Talk:Paradox

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193.203.83.xxx for which Newcomb that paradox stands for. The American astronomer? XJam [2002.03.26] 2 Tuesday (0)

Yes. He told the paradox to philosopher Robert Nozick, who introduced it to philosophers (with proper accreditation) in a 1963 essay called "Newcomb's Paradox and Two Principles of Choice." or some such.

There are various formulations given the name Control paradox.

One is the statement that "Man can never be free of control, for to be free of control is to be controlled by oneself".

External Links:

Half of the links in above list are either dead or online-shops are link farms. So what's the idea of this? Pjacobi 18:52, 15 Jul 2004 (UTC)

All paradoxes can be resolved. If there were an actual contradiction in the world, the world wouldn't exist (at least mathematically speaking) :-) AxelBoldt 02:09 Nov 11, 2002 (UTC)

Even the Liar paradox? I thought that one was a no-go.Cyan 07:40 Apr 12, 2003 (UTC)

I have a feeling that even the Liar paradox has a resolution in the real world, albeit a quantum one involving a superposition of lying and not-lying. -- Derek Ross

The liar paradox involves "pure states" that form a discrete set, whereas in quantum mechanics, my (completely non-expert) understanding is that the set of pure states is always continuous. Unless lying and not-lying can be embedded in some sort of continuous space, I find it implausible that QM could provide a resolution. (The question of observable quantities and appropriate measurements would also need to be resolved.) My feeling is that the liar paradox is a demonstration that some propositions of classical logic are non-Aristotelian, i.e. are neither true nor false. The existence of the liar paradox demonstrate the limits of classical logic in the same way the existence of Godel statements demonstrate the limits of formal systems of number theory. Cyan 06:33 Apr 21, 2003 (UTC)

I think the predestination paradox deserves to be listed separately from the grandfather paradox; although the examples used are similar, the point is different. The point of the predestination paradox is that the fact that you exist in the first place means that you are predestined to travel back in time and impregnate your great-great-grandmother. If you don't do it, you can't exist, so the fact that you do exist means that you must do it; you have no choice; it's going to happen. That idea is not present in the grandfather paradox. -- Shammack 17:59 Apr 20, 2003 (UTC)

From my reading of the grandfather paradox article, the predestination paradox isn't the topic at all. Only the line

"To avoid the getout of the time traveller being his own father, which would be possible genetically, though statistically unlikely, this would have to take place several months prior to his own conception."

suggests something like your "predestination paradox", and then only to state that it isn't the point of the article. So I think the predestination paradox does indeed need its own article. Go for it. Cyan 06:33 Apr 21, 2003 (UTC)

15/04/05 - for the grandfather paradox to work the killer has to exist, yet he can't. Since both these states MUST exist at the together surely there is a quantum solution? In which case the disruption of the time space continuum creates two universes and thus the time traveller travels to an alternate reality AS WELL AS time travelling in that reality. Travelling forward in time his grandfather would be dead, but then again he IS BORN in an alternate timeline!!!!!!

Isn't "Quin's Liar Paradox" the same as the normal "Liar Paradox"? user:J.J.

The difference is that Quine's is a predicate rather than a sentence. it is not itself false or true, butit yields falsehood when it is appended to its own quotation. That is:

(1)Yields falsehood when appended to its own quotation

is merely a predicate, which could be meaningfully applied to any expression. For example,

(2)"is a frog" yields falsehood when appended to its own quotation

is true, because

(3)"is a frog" is a frog

is false.The interesting case, of course, is whether the predicate is true of itself. what about:

(4) "Yields falsehood when appended to its own quotation" yields falsehood when appended to its own quotation.

Does it? Is 4 true or false?

