Editing Quine's paradox (section)

== Application ==
Quine suggested an unnatural linguistic resolution to such logical [[antinomy|antinomies]], inspired by [[Bertrand Russell]]'s [[type theory]] and [[Alfred Tarski|Tarski]]'s work. His system would attach levels to a line of problematic expressions such as ''falsehood'' and ''denote''. Entire sentences would stand higher in the hierarchy than their parts. The form {{"'}}Clause about falsehood<sub>0</sub>' yields falsehood<sub>1</sub>" will be grammatically correct, and {{"'}}Denoting<sub>0</sub> phrase' denotes<sub>0</sub> itself" – wrong.<ref name="Quine1962"/>

[[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.<ref name="Boolos"/>

In [[Gödel, Escher, Bach|''Gödel, Escher, Bach: An Eternal Golden Braid'']], author [[Douglas Hofstadter]] suggests that the Quine sentence in fact uses an [[Indirect self-reference|indirect type of self-reference]]. He then shows that indirect self-reference is crucial in many of the proofs of [[Gödel's incompleteness theorems]].<ref name="Hofstadter"/>