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:
“We have been here over forty years, a longer period than the children of Israel wandered through the wilderness, coming to this Capitol pleading for this recognition of the principle that the Government derives its just powers from the consent of the governed. Mr. Chairman, we ask that you report our resolution favorably if you can but unfavorably if you must; that you report one way or the other, so that the Senate may have the chance to consider it.”
—Anna Howard Shaw (1847–1919)
“Unfortunately, many things have been omitted which should have been recorded in our journal; for though we made it a rule to set down all our experiences therein, yet such a resolution is very hard to keep, for the important experience rarely allows us to remember such obligations, and so indifferent things get recorded, while that is frequently neglected. It is not easy to write in a journal what interests us at any time, because to write it is not what interests us.”
—Henry David Thoreau (1817–1862)
“It is a part of the American character to consider nothing as desperate; to surmount every difficulty by resolution and contrivance.”
—Thomas Jefferson (1743–1826)