I really want to separate the list of paradoxes into groups... Sociological/psychological paradoxes, Paradoxes of logical systems, Paradoxes of definition, Paradoxes of intuition, Paradoxes of physics, etc. The problem is that there are often no clear boundaries (especially counting paradoxes of intuition, which could be considered to contain everything). Yet some clearly fall into one group. Is this a meta-paradox? More importantly, is categorization possible? Paullusmagnus 22:11, 1 Oct 2003 (UTC)

Give it a shot. The people who care are watching this page. -- Cyan 22:14, 1 Oct 2003 (UTC)

And a fantastic job you have done! Before it was just a long list of paradoxes. Now it has structure and form in a way that allows one to grok the whole paradox space simultaneously. Good work Paullusmagnus (and Dandrake for finding a good structure to use)! Nanobug 02:46, 15 Oct 2003 (UTC)

Ditto! Cyan 03:02, 15 Oct 2003 (UTC)

Glad the Quine categories helped, but all credit for organizing the list goes to Paullusmagnus. I put in the Quine material because I thought it would be relevant, without thinking about using it to modify the list. This will remind me to be more diligent about reading the Talk pages before making changes. Meantime, organizing them this way made a real improvement.

However. When one organizes the entries rather than leaving their veridicality as an exercise for the reader, one will hit controversy. In this case I contend that the Monty Hell problem is falsidical, or at best an antinomy that's nearly two centuries out of date. The article now shows why this is, with an explanation that compensates for poor organization by running to excessive length.

In brief, we have here an argument that a function M(t), the money in the account, is non-zero at some point and increases monotonically, but is zero "at infinity". Not only monotonic, but strict. Not only increasing, but increasing without limit. Something is wrong, no?

Followups to Talk:Monty Hell problem. Dandrake 19:46, 15 Oct 2003 (UTC)

This article links to an article ethical paradox which it claims exists, but which apparently does not. ADMINS: was there ever such an article? Or is this a practical joke in this article?

Pakaran 19:51, 18 Oct 2003 (UTC)

It's probably just pre-emtive, waiting for someone to write the article. :-) Evercat 19:55, 18 Oct 2003 (UTC)

Ok thanks. Then there was no such article? Pakaran 19:59, 18 Oct 2003 (UTC)

Apparently not. There's no indication that it ever existed (and was deleted). Evercat 20:01, 18 Oct 2003 (UTC)

Ok thanks. I'm watching this article, and will write the ethical paradox article when I gather a few examples :) Pakaran 20:06, 18 Oct 2003 (UTC)

***** comment and question

01/14/04

The first line of this article is:

A paradox is an apparently true statement that seems to lead to a logical self-contradiction, or to a situation that contradicts common intuition

Why is a paradox "apparently true"? I intend to edit that first line to read "A paradox is a statement for which distinct, apparently valid modes of analysis lead to conflicting conclusions" unless there is some objection. Any better ideas?

***** end of comment

That is a MUCH MUCH better definition. Change it asap.

Here's a paradox that's bothered me ever since (believe it or not) I was eight years old:

Did time have a beginning?

If it did, then there must have been a moment before which there was no before. This is a paradox.

If it did not then the past is infinite, going back and back and back and never beginning at all. I'm not sure if that constitutes a paradox, but it makes my head spin.

Kant considers this in the (first) Critique, at B454 and following.

Comments? Lee M 04:29, 24 Jan 2004 (UTC)

From what I know, no one is really sure what time is, on a fundamental level. It's entirely possible that people's ways of thinking about and understanding time do not correspond to whatever feature of the universe it is that gives rise to the experience of time passing. Einstein's special relativity changed the way people thought about simultaneity; Stephen Hawking, if I recall correctly, once proposed that by treating time as an imaginary variable, one could formulate a model of the universe which was finite, but closed in such a fashion that there was no point at which time could be considered to have started. -- Cyan 06:07, 24 Jan 2004 (UTC)

Isn't Schrödinger's cat a scientific paradox? KRS 14:00, 9 Feb 2004 (UTC)

I believe that it's just an analogy to point out what's absurd about what goes on at the particle level. As soon as a particle is observed (interacts with anything else), it's wave function collapses, so the entire cat (or any collection of interacting particles) must have a real state. Paullusmagnus 23:15, 9 Feb 2004 (UTC)

Is Catch-22 an example of one of these types of paradoxes? Essentially, "to get out of the army, you have to be crazy. But if you want to get out of the army, you're clearly sane." The wiki entry on catch-22 refers to it as "circular logic," but doesn't that qualify under one or more of these categories? Elf 03:05, 10 Feb 2004 (UTC)

<Copied from user talk pages>

You <Paullusmagnus, that is> wrote:

"St. Petersburg isn't a paradox at all -- you have to assume that utility is proportional to quantity."

