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:
“Some hours seem not to be occasion for any deed, but for resolves to draw breath in. We do not directly go about the execution of the purpose that thrills us, but shut our doors behind us and ramble with prepared mind, as if the half were already done. Our resolution is taking root or hold on the earth then, as seeds first send a shoot downward which is fed by their own albumen, ere they send one upward to the light.”
—Henry David Thoreau (1817–1862)
“The passions do very often give birth to others of a nature most contrary to their own. Thus avarice sometimes brings forth prodigality, and prodigality avarice; a man’s resolution is very often the effect of levity, and his boldness that of cowardice and fear.”
—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)