Arbitrary classes?

It is quite clear that syntactic classes like Nouns and Verbs are not like other classes like Stop Consonants. The main difference is that the members of Nouns and Verbs do not share any obvious overt features; at best (as Chomsky said, re-citing structuralists before him (ah! "Recite" probably comes from re - cite; to cite again! :) ) they can be slotted into similar structural positions. Ansgar in this lab showed that the leading and trailing edges can be treated as positional variables: if A1-X-C1 and A2-X-C2, where X is an arbitrary element, then people accept A1-X-C2 as valid. Presumably, under these circs., the As and the Cs are classified as beginnings and ends of strings; so any A-X-C string is treated as valid. But still, one can asK: can these categories of arbitrary tokens be used in other contexts? What if I now introduced a rule, "C-A". Would participants learn this rule? This question came up with Jean-Remy. He is trying (currently) to understand what goes into generalizing the (AB)^n and the AnBn "grammars" popularized by Hauser, Chomsky & Fitch. We wondered: could positionally defined (arbitrary) classes be used to learn a rule like AnBn? Turns out that Ansgar DID try to induce rules like C-A, after training participants with A-X-C. The result: NO generalizations! The positional variable remain tied to the positions! So here is one possible interpretation: maybe, the (human) mind is capable of creating categories with truly arbitrary members ONLY when such categories are innately specified, like Nouns and Verbs. Sounds like an easy-to-falsify hypothesis; being so darn strong @ first glance.