I thought so too, until I read the external link (http://plato.stanford.edu/entries/paradox-stpetersburg/) at the bottom of the St. Petersburg paradox page. It turns out that you can reformulate the problem by paying off in "utiles" (the unit for measuring utility) instead of dollars, so that the structure of the paradox remains unchanged (i.e. infinite expected payoff but unwillingness to make the bet). -- Cyan 22:23, 25 Feb 2004 (UTC)

That'll teach me to think that I understand a paradox. The external link is a great explanation, and I'm partial to the "utility limit" theory, myself. Seeing as the solution depends on what exactly "utility" is, do you think we should move it to the "Conditional paradoxes" section? Paullusmagnus 18:32, 26 Feb 2004 (UTC)

<end of copied text>

Sounds good to me. I'll do it. -- Cyan 18:44, 26 Feb 2004 (UTC)

Does this need to be locked? Pakaran . 02:57, 18 Mar 2004 (UTC)

OK, it seems we have an edit war over the jaw-droppingly trivial issue of whether the line "Paradoxx is a hard rock band" should be included at the end of the article. What I'd like to know is why anybody thinks this is an issue worth edit warring over? --Camembert

Why? Because the two warriors are engaged in continuous edit wars wherever the possibility presents itself. (It may well be argued that one of them is more to blame than the other, but this is not the place for setting the record straight on the matter.) Edit wars involving these two and wars involving one of them and some other person have occupied an unconscionable amount of Wikipedians' time for a few weeks, but the new conflict resolution procedures have not yet had the power to stop the nonsense. (Or had not, as of yesterday.) Sit back and wait; an improvement is likely soon; and be glad that this page is one of the minor victims of the wars. Dandrake 03:46, Mar 18, 2004 (UTC)

Yes, I'm well aware of the history (I'm on the arbitration committee). I was hoping for an answer from the involved parties themselves. On the one hand, Paradoxx being mentioned at the bottom of the page is quite unobtrusive; on the other, Paradoxx are a tremendously obscure band, and the chances of somebody looking for them and making this spelling mistake are probably very slim. So I was wondering why this was a matter of such burning importance that they have to edit war over it. --Camembert

Edit warriors get into edit wars as a matter of principle. The obscurity of the issue has nothing to do with it. -- Arvindn 07:54, 18 Mar 2004 (UTC)

I'm really hoping for a reply from the involved parties. --Camembert

Perhaps you should leave a message for them on their respective talk pages. -- Cyan 19:45, 18 Mar 2004 (UTC)

Contents

1 Ethical paradox

2 new pic

3 Perpetual motion machine

4 Quine

5 How is this called?

6 Removed from page

7 "Dollyknot's Paradox"

Ethical paradox

Shouldn't the ethical paradox be, "Love thy enemy" rather than, "Love thy neighbour"? I think it would clear things up as neighbours don't, on the whole, kill each other, and, "Love thy enemy" is the Christian commanmant.--[[User:HamYoyo|ك|هام يويو]] 09:45, Jul 15, 2004 (UTC)

new pic

I like the new pic lots better, hoorah! Sam [Spade (http://en.wikipedia.org/w/wiki.phtml?title=User_talk:Sam_Spade&action=edit&section=new)] 17:43, 15 Jul 2004 (UTC)

Perpetual motion machine

Is a ppm a good example of a paradox? It's just bad physics, there is nothing really paradoxical about it. Mark Richards 23:54, 15 Jul 2004 (UTC)

Most paradoxes are just bad math, so I'm not sure how certain ppms are so different. anthony (see warning)

Quine

Quine did distinguish three classes of paradox. If his distinction has been questioned, someone might insert a reference to the problem. Meanwhile, what on earth is gained by the weasel-wording of saying he believed in them, as if they were Santa Claus? It looks to me like a misguided attempt to follow the guidelines about sneaking in assertions as if they were facts, with phrases like "noted that"; but it's not such an assertion. If someone else made a different distinction, and it's any good, we ought to hear about it.

