Talk:List of paradoxes

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This article is a fork of material originally contained in the article Paradox. --Jeffrey O. Gustafson - Shazaam! - <*> 03:05, 31 December 2005 (UTC)

Hey, please remove items in the article that do not belong - that are not paradoxes or paradoxical. The "Monty Hall Problem", for example, is not a paradox. It is not understood as one for those familiar with the problem, and it clearly does not fit the definition as stated in this Wikipedia article or elsewhere. In this case, even though many people "fall for it", it is a clear mathematical problem with a clear, logical, unambigious solution. Lets keep the list for paradoxes only! .......or, at least categorize these two: real or seemingly-real paradoxes VS. psuedo-paradoxes.

Absolutely correct. The Monty Hall problem is definitely not a paradox, and has been removed. MathStatWoman 03:57, 24 January 2006 (UTC)

We have some difficulties here. The twin paradox is not a paradox, since one twin experiences acceleration and the other does not. Will Rogers paradox is not a paradox. We need to clean up this article. MathStatWoman 08:57, 27 January 2006 (UTC)

Also: statistical "paradox": misinterpretation of correlation does not constitute a paradox! Please, let us clean up this page! I would start to do so, but I do not want to be unjustly accused of vandalism, so could we do it as a team? MathStatWoman 09:01, 27 January 2006 (UTC)

MathStatWoman seems to be using "paradox" to mean simply "contradiction". That's not the only meaning, and obviously not the one intended here. Monty Hall is definitely a paradox, whereas "defining sets of sets" does not lead to paradoxes (naive comprehension leads to a contradiction, and if you have an intuition that naive comprehension is true, then that fact will be paradoxical for you, but it doesn't have much to do with defining sets of sets). By the way, the term "real paradox" reminds me of the commercial that used to air on late-night TV in which "if you order now, we'll send you these genuine faux pearls!". --Trovatore 16:41, 27 January 2006 (UTC)

Yes, I think people are being absurd here. Almost none of the mathematical paradoxes are actually paradoxes in the strictest sense: Tarski-Banach, the Monty Hall problem or the Birthday Party paradox. However, they are called paradoxes because strange outcomes occur from the given situation. This is a perfectly normal use of the word paradox in mathematics. I don't think anything would be left in the Maths/Stats part (except maybe some Bayesian/frequentist wrangling about the two envelopes paradox) if we removed things on these grounds. --Richard Clegg 14:43, 30 January 2006 (UTC)

Actually I like my genuine faux diamonds. Don't you love these debates based on semantics? What fun. MathStatWoman 00:20, 28 January 2006 (UTC)

Maybe I'm missing something, but this list of paradoxes doesn't appear to contain the Prisoner's Dilemma. Surely PD is a bona-fide paradox, much more so than the examples correctly identified above as merely mundane faulty reasoning. A genuine paradox is non-resolvable, and the one-round PD qualifies in this respect, along with the similar 'Trajedy of the Commons' formulation. MelbournePaul 22:00, 30 January 2006

How is Unintended consequence a paradox??? 59.167.131.98 12:50, 3 June 2006 (UTC)

I had removed the "missing square puzzle", which is an optical illusion, but some genius has put it back in, giving the reason, and I quote Many of the listed things here are not really paradoxes. Help!!! --Arno Matthias 11:09, 1 October 2006 (UTC)

That was me. Taking just some examples, the missing dollar paradox, Hodgekinson's paradox, Monty Hall problem, Twins, Smale, Low Birth Weight Problem, everything (I think) in the "Geometry and Topology" are not really paradoxes. I would not be surprised if the majority of the things on this page are not really paradoxes. The point is that they appear paradoxial. --Richard Clegg 12:25, 1 October 2006 (UTC)

Oh for pete's sake - if you already know it doesn't belong here, then why do you put it in again?? Is this your idea of cleaning up this mess? The article is called "List of paradoxes", and not, for example, "List of puzzles that some people find difficult to solve" or "List of optical illusions". If some people want to keep these items in they should at least be in a different section "Things that may look like paradoxes but really aren't" - agreed? --Arno Matthias 11:38, 2 October 2006 (UTC)

Arno... please try and stay polite. Look at the rest of the discussion on this talk page. How is the "missing square puzzle" different to the "missing dollar paradox" for example. If we followed your idea I think most of the paradoxes on this page would not be here. Most of the things on this page are not paradoxes in the strictest sense. --Richard Clegg 11:42, 2 October 2006 (UTC)

