The massive and rapid leaps forward in the development in large language models (LLMs) have been matched by an equally massive and rapid increase in their commercial deployment. The current architecture of such LLM-type AIs suffers from a principled inability to distinguish between things that are merely accidentally not said (perhaps because they are not pertinent to the topic) and things that interlocutors are or should be intentionally silent about. We diagnose this failure to be the source of a variety of (severe) harms caused by AI in the past and present, and anticipated for the future. The LLM industry reacts to any of these problems with a "more data" strategy, resulting in some superficial success. This is veneer over a rotten core. The real problem is that the logic the LLMs are built on is too coarse-grained. We draw together recent research in a variety of different areas in logic and semantics (three-valued free logics and their proof-theory, bounds semantics, discourse representation, question-under-discussion framework, semantics for monstrous contents) to show how to build a better logical foundation that can handle deliberate silences in a contextually sensitive manner.