Application
Quine suggested an unnatural linguistic resolution to such logical antinomies, inspired by Bertrand Russell's Type theory and Tarski's work. His system would attach levels to a line of problematic expressions such as falsehood and denote. Entire sentences would use a higher hierarchy each of their parts'. The form "'Clause about falsehood0' yields falsehood1" will be grammatically correct, and "'Denoting0 phrase' denotes0 itself" – wrong.
George Boolos, inspired by his student Michael Ernst, has written that the sentence might be syntactically ambiguous, in using multiple quotation marks whose exact mate marks cannot be determined. He revised traditional quotation into a system where the length of outer pairs of so called q-marks of an expression is determined by the q-marks that appear inside the expression. This accounts not only for ordered quotes-within-quotes but also to, say, strings with an odd number of quotation marks.
In Gödel, Escher, Bach: An Eternal Golden Braid, author Douglas Hofstadter suggests that the Quine sentence in fact uses an indirect type of self-reference. He then shows that indirect self-reference is crucial in many of the proofs of Gödel's incompleteness theorems.
Read more about this topic: Quine's Paradox
Famous quotes containing the word application:
“I think that a young state, like a young virgin, should modestly stay at home, and wait the application of suitors for an alliance with her; and not run about offering her amity to all the world; and hazarding their refusal.... Our virgin is a jolly one; and tho at present not very rich, will in time be a great fortune, and where she has a favorable predisposition, it seems to me well worth cultivating.”
—Benjamin Franklin (1706–1790)
“The receipt to make a speaker, and an applauded one too, is short and easy.—Take of common sense quantum sufficit, add a little application to the rules and orders of the House, throw obvious thoughts in a new light, and make up the whole with a large quantity of purity, correctness, and elegancy of style.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“My business is stanching blood and feeding fainting men; my post the open field between the bullet and the hospital. I sometimes discuss the application of a compress or a wisp of hay under a broken limb, but not the bearing and merits of a political movement. I make gruel—not speeches; I write letters home for wounded soldiers, not political addresses.”
—Clara Barton (1821–1912)