Resolution
The Berry paradox as formulated above arises because of systematic ambiguity in the word "definable". In other formulations of the Berry paradox, such as one that instead reads: "...not nameable in less..." the term "nameable" is also one that has this systematic ambiguity. Terms of this kind give rise to vicious circle fallacies. Other terms with this type of ambiguity are: satisfiable, true, false, function, property, class, relation, cardinal, and ordinal. To resolve one of these paradoxes means to pinpoint exactly where our use of language went wrong and to provide restrictions on the use of language which may avoid them.
This family of paradoxes can be resolved by incorporating stratifications of meaning in language. Terms with systematic ambiguity may be written with subscripts denoting that one level of meaning is considered a higher priority than another in their interpretation. "The number not nameable0 in less than eleven words" may be nameable1 in less than eleven words under this scheme.
Read more about this topic: Berry Paradox
Famous quotes containing the word resolution:
“[A]s I am pretty well acquainted by great Opportunities with the Nature of Man, and know of a Truth, that all Men fight against their Will, the Danger vanishes, and Resolution rises upon this Subject. For this Reason I shall talk very freely on a Custom which all Men wish exploded, tho’ no Man has Courage enough to resist it.”
—Richard Steele (1672–1729)
“I had crossed de line of which I had so long been dreaming. I was free; but dere was no one to welcome me to de land of freedom. I was a stranger in a strange land, and my home after all was down in de old cabin quarter, wid de ole folks, and my brudders and sisters. But to dis solemn resolution I came; I was free, and dey should be free also; I would make a home for dem in de North, and de Lord helping me, I would bring dem all dere.”
—Harriet Tubman (c. 1820–1913)
“Compared to football, baseball is almost an Oriental game, minimizing individual stardom, requiring a wide range of aggressive and defensive skills, and filled with long periods of inaction and irresolution. It has no time limitations. Football, on the other hand, has immediate goals, resolution on every single play, and a lot of violence—itself a highlight. It has clearly distinguishable hierarchies: heroes and drones.”
—Jerry Mander, U.S. advertising executive, author. Four Arguments for the Elimination of Television, ch. 15, Morrow (1978)