Repair by means of supervaluations Suppose I am uncertain about something (e.g., the exact threshold for ``Tall``) Suppose p is true regardless of how my uncertainty is resolved... Then I can conclude that p
Consider [[Tall(John) Tall(John)]] The yes/no threshold for ``Tall`` can be anywhere between 165 and 185cm. Where-ever the threshold is, there are only two possibilities: 1. [[Tall(John)]] = True. In this case [[Tall(John) Tall(John)]] = True. 2. [[Tall(John)]] = False. In this case [[ Tall(John)]] = True. Therefore [[Tall(John) Tall(John)]] = True. The formula must therefore be True.
Partial Logic + supervaluations Supervaluations enable Partial Logic to be ``almost Classical`` in its behaviour. How good is this as a model of vagueness? Like the Classical model that put the threshold at 185cm, the partial model makes a distinction that people could never make:
Partial Logic This time, we even have 2 such artificial boundaries: This still contradicts the Principle of Tolerance 185.001cm Tall Not tall Gap 165.001cm 184.999cm 164.999cm