I think both the "missing square puzzle" and the "missing dollar paradox" (and maybe some others) should be removed because they are intentionally misleading rather than paradoxical. The missing dollar paradox tells you to do something stupid and then tells you to act surprised when it doesn't work. The missing square puzzle changes the situation without telling you and then the reader is supposed to be surprised. A strict definition of a paradox would eliminate most/all of the examples, but I think the loose definition of a paradox should eliminate situations that give an unexpected outcome only because the situation has not been accurately described.--216.165.42.225 20:32, 20 June 2007 (UTC)

[edit] Categorization

The categorization of paradoxes here is pretty rough and could use some work. Let's remember that paradoxes are only paradoxes-in-a-theory, so we have semantic paradoxes that are paradoxes due to our theory of truth, and set-theoretic paradoxes that are subsumed within our set theory. Things like the Monty Hall problem are properly called paradoxes as long as we recognize that they are paradoxes within decision theory. KSchutte 19:54, 12 March 2006 (UTC)

[edit] Petronius' paradox

I did a little searching around, and found that this is not his paradox. Unless someone can prove me wrong it should be removed.

It is a paradox because to have moderation of everything including moderation means to only have moderate moderation of everything which would go against the statement! 69.40.183.177 22:45, 4 June 2007 (UTC)

[edit] Clasifying paradoxes

There's a continual problem with this page that some of the things listed are "paradoxes" that is they have no resolvalbe answer e.g. Russell's paradox and its answers. Some seem paradoxes because the explanation has a "trick" Horse paradox. Some are not paradoxes but seemingly unlikely outcomes of a theory Twin Paradox or Banach-Tarski Paradox. This page occasionally suffers deletions because someone says "that's not a paradox" of something in the last two classes (usually the easier to understand ones). Would it be helpful to try to classify paradoxes as to their status? It would lead to countless disagreements I have no doubt. --Richard Clegg 12:53, 1 October 2006 (UTC)

I see no such distinction. A paradox is, by definition, an apparent contradiction that breaks a natural-seeming intuition. Russell's paradox is precisely of this sort, as is Banach-Tarski. --Trovatore 02:44, 2 October 2006 (UTC)

That is not how some people would see a "true" paradox. There is a fundamental difference between the two. Banach-Tarski is just a rather strange consequence which you might not expect -- it is peculiar but not paradoxical in a true sense. Russell's paradox leads to an undecidable consequence and shows an underlying problem with the system. It is more than a "strange consequence" it's a flat out inconsistency. Russell's paradox led to a reformulation of set theory because it highlighted a flaw with the theory of the time -- the axioms of the system were not consistent. Banach-Tarski did not lead to such a reformulation of set theory it was just one of the many strange consequences of the Axiom of Choice. Perhaps an even clearer example is Simpson's Paradox which is actually clear to anyone with basic maths once it's explained. --Richard Clegg 07:24, 2 October 2006 (UTC)

Sure. See Quine's classification, for example. But I underline that they are all still called paradoxes, not apparent paradoxes, so I don't exactly agree with the sentence you are trying to add. 192.75.48.150 13:59, 2 October 2006 (UTC)

OK -- Quine's classification is a useful one. I like it. What I'm trying to avoid is the continual problem of people who try to remove things off this page because "they're not paradoxes". I have added a link to Quine's classification above. I agree they're all still called paradoxes but still we get people deleting things because "they're not paradoxes" -- this particularly happens with the easier to understand ones. --Richard Clegg 14:45, 2 October 2006 (UTC)

One could argue here that there still is no fundamental difference, though. The "underlying problem with the system" is as much a consequence of the assumption that this kind of thing cannot happen, as it is actually happening. Indeed, all the self-referential paradoxes (which include all the Liar paradoxes) illuminate how the intuition about reference, use/mention, etc., is not always reliable; "a rather strange consequence which you might not expect." I point out the analogy of those who first dabled in non-Euclidean geometry and thought they disproved it because they (thought they) contradicted something Euclidean. Of course they didn't since the axioms themselves were inconsistent, but their intuition was assaulted.

Exapmple: note also that a contradiction is not found in the sentence "This sentence is false", because it is not both true and false. Indeed, it is neither. It is counterintuitive, though, as we tend to think any well formed sentence has to be either true, or false. The contradiction comes only when we assume this has to be the case. But as you allude to, it doesn't.

