Ordinary language, which uses symbolic conventions and associations which are often not logical, inherently contains many fuzzy concepts - "knowing what you mean" in this case depends on knowing the context or being familiar with the way in which a term is normally used, or what it is associated with.
But even using ordinary set theory and binary logic to reason something out, logicians have discovered that it is possible to generate statements which are logically speaking not completely true or imply a paradox,[REF] even although in other respects they conform to logical rules.