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human
A level philosophy help: analytic a posteriori

I'm teaching A level philosophy, part-time, this year.  I don't have a first degree in philosophy, but I do have a masters andam completing my PhD.  Most of the material I considered in my masters was modern, and my PhD is very technical and niche, so I may be missing some basics.

We were looking at the distinctions analytical/synthetic, a priori/posteriori and necessary/contingent. I made the point that they varied in scope: logical/linguistic, epistemic and ontological respectively. I also wanted to get across the idea that they might not be co-extensive. In the discussion, we considered the sentence 'water is H20'   
Cut to the chase, I told them that this sentence was analytic but a posteriori, which to me (and Kripke) seems to be self-evident. When I went home, I found out that this was a somewhat controversial idea. The course textbook says that analytic a posteriori statements are impossible (yet puts forward Kant's rather more dubious synthetic a priori) and that this reflects a sort of consensus.

So my question really is, how am I supposed to explain to my students that the analytic a posteriori is impossible, when it seem obvious to me (and Kripke) that there are many examples of such statements?
gpt
As Kant formulates it, an analytic proposition is one whose predicate is contained in its subject, or in other words, it is definitionally true - "all bachelors are unmarried" is true by definition, and requires no experience to be true (other than the experience of learning the language, arguably, but that's not what we're discussing here).

Synthetic statements are those statements whose predicates are not contained in the subject, and are therefore not true merely by definition necessarily, and must relate to the world in some way. "All bachelors are happy" is a synthetic statement, it requires a relationship to the real world rather than a merely linguistic or logical relationship to be accurate.

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In order for an *analytic a posteriori* statement to exist, it would have to be something that is true logically or linguistically without requiring a relationship to the world itself in order to be true, but also require experience and therefore is contingent on something occurring in the world. This doesn't seem to make sense, which is Kant's position. If it's an analytic statement, it doesn't need to relate to the world at all, it is true by relation of the concepts itself - "all bachelors are unmarried." You don't need any experience or empirical data to show that to be true. However, if it were *a posteriori*, then you would need experience in order to verify it. This is why it is often ruled as paradoxical.

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However, if you consider "water is made of H2O," this requires testing to determine if it is really made of two hydrogen atoms and one oxygen atom, and not some other combination of particles. It is not true by-definition, it was found by experimentation and experience. So, it's synthetic, and a posteriori (you can't know if water is made of H2O *a priori*)