About the use of "clear": We need to be careful to distinguish between "logically rigorous" (which your usage would support), and "intuitively obvious" (which it would not). Only careful familiarity with the rigor of the explanation can update one's intuition; that is a difficult process. This gets at use/mention again: I could accurately reword the end of your Simpson's sentence as follows: "Perhaps an even clearer example is Simpson's Paradox, the truth of whose unintuitive result is actually clear [...], once it's explained" The result can still be unintuitive, even if it is accepted. So I disagree as well with the sentence. Baccyak4H 14:34, 2 October 2006 (UTC)

Oh god, you're a philosopher aren't you. :-) What I'm trying to get at is that there is a fundamental difference between, say the "Horses are all the same colour" paradox (a false proof that all horses are the same colour as each other) this is just faulty reasoning, someone explains it and you go "oh yes, I see", the "Simpson's paradox" which is an unlikely outcome which seems counter-intuitive and the "Russell paradox" which indicated a fundamental flaw in the underlying axiomatic system. There are, of course, intermediates -- the Schrodingers cat paradox may be a counter-intuitive result of QM or a fundamental flaw in QM (maybe even some people would say it is just faulty reasoning) depending on just who you ask. --Richard Clegg 14:45, 2 October 2006 (UTC)

Well, I would argue that it is not fundamental, but a matter of degree. To the horse colors (low degree), a response might be "no, horses can be different colors, yuor argument is fallaceous." To something else, there might be a lot of handwaving and headscratching. "How can that be????"

But to be fair, it is not clear to me where the dividing line between paradox and outright fallacy is. People's intuitions are honed differently, etc. So there is some ambiguity here.

As for the wording, I would argue that all paradoxes have in principle a clear resolution, but I use clear to mean rigorous. But some are much harder to accept on a gut level (as opposed to a reason level). So let's go slowly here; your clarification is already a significant improvement.

I am not a professional philosopher, but I do "love knowledge". And where I come from, that is a compliment. :-) Baccyak4H 15:12, 2 October 2006 (UTC)

The dividing line, for me as a working mathematician, is whether or not the paradox indicates that your system is itself flawed. The Horse Colour paradox is fun because it's a nice example of trying to find a problem with the reasoning. It's like all of those proofs that 1 = 2 which rely on a "trick". It's an intellectual game of "spot the deliberate mistake". The Russell Paradox indicated a problem with the formulation of set theory and hence the underlying mathematics had to be developed to avoid the paradox. In other words, the clear resolution to the Russell Paradox was to develop a new form of mathematics where the Russell Paradox wasn't possible. The clear resolution to the Horse paradox was to say "you made a mistake here at step 2". This to me, is a fundamental difference. --Richard Clegg 15:46, 2 October 2006 (UTC)

I think we have to get clear about which "system" you're talking about, in the case of the Russell Paradox. The system directly refuted by Russell was Fregean set theory. Fregean set theory was flat-out falsified by the Russell Paradox, crushed beyond hope of resurrection. But Fregean set theory had never been "the" system; mathematics had never been based upon it, so a new form of mathematics was not needed, just a new understanding of sets (possibly not that new after all; it's a point of debate whether Cantor's unformalized conception was closer to Frege's or to the modern one).

But we don't call RP a "paradox" because it refuted Fregean set theory. Fregean set theory was simply in error; no paradox there. It's a "paradox" because it violates a natural-seeming intuition. In that sense it's just like Banach-Tarski. --Trovatore 16:02, 2 October 2006 (UTC)

Maybe my undersanding of history is in error here. As I understood it, Fregean set theory was the set theory of the day -- it was what people used to work with sets apart from a few people -- sure mathematics itself wasn't based on it but it was a respected branch of mathematics. Russell's paradox crushed it as you say, leading to new formulations of set theory. We call RP a paradox not just because it violates an intuition but because it shows up a flaw in a theory. There is no Russell Paradox in ZF set theory for example. This is different to the B-T paradox which, while intended to prove the incorrectness of the Axiom of Choice (as I understand it) in fact was just accepted as "one of those weird things". B-T paradox can be accepted within those formulations of set theory where it occurs, without destroying the theory. No theory which admits a Russell type paradox can be admitted within mathematics unless one is prepared to take an extremely anarchic definition of what is mathematics. --Richard Clegg 16:15, 2 October 2006 (UTC)

I'm no historian, but I kind of do think your history is in error. It's sort of a common error, though.

What is true, I think, is that mathematicians of the time used a sort of intuitive notion of set that can be roughly elucidated as follows:

The extensional notion of a set (determined by its members), and the intensional notion of a class (determined by its definition), are not really different, and may be uncritically interchanged.

