
:''For other meanings of "Paradox", see Paradox (disambiguation).'' [[Image:Boyle%27sSelfFlowingFlask.png|thumb|Robert Boyle's self-flowing flask fills itself in this diagram, but Perpetual motion do not exist.]] A paradox is an apparently true statement or group of statements that seems to lead to a contradiction or to a situation that defies intuition. Typically, either the statements in question do not really imply the contradiction; or the puzzling result is not really a contradiction; or the premises themselves are not all really true (or, cannot all be true together). The recognition of ambiguity, equivocations, and unstated assumptions underlying known paradoxes has often led to significant advances in science, philosophy and mathematics. The word ''paradox'' is often used interchangeably with ''contradiction''; but where a contradiction by definition cannot be true, many paradoxes do allow of resolution, though many remain unresolved or only contentiously resolved (such as Curry's paradox). Still more casually, the term is sometimes used for situations that are merely surprising (albeit in a distinctly "logical" manner) such as the Birthday Paradox. This is also the usage in economics, where a paradox is an unintuitive outcome of economic theory. The etymology of ''paradox'' can be traced back to the early Renaissance. Early forms of the word appeared in the late Latin ''paradoxum'' and the related Greek language ''paradoxon''. The word is composed of the preposition ''para'' which means "by way of", or "according to" conjoined to the noun stem ''doxa'', meaning "what is received". Compare orthodox (literally, "straight teaching") and heterodox (literally, "different teaching"). The liar paradox and other paradoxes were studied in medieval times under the heading ''insolubilia''. Common themes in paradoxes include direct and indirect self-reference, infinity, circular definitions, and confusion of levels of reasoning. Paradoxes which are not based on a hidden error generally happen at the fringes of context or language, and require extending the context (or language) to lose their paradox quality. In moral philosophy, paradox plays a particularly central role in debates on ethics. For instance, an ethical admonition to "love thy neighbor" is not just in contrast with, but in contradiction to an armed neighbor actively trying to kill you: if he or she succeeds, you will not be able to love him or her. But to preemptively attack them or restrain them is not usually understood as very loving. This might be termed an ethical dilemma. Another example is the conflict between an injunction not to steal and one to care for a family that you cannot afford to feed without stolen money. ==Types of paradoxes== W. V. Quine (1962) distinguished three classes of paradox: * A ''veridical paradox'' produces a result that appears absurd but is demonstrated to be true nevertheless. Thus, the paradox of Frederic's birthday in ''The Pirates of Penzance'' establishes the surprising fact that a person may be more than N years old on his Nth birthday. Likewise, Arrow's impossibility theorem involves behavior of voting systems that is surprising but all too true. * A ''falsidical paradox'' establishes a result that not only appears false but actually is false; there is a fallacy in the supposed demonstration. The various invalid proofs (e.g. that 1 = 2) are classic examples, generally relying on a hidden division by zero. Another example would be the Horse paradox. * A paradox which is in neither class may be an ''antinomy'', which reaches a self-contradictory result by properly applying accepted ways of reasoning. For example, the Grelling-Nelson paradox points out genuine problems in our understanding of the ideas of truth and description. ==List of paradoxes== Quine's classification, of course, is useful only once a paradox has a clear resolution. That question is treated on the page for each individual paradox; the following are grouped thematically. ===Logic (except mathematical)=== * Paradox of entailment: Inconsistent premises always make an argument valid. * Raven paradox (or Hempel's Ravens): Observing a red apple increases the likelihood of all ravens being black. * Horse paradox: All horses are the same colour. * Unexpected hanging paradox: The day of the hanging will be a surprise, so it can't happen at all, so it will be a surprise. * Barber paradox: The barber who shaves all men who don't shave themselves, and no-one else. (A close relative of Russell's paradox.) * Richard's paradox: We appear to be able to use simple English to define a decimal expansion in a way which is self-contradictory. ====Semantic paradoxes==== These form a well-known (and well-studied) class having in common that any permissible assignment of semantic value (truth, reference) to an expression immediately implies the assignment of a different value. * Berry paradox: What is "The first number not nameable in under ten words"? (And hasn't it just been named in nine?) * Curry's paradox: "If I'm not mistaken, the world will end in a week." * Epimenides paradox: A Cretan says "All Cretans are liars". * Grelling-Nelson paradox: Is the word "heterological", meaning "not applicable to itself," a heterological word? * Liar paradox: "This sentence is false." * Quine's liar paradox: "Yields a falsehood when appended to its own quotation." * Russell's paradox: Does the set of all those sets that do not contain themselves contain itself? * The Y combinator in the lambda calculus and combinatory logic has been called the paradoxical combinator since it is related to the self-referential antinomies. ====Vagueness==== * Ship of Theseus/George Washington's axe: When every component of the ship has been replaced at least once, is it still the same ship? * Sorites paradox: At what point does a heap stop being a heap as I take away grains of sand? Alternately, at what point does someone become bald? ===Mathematics and statistics=== Monty_Hall_problem:_which_door_do_you_choose?">Image:Monty-hall.png|thumb|right|The Monty Hall problem: which door do you choose? * Apportionment paradox: Some systems of apportioning representation can have unintuitive results ** Alabama paradox ** New states paradox ** Population paradox * Will Rogers phenomenon: the mathematical concept of an average, whether defined as the mean or median, leads to apparently paradoxical results - for example, it is possible that moving an entry from Wikipedia to Wiktionary would increase the average entry length on both sites * Berkson's paradox * Bertrand's paradox (probability): Different common-sense definitions of randomness give quite different results. * Birthday paradox: What is the chance that two people in a room have the same birthday? * Borel's paradox: Conditional probability density functions are not invariant under coordinate transformations. * Elevator paradox: Elevators can seem to be mostly going in one direction, as if they were being manufactured in the middle of the building and being disassembled on the roof and basement. * Hodgson's paradox: the ratio of two Gaussian random variables has neither mean nor variance. * Richard's paradox: A complete list of definitions of real numbers doesn't exist. * Monty Hall problem: An unintuitive consequence of conditional probability. * Simpson's paradox: An association in sub-populations may be reversed in the population. It appears that two sets of data separately support a certain hypothesis, but, when considered together, they support the opposite hypothesis. * Sleeping beauty paradox: One half or one third? news://rec.puzzles cannot agree on a probability. * Statistical paradox: It is quite possible to draw wrong conclusions from correlation. For example, towns with a larger number of churches generally have a higher crime rate — because both result from higher population. A professional organization once found that economists with a Doctor of Philosophy actually had a lower average salary than those with a Bachelor of Science — but this was found to be due to the fact that those with a Doctor of Philosophy worked in academia, where salaries are generally lower. This is also called a spurious relationship. * Low birth weight paradox: Low birth weight babies have a higher mortality rate, babies of smoking mothers have lower average birth weight, babies of smoking mothers have a higher mortality rate, but low birth weight babies of smoking mothers have a lower mortality rate than other low birth weight babies. * Two-envelope paradox: Given two envelopes, one of which contains twice as much money as the other, the benefit seems always to lie in switching from one to the other. ====Infinity==== * Burali-Forti paradox: If the ordinal numbers formed a set, it would be an ordinal number which is smaller than itself. * Galileo's paradox: Though most numbers are not squares, there are no more numbers than squares. (See also Cantor, Cantor's diagonal argument) * Hilbert's paradox of the Grand Hotel: If a hotel with infinitely many rooms is full, it can still take in more guests. * Monty Hell problem: Positive daily profits yield zero assets in the (infinite) limit. * Skolem's paradox: countable infinite models of Axiomatic set theory contain uncountable infinite sets. ====Geometry and topology==== * Banach-Tarski paradox: Cut a ball into 5 pieces, re-assemble the pieces to get two balls, both of equal size to the first. * Gabriel's Horn or Torricelli's trumpet: A simple object with finite volume but infinite surface area. Also, the Mandelbrot set and various other fractals have finite area, but infinite perimeter. * Hausdorff paradox: There exists a countable subset C of the sphere S such that S\C is equidecomposable with two copies of itself. * Smale's paradox: A sphere can, topologically, be turned inside