fbpx
Wikipedia

Quine's paradox

Quine's paradox is a paradox concerning truth values, stated by Willard Van Orman Quine.[1] 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 demonstratives or 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 edit

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.[2]

Application edit

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 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, 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.[3]

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.[4]

See also edit

References edit

  1. ^ a b Quine, W.V.O (1962). "Paradox". Scientific American. 206 (4): 84. Bibcode:1962SciAm.206d..84Q. doi:10.1038/scientificamerican0462-84. reprinted as "The Ways of Paradox". The Ways of Paradox and Other Essays. Cambridge: Harvard University Press. 1966. pp. 1–21.
  2. ^ Quine, W. V. O. (1987). "Paradoxes". Quiddities: An Intermittently Philosophical Dictionary. Harvard University Press. pp. 145–149. ISBN 0-674-74352-0.
  3. ^ Boolos, George (1995). Leonardi, P; Santambrogio, M (eds.). On Quine: New Essays. Cambridge University Press. pp. 283–2296. ISBN 978-0-521-47091-9. Reprinted in Boolos, George (1998). "Quotational Ambiguity". Logic, Logic and Logic. Harvard University Press. pp. 392–405. ISBN 0-674-53766-1.
  4. ^ Hofstadter, Douglas (1979). Gödel, Escher, Bach: An Eternal Golden Braid. New York: Basic Books.

External links edit

quine, paradox, paradox, concerning, truth, values, stated, willard, orman, quine, related, liar, paradox, problem, purports, show, that, sentence, paradoxical, even, self, referring, does, demonstratives, indexicals, does, explicitly, refer, itself, paradox, . Quine s paradox is a paradox concerning truth values stated by Willard Van Orman Quine 1 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 demonstratives or 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 Contents 1 Motivation 2 Application 3 See also 4 References 5 External linksMotivation editThe 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 2 Application editQuine 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 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 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 3 In Godel 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 Godel s incompleteness theorems 4 See also editGrelling paradox List of paradoxes Quine a computer program that produces its source code as output Self reference Russell paradox Yablo s paradoxReferences edit a b Quine W V O 1962 Paradox Scientific American 206 4 84 Bibcode 1962SciAm 206d 84Q doi 10 1038 scientificamerican0462 84 reprinted as The Ways of Paradox The Ways of Paradox and Other Essays Cambridge Harvard University Press 1966 pp 1 21 Quine W V O 1987 Paradoxes Quiddities An Intermittently Philosophical Dictionary Harvard University Press pp 145 149 ISBN 0 674 74352 0 Boolos George 1995 Leonardi P Santambrogio M eds On Quine New Essays Cambridge University Press pp 283 2296 ISBN 978 0 521 47091 9 Reprinted in Boolos George 1998 Quotational Ambiguity Logic Logic and Logic Harvard University Press pp 392 405 ISBN 0 674 53766 1 Hofstadter Douglas 1979 Godel Escher Bach An Eternal Golden Braid New York Basic Books External links edit Liar Paradox Internet Encyclopedia of Philosophy Logic and Language website Retrieved from https en wikipedia org w index php title Quine 27s paradox amp oldid 1142303897, wikipedia, wiki, book, books, library,

article

, read, download, free, free download, mp3, video, mp4, 3gp, jpg, jpeg, gif, png, picture, music, song, movie, book, game, games.