This intuition, as we now know, was simply wrong. While there had been earlier indications of problems with it, it was RP that finished it off. Now, there was another intuition that had perhaps never been formalized, that went something like this:

Sets of points in R³ are like physical objects, to the extent that it should be possible to assign to every such set a "volume" or "mass" that behaves the way we expect it to, based on our physical experience

This latter intuition was also wrong, and we know it because of BT. These cases, to me, seem very closely parallel. --Trovatore 17:47, 2 October 2006 (UTC)

I think we will have to agree to disagree on this one -- the cantor middle third set would disprove that intuition about sets well before BT. However, both cases I hope you would agree, are very very different to the "All horses are the same colour" type paradox which is simply a "quickness of the hand deceives the eye" type "fake" proof. --Richard Clegg 17:56, 2 October 2006 (UTC)

Yeah, I guess I agree that the "horse" and "2=1" proofs are a different sort of thing from (not "different to", please! after all, I avoid saying "different than") the BTP and RP. However I don't really buy the thing about the middle thirds set--that just has zero measure, and there's nothing particularly unintuitive about that, as far as I can see. Not being able to assign a physics-respecting measure, even to elements of a partition into finitely many pieces, is much more troublesome. --Trovatore 05:27, 3 October 2006 (UTC)

[edit] benford's law

I don't know much about paradoxes and was just browsing this page, but it seems to me that Benford's Law should not be on this list. I don't think it is a paradox, but then again I'm no logician. I think if something is a scientific "law" (as the name purports), then by definition it cannot be a paradox. Thoughts?

See the above discussions and the wording at the top of the page about many of the paradoxes having a clear resolution. --Richard Clegg 11:03, 14 October 2006 (UTC)

[edit] Possession paradox

Has this paradox been included on the list - "a claim to having a right is only required when the subject does not have the object of that right". - Shiftchange 03:32, 3 November 2006 (UTC)

No, your fake paradox has not been included because it is fake and wrong. BonniePrinceCharlie 22:35, 6 December 2006 (UTC)

[edit] Intentionally blank pages

I don't really see how pages being left intentionally blank is really a paradox. It may fit the definition of a paradox, but I don't think tthat's what most people are thinking when they're thinking about them. - Celarnor 15:38, 15 December 2006 (UTC)

The paradox lies in the fact that these pages aren't really blank at all, but instead have a sentence like "This page is blank (and not by accident)" printed on them. --Arno Matthias 01:32, 16 December 2006 (UTC)

That's not a paradox. It's just untrue. BonniePrinceCharlie 02:06, 16 December 2006 (UTC)

[edit] Free will and omniscience paradox

Quoting from the article: Free will and omniscience paradox: If there is an omniscient being then it is impossible to have free will, for the omniscient being already knows what you are going to decide, therefore you can't decide because the decision has already been made. - An alternative explanation would be that the omniscient being is only able to perfectly know the present state of the universe. There is an implicit supposition that if you perfectly know the state of a system at a moment in time, you can predict its future evolution - that is certainly contradicted by quantum physics.

So, free will is not contradicted if you think this way. The omniscient being will certainly know what you are most likely to do (probabilities), yet not be able to predict your exact choice in the future. Also, on a large scale - thinking of millions of people - there might emerge statistical properties that are predictable - much like thermodynamics is versus analyzing a single particle at a time. Just my 0.02$

[edit] Psychological

One of these sections is not like the others! I am going to remove all the entries with the exception of Double Bind. If someone wants to keep any of them, you can link to an article about it (that actually describes it as a paradox, and which doesn't promptly get deleted). 192.75.48.150 18:10, 25 January 2007 (UTC)

Complete agreement. Most of the "Psychological" section is nonsense or waffle in breach of WP:OR, and should be deleted. Keep only what links to a wiki article. Snalwibma 18:19, 25 January 2007 (UTC)

[edit] Buddhism Paradox isn't a paradox

I removed it twice now... It's not really a paradox. You don't have to desire to be a Buddha in order to become one, and the two usages of the word "Desire" are different. Desire has varying degrees. There is a difference between having intention of and aspiring to do something and "Desiring" it. If it were a paradox it should have its own page, which it doesn't because it is not a paradox. Please don't re-post it, and if anybody does please note that there is some ambiguity to the word 'desire'

Konamiuss 21:02, 23 March 2007 (UTC)

[edit] "No Shortcuts" - a paradox?

