Talk:Richard's paradox

message: A google search seems to prefer the name "Richard's paradox". --Brion 23:49 Oct 1, 2002 (UTC)
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I don't believe that anyone not previously familiar with this paradox would be able to follow this article.  I sure can't.  For example, this
:One example sentence would be "That positive real number whose square is two."
The sentence quoted is not a sentence.  Ortolan88
Probably the one who wrote above isn't a native English speaker (neither am I, anyway) and got confused between sentence and phrase.
I think the article use the word "sentence" in the technical sense...e.g. the phrase "red car" is a sentence because its "logical form" is "there exists and x such that x is red and x is a car"  Philosophy.dude (talk) 05:57, 21 July 2008 (UTC)
thread_title:  Pre-[http://en.wikipedia.org/w/index.php?title=Richard%27s_paradox&oldid=9461661 major-revision] comments 

message: The paradox is implying that the set of these phrases (let's call it P) is countable. If it is, then the "paradox" is quite obvious, as R is an uncountable set. 
If P isn't countable, then it makes no sense to say "the nth phrase" because doing so requires a mapping between N and P.
And it is by no means explained why couldn't P be uncountable.
I`m absolutely not mathematical, and maybe I`m just being dumb, but I don`t understand this:-
"Thus, if a number is Richardian, then the definition corresponding to that number is a property that the number itself has.
(More formally, "x is Richardian" is equivalent to "x does not have the property designated by the defining expression with which x is correlated in the serially ordered set of definitions".)"
Seems to be self-contradictory.
: You're right.  Thanks for the catch.  Typos usually aren't that bad, but they tend to be really nasty when you forget to use the word "not".  Heh.  Eric Herboso 01:05, 23 Jan 2005 (UTC)
replies: text: Also, the reason why the set P is definitely countable is because every element in P is a string of characters, and we order the set by putting each element with a lower amount of characters before any element with a higher amount; and for any two elements with the same number of characters, we order according to standard alphabetical order (including extra characters in the order as well).  If this isn't sufficiently clear in the article, feel free to more specifically address this issue there.  Hope this helps.  Eric Herboso 01:13, 23 Jan 2005 (UTC)
replies: text:  That's true if we explicitly require to use finitely long phrases. If we use infinitely long phrases, we can express any real number, for example the one for pi begins "the real number whose floor is three, whose first decimal digit is one, whose second decimal digit is four..." And in the article, nowhere is it stated that definition must be finite. --Army1987 22:06, 9 August 2005 (UTC)
replies: text:  I am confused, I hope. As to each phrase being finite, it does (now) say "Thus there is an infinite list of English phrases (such that each phrase is of finite length, but lengths vary in the list) that define real numbers unambiguously; ...". However, as you point out, a phrase of finite length cannot be used to point to "pi" (or to any list of random digits). So that it should be no surprise that the list of numbers that are within the range of this (countably!) infinite list cannot not be thought to be the set of all real numbers. Is this list complete or incomplete? If "it" is incomplete, it should not be a surprise that "it" can be added to. But which list, the old list or the old list + 1, should be considered the infinite list?  You would have to argue that after you have finished(!) adding all the possible "paradoxical" phrases to it, you could still construct a new number using this, or some other unspecified, method. I think.  ( Martin |  talk • contribs  11:36, 12 September 2015 (UTC)
thread_title:  Post-major-revision comments 

message: A substantial portion of this article appears to be taken from the book Gödel's Proof by Nagel & Newman (link goes to Amazon).  While there aren't any direct quotes, phrases such as "an essential but tacit assumption" appear in both, and are unlikely to have been developed independently.  I don't think it quite warrants blanking the article, but a serious rewrite and/or citations are needed.  I don't have time to work on it, though. Benandorsqueaks 23:55, 27 March 2006 (UTC)
replies: text: I was the one who wrote that substantial portion of the article.  I did use Nagel & Newman's book as a reference when rewriting this article, so this might explain my particular choice of phrases being similar to Nagel and Newman.  Indeed, the flow of the argument is also taken from Nagel and Newman, since I felt their order of presentation was very good for their discussion of Richard's paradox.  But I do not feel that there has been a copyright violation here, as the source material was merely used as a reference when rewriting the article due to its ideas on how to present Richard's paradox most efficiently and readably.  If such a use of reference were considered a copy vio, then when writing an article on calculus, you wouldn't be able to reference a calculus book's presentation flow, or when writing an article on history, you wouldn't be able to make the same points that some recent book you'd read had talked about.  Because I merely took the ideas from Nagel and Newman and used them to write the article, rather than quote from the text, I feel that this does not constitute a copyright violation.  Of course, I am no lawyer, so if someone who knows more on this disagrees with me, then they should say so on my talk page, and I will rewrite the appropriate sections.  — Eric Herboso 20:42, 3 April 2006 (UTC)
thread_title:  POSSIBLE COPYRIGHT VIOLATION (sorry about the caps, but it's important) 

