Formal proof that Raven matrices have no unique solution without assuming a transformation grammar — feedback welcome
I'm an independent researcher (CNC machinist by trade, no academic affiliation) who encountered intelligence test items and noticed that the uniqueness of the expected answer was assumed rather than demonstrated.
I wrote a short paper that formalizes this via Lagrange interpolation for numerical sequences, and extends it to Raven matrices with a conditional uniqueness theorem. The main result is that every distractor in a multiple-choice Raven item corresponds to a logically valid completion under some rule outside the standard grammar.
I'm aware that the non-uniqueness of numerical sequences has been noted before — Sternberg and others have made the observation at a conceptual level, and the broader philosophical problem connects to Goodman's new riddle of induction and Quine's underdetermination. What I don't find in the literature is a compact formal proof via Lagrange interpolation applied to psychometric items, nor a rigorous extension of the same argument to Raven matrices with an explicit grammar-based conditional uniqueness result and a distractor corollary. If I've missed something, I'd genuinely like to know.
I'm not claiming tests are useless, the argument is narrower than that. Looking for feedback, especially from anyone who knows this literature better than I do.