Perhaps I am unclear as to what makes a paradox, but I cannot see this one. All I can see is an erroneous, counter-intuitive conclusion made from a mathematical error. This is unlike the Banach-Tarski paradox, which is a valid, counter-intuitive conclusion made from sound mathematical reasoning. This is no more worthy to be called a paradox than the "proof" that -1=1: $-1=i\cdot i=\sqrt{-1}\cdot\sqrt{-1}=\sqrt{(-1)(-1)}=\sqrt{1}=1$ Daniel Walker 20:21, 30 May 2007 (UTC)

Unlike in your example there is no fault in the mathematical part of the proof in the "no shortcuts" paradox. The limit of the the Manhatten distance (n -> infinity) is actually "h+v", there is no error in this. The paradox consists of the nonintuitive fact that the length of the zig-zag path made up of orthogonal segments does not approximate the length of the direct connection between the two points, even though the overall shape of the zig-zag path does approximate the direct connection between the two points. Do you see my point? ClassA42 15:34, 1 June 2007 (UTC)

As a general statement, I think this is what we can say from the "no shortcuts" paradox. Should the length of some curve B approximate the length of some curve A if, B is iteratively constructed of 2n line segments and as n tends towards infinity, the mean shortest distance of the points of B to the points of A tends towards zero? When put in abstract terms, it is not so clear that the lengths could be different, and that is what makes it paradoxical. Of course, my attempt at abstracting the results may be flawed, and a more correct, abstract view of it may not lend itself to be viewed as a paradox. Root⁴(one) 20:21, 1 June 2007 (UTC)

Hm, I guess that I can see your point. Daniel Walker 17:24, 2 June 2007 (UTC)

[edit] I don't believe...

I don't believe the Monty Hall Problem is actually a paradox. Could someone look at this? Technical Wiz 17:22, 31 May 2007 (UTC)

It is a paradox precisely because so many people do get the probabilities wrong upon first looking at the problem (as I see the introduction says). If you define a paradox as some result that is counter-intuitive, then yes, because many people's intuition leads them to select the incorrect answer. Of course, a more mathematically refined intuition, or one that specifically remembers this or a related problem, may not immediately conclude the same results or decide it is necessary to perform the particular calculations to find the true probabilities. Intuition is a funny thing. We do have to be careful, because the answer to any question may be counter-intuitive to somebody. But as I assume this to be a list of famous and notable, I can't see removing Monty Hall... If anything, I'd say that's the most famous probability problem. Also, the same mechanisms that may call this a paradox would equally fail for a number of the more familiar probability paradoxes. Boy or Girl paradox or Birthday paradox to name a couple. If you understand probability, the results of either are not counter-intuitive. Root⁴(one) 19:33, 31 May 2007 (UTC)

[edit] Logical (except mathematical)?

Isn't logic mathematics? And, if you click on many of the examples in the list under this section, the linked article will either use mathematical notation or cite a mathematical reference. Shouldn't the mathematical section say "(except logical)" rather than the way it is now? Leon math 19:04, 4 June 2007 (UTC)

No. Mathematics is a subset of logic. Although the sections with math and logic should probably be organized more closely together. Gregbard 10:46, 3 July 2007 (UTC)

[edit] Hegel

The link on Hegel's paradox leads to the entry on Hegel himself. Is this correct?

[edit] Jesse's paradox

Jesse's paradox: "It is a gamble to trust anyone. Then again, can a gambler be trusted?"

I was sad to see this one deleted. Although I guess I see why. A person who is considering whether or not to trust someone does not themself need to be trustworthy to do so. Maybe there's a place for it? Perhaps "rhetorical paradoxes?" Gregbard 10:53, 3 July 2007 (UTC)

[edit] City of Mayors Paradox

I didn't see this one listed. Is there another version?

The King has decreed that all mayors who do not live in their own cities, shall live in the City of Mayors. Where does the Mayor of the City of Mayors live?

Well, I thought of so many solutions to this paradox...maybe that's why you didn't bother listing it? :)

The Mayors, noticing the paradox, agree among themselves that they shall all live in their own cities. The City of Mayors, being empty, is turned into a tourist resort instead.

Only two Mayors do not live in their own city, so the City would be a Hamlet instead, and doesn't need a Mayor. So they share an apartment instead and the City of Mayors is turned into a tourist resort.

The City of Mayors is so small, it doesn't have a Mayor, it has a Village President.

The King, being informed of the paradox, makes himself Mayor and is exempt from his own rules.

The Mayor lives in the city, violates the rule and pays a fine of one gold piece.

The Mayor is a foreigner and therefore is not subject to the king's law.

