Editing Quine's paradox

{{Short description|Logical paradox concerning truth values}}
'''Quine's paradox''' is a [[paradox]] concerning [[truth value]]s, stated by [[Willard Van Orman Quine]].<ref name="Quine1962"/>  It is related to the [[liar paradox]] as a problem, and it purports to show that a sentence can be paradoxical even if it is not self-referring and does not use [[demonstrative]]s or [[indexicality|indexicals]] (i.e. it does not explicitly refer to itself). The paradox can be expressed as follows:

:"yields falsehood when preceded by its quotation" yields falsehood when preceded by its quotation.

If the paradox is not clear, consider each part of the above description of the paradox incrementally:

:it = ''yields falsehood when preceded by its quotation''
:its quotation = ''"yields falsehood when preceded by its quotation"''
:it preceded by its quotation = ''"yields falsehood when preceded by its quotation" yields falsehood when preceded by its quotation.''

With these tools, the description of the paradox may now be reconsidered; it can be seen to assert the following:
:The statement "''{{'}}yields falsehood when preceded by its quotation{{'}}'' yields falsehood when preceded by its quotation" is false.

In other words, the sentence implies that it is false, which is paradoxical—for if it is false, what it states is in fact true.

== Motivation ==
The [[liar paradox]] ("This sentence is false", or "The next sentence is true. The previous sentence is false") demonstrates essential difficulties in assigning a truth value even to simple sentences. Many philosophers attempting to explain the liar paradox – for examples see that article – concluded that the problem was with the use of [[demonstrative]] word "this" or its replacements.  Once we properly analyze this sort of [[self-reference]], according to those philosophers, the paradox no longer arises.

Quine's construction demonstrates that paradox of this kind arises independently of such direct self-reference, for, no [[lexeme]] of the sentence refers to the ''sentence,'' though Quine's sentence does contain a lexeme which refers to one of its ''parts''. Namely, "its" near the end of the sentence is a [[possessive pronoun]] whose antecedent is the very predicate in which it occurs. Thus, although Quine's sentence ''per se'' is not self-referring, it does contain a self-referring predicate.<ref name="Quine1987"/>

== 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"/>

== See also ==
* [[Grelling paradox]]
* [[List of paradoxes]]
* [[Quine (computing)]], a computer program that produces its [[source code]] as output
* [[Russell paradox]]
* [[Self-reference]]
* [[Yablo's paradox]]

==References==
{{reflist|refs=
<ref name="Boolos">{{cite book|last=Boolos|first=George|editor1-last=Leonardi|editor1-first=P|editor2-last=Santambrogio|editor2-first=M|title=On Quine: New Essays|year=1995|publisher=Cambridge University Press|pages=283–2296|isbn=978-0-521-47091-9}} Reprinted in {{cite book|last=Boolos|first=George|title=Logic, Logic and Logic|year=1998|publisher=Harvard University Press|isbn=0-674-53766-1|pages=392–405|chapter=Quotational Ambiguity}}</ref>
<ref name="Hofstadter">{{Cite book|last=Hofstadter|first=Douglas|year=1979|title=[[Gödel, Escher, Bach|Gödel, Escher, Bach: An Eternal Golden Braid]]|place=New York|publisher=Basic Books}}</ref>
<ref name="Quine1962">{{Cite journal|last=Quine|first=W.V.O|year=1962|title=Paradox|journal=Scientific American|volume=206|issue=4|page=84 |doi=10.1038/scientificamerican0462-84 |bibcode=1962SciAm.206d..84Q }} reprinted as {{Cite book|chapter=The Ways of Paradox|year=1966|title=The Ways of Paradox and Other Essays|place=Cambridge|publisher=Harvard University Press|pages=1–21|url=http://www.math.dartmouth.edu/~matc/Readers/HowManyAngels/Paradox.html}}</ref>
<ref name="Quine1987">{{Cite book
| publisher = Harvard University Press
| isbn = 0-674-74352-0
| last = Quine
| first = W. V. O.
| title = Quiddities: An Intermittently Philosophical Dictionary
| chapter = Paradoxes
| year = 1987
| pages = 145–149
}}</ref>
}}

==External links==
*{{cite IEP |url-id=par-liar |title="Liar Paradox"}}
*" "[https://www.jamesrmeyer.com/paradoxes/quine-paradox.html Logic and Language website]

{{Paradoxes}}

[[Category:Self-referential paradoxes]]
[[Category:Willard Van Orman Quine]]