We may want, though to restructure the entire article, which is organized around this distinction.

I changed the footnote style to one that's widely used in scientific work. There's no standard at Wikipedia, but numeric footnotes are a really hopeless idea in a work that's subjcet to eternal revision and has no mechanism for automatic renumbering. Let's go to numeric footnotes when we chagne the Wikipedia format to LaTeX! Dandrake 19:02, Jul 16, 2004 (UTC)

How is this called?

1. All the sentences in this box are false.
2. Nothing Else Matters is the best ballad ever.

Sentence 1 can't be true, because it would imply itself to be false, which is a contraddiction. So it must be false.

If Sentence 2 were false, both sentences would be false, but this is not possible, because Sentence 1 would be true, which would be a contraddiction.

So the only possible truth values are FALSE - TRUE. Sentence 2 is true, and Nothing Else Matters is the best ballad ever, Q.E.D.

You could use this to prove anything, including obviously absurd sentences such as "I don't exist" or "4 is a prime number". You just need to replace Sentence 2 with anything.

I don't know how this is called, so I would not know how to title an article about it. If you know its name, create a new article with the appropriate title and move it there.

Well, it's equivalent to a simple variation on Curry's paradox. But it's also equivalent to simple variations on the liar paradox, and to stuff Russelll toyed with at the turn of the century. But it's a mug's game to generate new ones, so I very much doubt that the Nothing Else Matters version has a name. Call it the Hetfield paradox, maybe. Inceidentally, exactly that paradoxical proof method was used by Raymond Smullyan in What is the Name of This Book?, but I doubt he was the first.

Actually I just chose a random sentence. I read about that paradox somewhere, but I don't remember what sentence was used. --Army1987 21:52, 21 Jun 2005 (UTC)

Removed from page

The following text was removed:

Dollyknot's Paradox: A paradox is something that contradicts itself - therefore it is not a paradox.

The term "Dollyknot's Paradox" has zero Google hits except on this page, so this looks like an idiosyncratic term created here. Unless, of course, someone can provide evidence that this is a known paradox? -- The Anome 14:16, Nov 8, 2004 (UTC)

"Dollyknot's Paradox"

"Dollyknot's Paradox" doesn't, I'm afraid, make sense anyway. First, a paradox doesn't necessarily contradict itself; as the main article makes clear, many of the most famous and argued-over paradoxes contradict commonly held beliefs (as, for example, most of Zeno's paradoxes, the Twins paradox, etc.). Secondly, even if paradoxes were all self-contradictory, the consequent – "therefore it is not a paradox" – is a non sequitur.

I've re-organized the categories. As they stood there were at least two problems with them. (1) Sorting paradoxes into the veridical/falsidical lists presupposes determinate solutions which almost none of those have. Some of the other category headings and descriptins, such as conditional paradoxes, likewise made a number of claims about the paradoxes that were highly contentious. (E.g.: A great number of philosophers working today don't think that the problem of Theseus' ship is a problem of definition. They think it's a real (and deep) metaphysical problem. Sure, they're a lot of fools, but who is wikipedia to say so? Ditto the Sorites paradox, and a heap of others. It's not even widely agreed where the problem lies in many of the paradoxes that had already been sorted for "truth value". (2) The previous categories reflected (at least) two classification systems working at odds with one another. Some paradoxes were sorted by subject matter, others by veridicality. Imagine is I sorted sentences into four groups: (a) true ones (b) false ones (c) Those about mathematics and (d) Those that involve presuppositions. You can see the problem? Barring massive repetition on this page, it seems to me the simplest thing to do is to sort the paradoxes thematically, and leave all questions as to why they are paradoxes, and how to resolve them, to be discussed on the page for each individual paradox.

The "paradox of denial" seems to me to be more a play on words than a paradox. Two different connotations of the word "accept" are being used. First it asks how can one accept ("be satisfied with") oneself if one is unhappy with oneself. Then it asks how can one change if one does not accept ("have a realistic image") of oneself. I think many, many paradoxes could be generated along these lines. Is this some kind of joke? Who proposed this as a paradox?

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Ethical paradox

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