The Mayor is a zombie so he isn't "living" anywhere.

I suppose this is a variant of the Barber Paradox, but the solutions are distinct from the solution to the Barber Paradox, and I had fun making this list.

206.148.168.107 02:39, 8 July 2007 (UTC)NotWillDecker

Exactly. Both this and the Barber Paradox are variants of the famous Russell's Paradox.Daniel Walker 03:22, 24 July 2007 (UTC)

[edit] CORUANS - Country Or Regions Used As Names

CORUANS - Country Or Regions Used As Names http://en.wikipedia.org/wiki/Coruans

Do these count as paradoxes and is there a proper name for this sort of thing already?

Things like " what do the Danes call Danish Pastry - (Answer - Viennese Breads....- but in Vienna they call them....Copenhagen Breads....)

What do they call Brazil nuts in Brazil? (chestnuts from Para) etc — —Preceding unsigned comment added by Engineman (talk • contribs) 13:05, 7 October 2007 (UTC)

Just one note: in the Diamond-Water paradox it is stated that both of them is plenty of, while on the page dedicated to this paradox, the central point of the explaination is that diamonds are indeed rare. —Preceding unsigned comment added by 87.5.223.183 (talk) 12:27, 20 December 2007 (UTC)

[edit] What kind of paradox

would this count as: "I bet you $50 that you'll win this bet"? -Ein Poltergeist —Preceding unsigned comment added by 70.108.28.225 (talk) 02:03, 3 February 2008 (UTC)

It is a self-referential paradox ("this bet"), and essentially the same as the Liar paradox. There the truth of a sentence is defined as its falsehood; here the winning condition of a bet is defined as losing it. --Lambiam 16:13, 3 February 2008 (UTC)

[edit] How about this one

Hi. Um, how about this old Ancient Chinese Paradox? A man creates a sword that will cut through anything, and a shield that will protect against anything. Someone asks, what happens if you use the sword to cut into the shield, what will happen? Thanks. ~A H 1^(TCU) 02:43, 23 February 2008 (UTC)

See Irresistible force paradox. --Lambiam 21:35, 23 February 2008 (UTC)

[edit] Nascent Paradox

My boss was talking about the Nascent Paradox, but I didn't see it here. What is it? —Preceding unsigned comment added by 75.11.69.57 (talk) 19:45, 31 March 2008 (UTC)

[edit] Paradox of Fiction?

What about the paradox of fiction? It doesn't have a wiki page, but I've come across it in both a module on paradoxes and a module on aesthetics. It goes like this: 1) We pity Anna Karenina, admire Superman and fear the green slime oozing towards us; 2) We can only pity or admire people if they exist, and fear things if they pose a threat to us; 3) We know throughout the book, play or movie that the characters are only fictional. 82.152.195.223 (talk) 08:39, 18 April 2008 (UTC)Nasta

I'm not familiar with this, but doesn't premise one show that premise two is false? Djk3 (talk) 15:45, 18 April 2008 (UTC)

Premise two is true in non-fictional contexts. (An example: If someone told you that his sister was dying prematurely of an illness, you might feel pity for her. But if you were then to discover that he did not have a sister you could no longer feel pity for her, because she does not exist and your pity would be directed at nothing.) You could also deny premise one, in favour of the view that what we feel is not really fear or pity but only quasi-fear or quasi-pity, tempered with a sense of pleasure. Neither arguments are without their problems: http://www.iep.utm.edu/f/fict-par.htm

[edit] Another possible Paradox

This is paradox i came up with while watching The pirates of the Carribeans, and it's probably nonsensical, but I want to put in here nonetheless, see what you guys think.

If a person is a immortal (unable to die), and loses his immortality later, was he ever immortal in the first place?

I know this is taken out of fiction since immortality is impossible, but still ;-) Лёха Фурсов: Sacrublood (talk) 08:06, 16 May 2008 (UTC)

There are mythical stories in which a being that could have remained immortal willingly gives up that status and chooses to become mortal, such as in the sacrifice of Chiron. A modern example is the narrative of Wings of Desire. Of course, one can define "immortality" in such a way that it implies an absolute inability to die. With that absolute definition, beings who can opt for mortality were never immortal in the first place. However, in the common use of the word the meaning is not so absolute but indicates rather that immortals do not have to die; they have the ability to live forever. One would then indeed say that they were immortal but lost their immortality. With neither meaning (absolute or relative) do we get a paradox, as long as we apply that meaning consistently. --Lambiam 11:45, 20 May 2008 (UTC)