I am somewhat uncertain whether there is a definite factual question as to whether natural language handles truth-value gaps. Nor am I even quite sure that there is a definite question of fact as to whether natural language should be evaluated by the minimal fixed point or another, given the choice of a scheme for handling gaps. We are not at the moment searching for the correct scheme.
"Philosophical Troubles: Collected Papers". Book by Saul Kripke, 2011.
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