out. ===Psychology, action, and practical reason=== * Abilene paradox: People can make decisions based not on what they actually want to do, but on what they think that other people want to do, with the result that everybody decides to do something that nobody really wants to do, but only what they thought that everybody else wanted to do. * Buridan's ass: How can a rationality choice be made between two outcomes of equal value? * Control paradox: Man can never be free of control, for to be free of control is to be controlled by oneself. * Paradox of hedonism: When one pursues happiness itself, one is miserable; but, when one pursues something else, one achieves happiness. * Newcomb's paradox: How do you play a game against an omniscient opponent? * Kavka's toxin puzzle: Can one ''intend'' to drink the nondeadly toxin, if the intention is the only thing needed to get the reward? * Socratic Paradox: One can never knowingly choose the lesser good or willingly do the wrong thing. * Cursed Friend: If one is cursed into hurting one’s friends by just being with them, can one still be a friend and seek the other's company? * Paradox of Denial: How can one accept oneself as one is, if one is not the way one thinks one should be? Yet, how does one effectively change oneself without accepting oneself as one is, and working from that? * Hypocritical paradox: I hate hypocrites, but one thing I hate even more is intolerant hypocrites. ===Physics=== * Braess' paradox: Sometimes adding extra capacity to a network can reduce overall performance. * Carroll's paradox: the angular momentum of a stick should be zero, but isn't * D'Alembert's paradox: An viscosity liquid produces no drag. * Denny's paradox: Surface-dwelling arthropods (such as the water strider) should not be able to propel themselves horizontally. * Einstein-Podolsky-Rosen paradox: Can far away events influence each other in quantum mechanics? * Gibbs paradox: In an ideal gas, is entropy an extensive variable? * The GZK paradox: High-energy cosmic rays have been observed which seem to violate the Greisen-Zatsepin-Kuzmin limit which is a consequence of special relativity. * Loschmidt's paradox: Why is there an inevitable increase in entropy when the physical law are T-symmetry? The time reversal symmetry of physical laws appears to allow the second law of thermodynamics to be broken. * Mpemba effect: Hot water can under certain conditions freeze faster than cold water, even though it must pass the lower temperature on the way to freezing. * Olbers' paradox Why is the night sky black if there is an infinity of stars? * Twin paradox: When the travelling twin returns, he's younger and older than his brother who stayed put. * Black hole information paradox * Supplee's paradox: the buoyancy of a relativistic object (such as a bullet) appears to change when the reference frame is changed from one in which the bullet is at rest to one in which the fluid is at rest ===Philosophy=== * Fermi paradox: If there are many other sentient species in the Universe, then where are they? Shouldn't their presence be obvious? * Grandfather paradox: You time travel and kill your grandfather before he meets your grandmother which precludes your own conception and, therefore, you couldn't go back in time and kill your grandfather. * Mere addition paradox: Is a large population living barely tolerable lives better than a small happy population? * Nihilist paradox: If truth does not exist, the statement "truth does not exist" is a truth, thereby proving itself incorrect. * Omnipotence paradox: Can an omnipotent being create a rock too heavy to lift? Can an irresistible force move an unmovable object? * Predestination paradox: A man travels back in time and impregnates his great-great-grandmother. The result is a line of offspring and descendants, including the man's parent(s) and the man himself. Therefore, unless he makes the time-travel trip at all, he will never exist. * Epicurean paradox, or Problem of evil: The existence of evil is incompatible with the existence of an omnipotent and caring God. * Moore's paradox: "It's raining but I don't believe that it is." * Zeno's paradoxes: When you reach the turtle's spot, it has already advanced a bit, so you can never catch it. * Locudox - The opposite of a Paradox: First imagined by Portugese Mathematician Pedro Nunes. Given the human brain can describe a paradox it must be able to contain it, and the state where any given paradox ceases to display its inherent conflicting characteristics is decribed as a Locudox. ===Economics=== * Abilene paradox: A group of people often has to decide against its own interests. * Arrow's impossibility theorem/Voting paradox/Condorcet paradox: You can't have all the attributes of an ideal voting system at once. * Bertrand paradox (economics): Two players reaching a state of Nash equilibrium both find themselves with no profits. * Bird in