Talk:Quine's paradox

A View From Computer Science

Quine's Paradox is closely related to the halting problem, a fundamental result from computer science. I think it may clear things up a bit about the self reference is one realizes that it is not so much the presence of self-reference in a language that leads to this kind of paradox, but the meaning of the operation that is being defined.

If I told you that from this point on, "Do the opposite of what you were told," what would you then do if at some point in the series of commands I told you to "Do the opposite of what you were told." You would start doing what I literally told you again right?

But what if I told you to "If I tell you 'Do the opposite of what you were told' then do the opposite of what you were told." There is no self-reference in this sentence, if you do not believe me then rephrase the 'Do the opposite of what you were told' to be some other sentence that means the same thing, like 'Do something contradictory to what I tell you.'

In other words, it isn't the exact self reference in the language or words of the language, but it is in the semantics. The words 'Do the opposite of what you were told' once heard and understood and then applied to another command that once understood means the same thing leads to an infinite loop.

It is possible to do this on a computer without self reference in the text of a computer program, however the meaning of the program would basically be instructions on how to build an infinite loop or recursion from the various parts.

At least, I think that is what Quine was trying to get at. Ridding a language of direct self-reference would not get rid of these sorts of problems because it is always possible for some other part of the language to piece together some other aspects of the language in ways that cause them to reference each other.

One could say that the quotation of a sentence "compiles" into a predicate for that sentence.

--74.194.27.5 (talk) 08:04, 5 December 2007 (UTC)

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)

Just a side note--if you look in Quine's lead essay in The Ways of Paradox and Other Essays, the paradox is not taken to show that paradox still exists after eliminating all self-reference (at least, not at first). Rather, it is taken to show that a certain strategy for solving the Liar will not extend to all paradoxes. The strategy is one where 'This sentence' in the Liar is substituted with a name for the Quine-sentence. This is supposed to result in an equivalent sentence to the Liar, viz., ' 'This sentence is false' is false.' But Quine notes that with his paradox, you can't perform such a substitution. That's because the Quine-sentence does not contain a demonstrative (or any other lexeme) that refers to the Quine sentence. So trivially, there's no substituting such a lexeme with a name for the Quine-sentence.Tsparent 19:28, 21 June 2007 (UTC)

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)

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)

Actually, the Quine sentence is a bit different from your Manchester sentence. That's because the Manchester sentence does not refer to any part of the Manchester sentence. Rather, the Manchester sentence contains a name for a self-referring predicate. And to contain a name for a self-referring predicate is not to contain a self-referring predicate per se. As a parallel case, the sentence ' "water" is a word' does not contain the word "water." Rather, it contains a name for that word, viz. ' "water" '

Also, it is worth noting the the Quine-sentence entails something about the Quine-sentence itself, even though it contains no particle that refers to the Quine-sentence. So weirdly, the Quine-sentence does not refer to itself (i.e. the Quine sentence) even though in terms of its logic, the Quine-sentence is about the Quine-sentence.Tsparent 19:28, 21 June 2007 (UTC)

I agree with Dan. It's self-referential because it refers quite explicitly to its own quotation - it refers to its own citation. How is that not self-referential? Matt2h

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)

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)

Article title capitaliztion

Why "Quine's Paradox" and not "Quine's paradox"? -- Dominus 09:53, 19 November 2006 (UTC)

Reference

I am having trouble in finding a reference on "Quine's Paradox" as mentioned in this article other than GEB (and articles citing it or this wiki page), so that is probably a name coined by the author of GEB. It seems that there is another paradox in philosophy that is called "Quine's Paradox". If you know any sources other than GEB (or articles citing GEB or this wiki page as reference) for calling that sentence Quine's Paradox, please add it to the article, otherwise this article is missing citations. 128.100.3.41 (talk) 23:28, 4 November 2010 (UTC)