationally, as Descartes did. And issues surrounding the myth of the given and the problem Kant tries to address in the Schematism (and the third critique as an attempt to patch that). But I think I've said enough here.
Finally, I just realized that I didn't bring Gödel in at all. Gödel's incompleteness theorems are usually taken to be one of the death blows to the claim that mathematical truths are analytic (in the modern sense of being true in virtue of meaning). But I think there's an epistemic undercurrent, since analyticity was supposed to overlap with (again, in the modern sense) a prioricity. One might change one's Whig history of the contemporary philosophy of mathematics as well, reading the upshot of the incompleteness theorems as a problem for the a prioricity of mathematical claims. This fits again very nicely into the Whig history in terms of the necessary a priori.
So, out of the ashes of positivism, we see that Kant was not only to a large extent right about the problem space facing the metaphysics of natural science, but with respect to mathematics too.