# Quine's paradox > Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Quine's_paradox > Markdown URL: https://mediated.wiki/source/Quine's_paradox.md > Source: https://en.wikipedia.org/wiki/Quine's_paradox > Source revision: 1342778228 > License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) Logical paradox concerning truth values Not to be confused with [Quine (computing)](/source/Quine_(computing)). **Quine's paradox** is a [paradox](/source/Paradox) concerning [truth values](/source/Truth_value), stated by [Willard Van Orman Quine](/source/Willard_Van_Orman_Quine).[1] It is related to the [liar paradox](/source/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 [demonstratives](/source/Demonstrative) or [indexicals](/source/Indexicality) (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](/source/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](/source/Demonstrative) word "this" or its replacements. Once we properly analyze this sort of [self-reference](/source/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](/source/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](/source/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.[2] ## Application Quine suggested an unnatural linguistic resolution to such logical [antinomies](/source/Antinomy), inspired by [Bertrand Russell](/source/Bertrand_Russell)'s [type theory](/source/Type_theory) and [Tarski](/source/Alfred_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 falsehood0' yields falsehood1" will be grammatically correct, and "'Denoting0 phrase' denotes0 itself" – wrong.[1] [George Boolos](/source/George_Boolos), inspired by his student Michael Ernst, has written that the sentence might be [syntactically ambiguous](/source/Syntactically_ambiguous), in using multiple [quotation marks](/source/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.[3] In [*Gödel, Escher, Bach: An Eternal Golden Braid*](/source/G%C3%B6del%2C_Escher%2C_Bach), author [Douglas Hofstadter](/source/Douglas_Hofstadter) suggests that the Quine sentence in fact uses an [indirect type of self-reference](/source/Indirect_self-reference). He then shows that indirect self-reference is crucial in many of the proofs of [Gödel's incompleteness theorems](/source/G%C3%B6del's_incompleteness_theorems).[4] ## See also - [Grelling paradox](/source/Grelling_paradox) - [List of paradoxes](/source/List_of_paradoxes) - [Quine (computing)](/source/Quine_(computing)), a computer program that produces its [source code](/source/Source_code) as output - [Russell paradox](/source/Russell_paradox) - [Self-reference](/source/Self-reference) - [Yablo's paradox](/source/Yablo's_paradox) ## References 1. ^ [***a***](#cite_ref-Quine1962_1-0) [***b***](#cite_ref-Quine1962_1-1) Quine, W.V.O (1962). "Paradox". *Scientific American*. **206** (4): 84. [Bibcode](/source/Bibcode_(identifier)):[1962SciAm.206d..84Q](https://ui.adsabs.harvard.edu/abs/1962SciAm.206d..84Q). [doi](/source/Doi_(identifier)):[10.1038/scientificamerican0462-84](https://doi.org/10.1038%2Fscientificamerican0462-84). reprinted as "The Ways of Paradox". [*The Ways of Paradox and Other Essays*](http://www.math.dartmouth.edu/~matc/Readers/HowManyAngels/Paradox.html). Cambridge: Harvard University Press. 1966. pp. 1–21. 1. **[^](#cite_ref-Quine1987_2-0)** Quine, W. V. O. (1987). "Paradoxes". *Quiddities: An Intermittently Philosophical Dictionary*. Harvard University Press. pp. 145–149. [ISBN](/source/ISBN_(identifier)) [0-674-74352-0](https://en.wikipedia.org/wiki/Special:BookSources/0-674-74352-0). 1. **[^](#cite_ref-Boolos_3-0)** Boolos, George (1995). Leonardi, P; Santambrogio, M (eds.). *On Quine: New Essays*. Cambridge University Press. pp. 283–2296. [ISBN](/source/ISBN_(identifier)) [978-0-521-47091-9](https://en.wikipedia.org/wiki/Special:BookSources/978-0-521-47091-9). Reprinted in Boolos, George (1998). "Quotational Ambiguity". *Logic, Logic and Logic*. Harvard University Press. pp. 392–405. [ISBN](/source/ISBN_(identifier)) [0-674-53766-1](https://en.wikipedia.org/wiki/Special:BookSources/0-674-53766-1). 1. **[^](#cite_ref-Hofstadter_4-0)** Hofstadter, Douglas (1979). *[Gödel, Escher, Bach: An Eternal Golden Braid](/source/G%C3%B6del%2C_Escher%2C_Bach)*. New York: Basic Books. ## External links - Fieser, James; Dowden, Bradley (eds.). [""Liar Paradox""](https://iep.utm.edu/par-liar). *[Internet Encyclopedia of Philosophy](/source/Internet_Encyclopedia_of_Philosophy)*. [ISSN](/source/ISSN_(identifier)) [2161-0002](https://search.worldcat.org/issn/2161-0002). [OCLC](/source/OCLC_(identifier)) [37741658](https://search.worldcat.org/oclc/37741658). - " "[Logic and Language website](https://www.jamesrmeyer.com/paradoxes/quine-paradox.html) v t e Paradoxes Philosophical Analysis Buridan's bridge Dream argument Epicurean Fiction Fitch's knowability Free will Goodman's Hedonism Liberal Meno's Mere addition Moore's Nihilism Omnipotence Preface Rule-following Sorites Theseus' ship White horse Zeno's Logical Barber Berry Bhartrhari's Burali-Forti Court Crocodile Curry's Epimenides Free choice paradox Grelling–Nelson Kleene–Rosser Liar Card No-no Pinocchio Quine's Yablo's Opposite Day Paradoxes of set theory Richard's Russell's Socratic Temperature paradox Barbershop Catch-22 Chicken or the egg Drinker Entailment Lottery Plato's beard Raven Ross's Unexpected hanging "What the Tortoise Said to Achilles" Heat death paradox Olbers's paradox Economic Allais Antitrust Arrow information Bertrand Braess' Competition Income and fertility Downs–Thomson Easterlin Edgeworth Ellsberg European Gibson's Giffen good Icarus Jevons Leontief Lerner Lucas Mandeville's Mayfield's Metzler Plenty Productivity Prosperity Scitovsky Service recovery Siegel's St. Petersburg Thrift Toil Tullock Value Decision theory Abilene Apportionment Alabama New states Population Arrow's Buridan's ass Chainstore Decision-making Downs Ellsberg Fenno's Fredkin's Green Hedgehog's Inventor's Kavka's toxin puzzle Morton's fork Navigation Newcomb's Parrondo's Preparedness Prevention Prisoner's dilemma Sleeping Beauty Tolerance Two envelopes Willpower Veridical Birthday Boy or girl Condorcet Hilbert's paradox of the Grand Hotel Monty Hall Three prisoners List Category --- Adapted from the Wikipedia article [Quine's paradox](https://en.wikipedia.org/wiki/Quine's_paradox) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Quine's_paradox?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.