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:
“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)
“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)
“Had I been less resolved to work, I would perhaps had made an effort to begin immediately. But since my resolution was formal and before twenty four hours, in the empty slots of the next day where everything fit so nicely because I was not yet there, it was better not to choose a night at which I was not well-disposed for a debut to which the following days proved, alas, no more propitious.... Unfortunately, the following day was not the exterior and vast day which I had feverishly awaited.”
—Marcel Proust (1871–1922)