message: For the original paradox by Jules Richard compare:
*J. Itard: Richard, Jules Antoine, Dictionary of Scientific Biography, 11, Charles Scribner's Sons, New York (1980) 413-414.
*Les principes des mathématiques et le problème des ensembles, Revue générale des sciences pures et appliquées 16 (1905) 541-543. 
*The principles of mathematics and the problem of sets (1905), englische Übersetzung in Jean van Heijenoort, "From Frege to Gödel - A Source Book in Mathematical Logic", 1879-1931. Harvard Univ. Press, 1967, p. 142-144.
*Lettre à Monsieur le rédacteur de la Revue Générale des Sciences, Acta Math. 30 (1906) 295-296.
* Jules Richard
217.94.215.52 07:26, 1 April 2007 (UTC)
replies: text: I'm afraid I'm not following you.  Are you saying that the explanation of his paradox is not the same in this article as the way he originally explained it?  If so, I agree with you.  But the explanation given here is far easier to understand, and is functionally equivalent to his original.  Furthermore, it is the version that is most popular in texts that are attempting to delve into the workings of the paradox (see Nagel & Newman's Godel's Proof).  A quicker version, of course, is the enigmatic: the smallest natural number without any interesting properties, which, after a moment's thought, is actually equivalent to Richard's paradox.  — Eric Herboso 17:10, 27 April 2007 (UTC)
thread_title:  The paradox described in this article is not Richard's paradox 

message: It's not clear in the description of the paradox what is an "arithmetical property". I also don't understand why do we speak about "arithmetical properties" and not just "properties" (which would make the paradox much harder to be solved).--Pokipsy76 20:21, 25 September 2007 (UTC)
thread_title:  Arithmetical properties ? 

message: Basically I interchanged the info in the articles about Richard and the paradox. The description of the paradox in the article about Richard was much the better than the description previously given here. I didn´t modify the text at all, just swapt the articles.Alterationx10 (talk) 19:41, 28 June 2008 (UTC)
thread_title: Changes

message: The 05:49, 20 September 2008 18.208.1.137 version of this article is translated into Chinese Wikipedia.--Wing (talk) 19:01, 20 September 2008 (UTC)
thread_title:  Translation into Chinese Wikipedia 

message: I'm not sure why this section introduces the concept of a number "fitting" its definition.  It's not used.--Antendren (talk) 04:37, 27 August 2011 (UTC)
thread_title:  "Fits" in Variation 

message: It helps to read the original. If you do, you'll realize that the article and this talk page reflect a number of misunderstandings.
  
You can also read it at [Les principes des Mathématiques et le problème des ensembles]. (Scroll the page down a little.) 
If your French is a little rusty (as is mine), use Google Translate. Don't worry about letters such as à, ç, è, é, ê, ô, ù, etc. Typing a, c, e, o, u respectively will be good enough. The translation won't be 100% correct either. But again, it will be good enough.  — Preceding unsigned comment added by 70.15.208.208 (talk) 23:10, 25 December 2014 (UTC)
thread_title:  The paradox as described by M.J. Richard himself in 1905 

message: I know, discuss the article, not the subject, etc. but one would suspect this connection would be pretty obvious to at least some reliable source.
181.115.8.39 (talk) 06:59, 23 December 2017 (UTC)
thread_title:  Isn't this just Cantor's diagonal in a really roundabout way? 

message: The paradox assumes some properties cannot be defined explicitly. Well, can they be defined and yet not-explicitly? Is not the purpose of a definition to distinguish an object from everything else? Either an object is defined or not defined. You make secondary the proper definition of "define": to set boundaries or limitations that distinguish an object from what is not that object. You declare subjectivity over definition and invite a whole host of errors.  — Preceding unsigned comment added by 174.250.64.218 (talk) 02:28, 20 March 2021 (UTC)
thread_title:  Who is anyone to say what can't be defined explicitly?