It's time to face two problems that we sidestepped while exploring three-valued logical systems for vagueness.

Although the Sorites argument is valid in all of the systems we've presented, we claimed that the paradox can nevertheless be dissolved in three-valued logic because the Principle of Charity premise is not true on any reasonable interpretation. The first problem concerns the exact nature of the principle's nontruth. Our sample interpretations rendered the premise false in Bochvar's external system, which didn't sound right because its negation – which states that 1/8″ does make a difference – must then be true. However, the situation looked more promising in the other three systems, where the Principle of Charity and its negation were neither true nor false. But now let us recall that the Principle of Charity is so called by virtue of the colloquial reading, One-eighth of an inch doesn't make a difference. Put that way, the Principle of Charity seems true, or close to it, doesn't it? If you shrink a tall person by 1/8″, surely that person will still be tall. (If you disagree, change the shrinking to 1/100″ – we'll still get the paradox, but surely 1/100″ doesn't make a difference.) Three-valued accounts can avoid the paradox by claiming that the Principle of Charity is either false or neither true nor false, but that leaves another puzzle: why does the principle seem to be true?