Quine's paradox is a paradox concerning truth values, attributed to W.V.O. Quine. 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, we may now reconsider the description of the paradox. 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.

While certain semantics of this observation are valid, the theory itself is incorrect. The above mentioned sentence in it's entirety doesn't evaluate to false. It simply states that the latter portion is false in a certain lexical context. To make that above mentioned statement doesn't imply self-contradiction, nor does it imply paradox of any kind. Quine's Paradox is thus invalid. A statement cannot be paradoxical without deixis or indexicality. This is a basic property of linguistics and the formation of statements. As a lexicon a statement is like an object which cannot declare itself void of value or truth without being self aware (using indexicality). The statement, "Never say 'never.'", although at first glance appears to be self-contradictory, is again not. It is a correct statement, and if followed, the rule "Never say 'never'" would take effect at the close of the statement.

Contents 1 Motivation 2 Application 3 See also 4 Bibliography

[edit] 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, concluded that the problem was with the word "this". Once we properly understand this sort of self-reference, they claimed, the paradox no longer arises.

Quine's construction demonstrates that paradox of this kind arises independently of such direct self-reference. In fact, there is no way to eliminate the paradoxes short of a severe crippling of the language. Any system, such as English, that contains entities such as words or sentences that can be used to apply to themselves, must contain this type of paradox.

[edit] Application

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 the proofs of Gödel's incompleteness theorems.

[edit] See also

• Grelling paradox
• Russell paradox
• List of paradoxes

[edit] Bibliography

• Hofstadter, Douglas. (1979) Gödel, Escher, Bach: An Eternal Golden Braid New York: Basic Books.

• Quine, W. V. O. (1962) "The Ways of Paradox" reprinted in Quine (1966) The Ways of Paradox and Other Essays Cambridge: Harvard Univ. Press. pp. 1-21.