The Geometry of Semantic Opposition Why Distributional Embeddings Resist Abstract Antonym Detection

We present a systematic investigation into why antonym detection fails for abstract semantic axes in 50-dimensional GloVe embeddings, whereas it succeeds for concrete physical axes. Through five experiments (Experiments 19-23), we establish that the failure is not caused by insufficient dimensions, insufficient training, incorrect opposition logic, or axis definition errors. It is caused by the distributional training objective itself: co-occurrence-based training pushes abstract antonym pairs together in embedding space, because abstract antonyms appear in nearly identical linguistic contexts. We document the Gram matrix of the 13 KAIA semantic axes, confirming that moral and truth are 74.4% similar in GloVe space (nearly the same direction), and that valence, moral, truth, and social form a dense evaluative cluster. We show that this structure is not E8-symmetric (all residuals 24-40°) and that contrastive fine-tuning collapses all negative poles into a single region. The finding is definitive: the ceiling is a property of distributional training objectives, not of embedding dimensionality or axis design.