The unprecedented success of LLMs in carrying out linguistic interactions disguises the fact that, on closer inspection, their knowledge of meaning and their inference abilities are still quite limited and different from human ones. They generate human-like texts, but still fall short of fully understanding them. I will refer to this as the “semantic gap” of LLMs. Some claim that this gap depends on the lack of grounding of text-only LLMs. I instead argue that the problem lies in the very typ...