Indeterminate

From Logic

A reason for postulating a third truth-value 'indeterminate' is the problem of vagueness. Vagueness exists in the real world, because the real world is not a set of discrete catergories - it is a continuum. Therefore, attempts to apply deductive logic to the real world are always as imperfect as attempts to apply geometrical patterns like squares and circles to a world filled with ovals and rectangles.

Consider a color spectrum between red and orange. Let us also call the statement, 'It is red here', 'p'. Now, it is obvious that there are "clear enough" cases where 'p' is true (the red case) and "clear enough" cases where 'p' is false (the orange case). However, between the two extremes there seems to be a large class of colors where we just cannot say whether 'p' is true or false. Hence, some have suggested that in such cases 'p' is neither true nor false and that a third truth-value — indeterminate — is needed. Such a suggestion would rule out bivalence but retain the law of excluded middle. The best book on this distinction and the problem of vagueness is Timothy Williamson's book Vagueness.