Vagueness, Rationality And Undecidability: A Theory Of Why There Is Vagueness

Vagueness is not undecidability, but undecidability does enter into an explanation of why there is vagueness. My theory, called the Undecidability Theory of Vagueness, explains vagueness largely as a result of the fact that we are computationally bound.1 Vagueness is not due to any particularly human weakness, but due to a weakness that any computationally bound agent possesses; even HAL from 2001: A Space Odyssey will probably experience vagueness. Furthermore, I will argue that vagueness is good for you. I will do so by showing that if you were a computationally bound, rational alien agent given the task of figuring out what our natural language predicates mean, you would very probably end up with vagueness. That is, unless two highly plausible hypotheses are false, it would be rational for you—i.e., in your best interest—to choose concepts in such a way that they are vague. Given that you are computationally bound, avoiding vagueness brings in greater costs than accepting it. ∗This paper appeared in Synthese 120, pp. 345–374, 1999. †Current address of correspondence can be obtained at http://www.changizi.com, or by contacting [email protected] Very early ideas of mine along these lines appeared in Changizi ([Cha95]). A paper on my theory was presented at the 1998 vagueness conference in Bled, Slovenia (Changizi, [Cha99b]), and at the 1998 Irish Conference on Formal Methods (Changizi, [Cha99a]). The latter concentrates on logics and semantics of vagueness motivated by the Undecidability Theory of Vagueness.