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 great many will find fault in the resolution that the negro shall be free and equal, because our equal not every human being can be; but free every human being has a right to be. He can only be equal in his rights.”
—Mrs. Chalkstone, U.S. suffragist. As quoted in History of Woman Suffrage, vol. 2, ch. 16, by Elizabeth Cady Stanton, Susan B. Anthony, and Matilda Joslyn Gage (1882)
“We often see malefactors, when they are led to execution, put on resolution and a contempt of death which, in truth, is nothing else but fearing to look it in the face—so that this pretended bravery may very truly be said to do the same good office to their mind that the blindfold does to their eyes.”
—François, Duc De La Rochefoucauld (1613–1680)
“The changes in our life must come from the impossibility to live otherwise than according to the demands of our conscience ... not from our mental resolution to try a new form of life.”
—Leo Tolstoy (1828–1910)