Approximate truth (Q580322)

Based on two intuitively motivated principles, an accuracy principle and an equivalence principle, the author first proves that no many-valued logic with truth functional implication and negation connectives can meet both of these principles. Then he starts to develop his own theory of approximate truth which formalizes the idea that something is approximately true iff something ``nearby'' is really true. Here, this ``nearby'' is made precise using variations of quantitative measurements of suitable objects. This idea works in an interesting way, but it is a nontrivial matter to find suitable generalizations of some very simple, commonly used inference schemata like modus ponens.