Talk:Quine's Paradox
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[edit] Self-Reference
i don't see how this "demonstrates that eliminating such direct self-reference is insufficient to resolve the paradox" - it didn't eliminate anything! "'blah when preceded by its quotation' blah when preceded by its quotation" is only a fancy way of saying 'this sentence' by specifying its parts and their order instead of directly addressing it. it removes the phrase 'this sentence', but not the meaning or the self-reference. and i know my own views aren't valid for a wiki article, but they're still valid for a discussion of it. and besides, this doesn't give any sources anyway. --dan 18:22, 4 July 2006 (UTC)
- While you are right that the two formulations are logically equivalent, they are not syntactically equivalent. The same can be said for the pair of sentences: "The following sentence is true. The preceding sentence is false." Or even a thousand sentences, the first 999 being "The following sentence is true." and the last one being "The first sentence is false." None of these constructions has the syntactic equivalent of one sentence whose subject is "this sentence". But logically they are all the same.
- I think the hope was at one time that if this direct self reference (constructions having the syntactic equivalent of one sentence whose subject is "this sentence") were deemed an invalid construction, and was thus "forbidden", then this type of paradox would not occur. Turns out that hope was not realized.
- Yes, your views are more than welcome on the Talk page. And I do believe the Hofstadter book referenced herein does give a good overview (and itself has prolific citations) of this direct/indirect distinction.
- Baccyak4H 14:38, 7 September 2006 (UTC)
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- it didn't remove self reference at all, though, is my point. i see what you're saying about "the following sentence is true" etc, but quine's paradox still only uses one sentence, albeit a more grammatically complex one than "this sentence is false". instead of referencing the entire sentence, it references a part of itself. is it self-reference when i'm talking about my own arm? i'd say so. --dan 02:46, 16 October 2006 (UTC)
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- It has to be there, somehow, otherwise no paradox. But its construction is syntactically different. In this sense: "This sentence is false" refers directly to itself. But Quine's only refers directly to a curious predicate, in the same way that "'yields falsehood when preceded by its quotation' should be Manchester United's new motto" does. And see the discussion here. Baccyak4H 18:27, 16 October 2006 (UTC)
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[edit] Related paradox?
Would this paradox be related to the one arrived at if you say 'Nothing is impossible'? (If nothing is impossible, then being impossible is impossible. It's similar if you say nothing is certain.) Also, does this paradox have a name (or is it even a paradox)? MagiMaster 08:29, 11 July 2006 (UTC)
- They are related; deep down this, your statement, and many other paradoxes are just fancy elaborations on the Liar's Paradox: "This statement is false." Although (POV warning) Quine's is my favorite version. Baccyak4H 14:22, 7 September 2006 (UTC)
[edit] Hofstadter
since someone mentioned Hofstadter's use of it -- it's been awhile, but as i remember, he actually calls those sorts of phrases that do strange things when quoting themselves 'Quines'. anyone with the book handy want to check on that? it'd make a nice bit of trivia and show that people actually care about this stuff. --dan 08:57, 10 August 2006 (UTC)
- It looks like the Hofstadter stuff was removed, not sure why.
- I haven't read it in a while, but I recall he called the process itself "Quining", or "arithmoquining" in the case of the analogous process in typographical number theory (in the spirit of Gödel). He then played with the quote fragments, going from nonsensical ("'I like chocolate' I like chocolate." - my example, not his), to actually true ("'is a sentence fragment' is a sentence fragment."), to the subject of this article.
- I think I will revert at least a reference to his usage, since it was used to help demystify a very deep and important result of mathematical logic.
- Baccyak4H 14:17, 7 September 2006 (UTC)
[edit] Article title capitaliztion
Why "Quine's Paradox" and not "Quine's paradox"? -- Dominus 09:53, 19 November 2006 (UTC)