the bush paradox: Why are people so risk-averse? * Diamond-water paradox Why is water cheaper than diamonds, when humans need water to survive, not diamonds? * Edgeworth paradox: with capacity constraints, there may not be an equilibrium. * Ellsberg paradox: A paradoxical result in experimental decision theory. * Giffen good: Can increasing the price of bread make poor people eat more of it? * Jevons paradox: Increases in efficiency lead to even larger increases in demand. * St. Petersburg paradox: People will only offer a modest fee for a reward of infinite value. ==References== * Quine, W. V. (1962). "Paradox". ''Scientific American'', April 1962, pp. 84–96. * Clarke, Michael (2002). ''Paradoxes from A to Z''. London: Routledge. ==See also== * Impossible object * Logical fallacy * Puzzle ==External links== *Open Directory Project: [http://www.dmoz.org/Society/Philosophy/Philosophy_of_Logic/Paradoxes/ Paradoxes] *[http://www.dpmms.cam.ac.uk/~wtg10/richardsparadox.html Definability paradoxes] *[http://plato.stanford.edu/entries/insolubles Insolubles] ''(at the [http://plato.stanford.edu Stanford Encyclopedia of Philosophy])'' Logic Paradoxes simple:Paradox
---- 193.203.83.xxx for which Newcomb that paradox stands for. The American astronomer? user:XJamRastafire [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: *http://www.etext.org/Fiction/PurpleNotebook/ch442.html The Paradox of 'Freedom of Will' * http://sprott.physics.wisc.edu/pubs/paper251/paper251.htm *http://www.uchicago.edu/research/jnl-pub-cult/backissues/pc18/gladney.html *http://www.etext.org/Fiction/PurpleNotebook/ch442.html *http://www.counterpunch.org/jensen1012.html *http://www.animalfreedom.org/english/opinion/paradox.html *http://min.ecn.purdue.edu/~butta/ *http://www.newamerica.net/index.cfm?pg=article&pubID=18 *http://showcase.netins.net/web/paradox/box/014letgo.html *http://www.gvsu.edu/gened-tme12/ *http://www.dreamstrike.com/control.html *http://www.praxagora.com/stevet/netfuture/fwd/1998/2.html *http://www.geocities.com/~n4bz/feedbk.htm *http://www.geocities.com/~n4bz/gst/gst8.htm *http://www.geocities.com/Athens/4690/locke.html *http://www.geocities.com/Athens/Acropolis/9356/thesis/chap31.html *http://www.kuro5hin.org/comments/2001/11/18/141521/31?pid=34 *http://www.uh.edu/engines/epi1288.htm *http://hellomo.com/content/lose.control/content.html *http://www.gerrymcgovern.com/nt/1998/nt_1998_11_16_libertarian.htm *http://www.religiousstudies.co.uk/alevel/omnipot.htm *http://www.philosophypages.com/dy/s7.htm *http://www.sussex.ac.uk/Users/sefd0/bib/polphil.htm *http://www.nyu.edu/gsas/dept/politics/faculty/landa/LandaEarlyModernSyl.html *http://www.popecenter.org/clarion/2000/jul-aug/review.html *http://newtexts.com/newtexts/book.cfm?book_id=542 *http://www.inq7.net/vwp/2001/mar/25/vwp_1-1.htm *http://www.papers24-7.com/categories/161-005.html *http://www.phil.uga.edu/faculty/wolf/study1.htm *http://www.erraticimpact.com/~modern/html/modern_jean_jacques_rousseau.htm *http://www.westminster.edu/staff/brennie/group1/rousseaulink5.htm *http://www.interconnect.is.it/capitalism/first.html : Half of the links in above list are either dead or online-shops are link farms. So what's the idea of this? User: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.User: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. -- User: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 Gödel's incompleteness theorem demonstrate the limits of formal systems of number theory. User: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. -- User: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. User: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? User:Paullusmagnus 22:11, 1 Oct 2003 (UTC) : Give it a shot. The people who care are watching this page. -- User: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 User:Paullusmagnus (and User:Dandrake for finding a good structure to use)! User:Nanobug 02:46, 15 Oct 2003 (UTC) ::Ditto! User: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. User: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? User:Pakaran 19:51, 18 Oct 2003 (UTC) : It's probably just pre-emtive, waiting for someone to write the article. :-) User:Evercat 19:55, 18 Oct 2003 (UTC) :: Ok thanks. Then there was no such article? User:Pakaran 19:59, 18 Oct 2003 (UTC) : Apparently not. There's no indication that it ever existed (and was deleted). User: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 :) User: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? User: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. Albert 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 number 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. -- User:Cyan 06:07, 24 Jan 2004 (UTC) ------ Isn't Schrödinger's cat a scientific paradox? User: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. User: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? User: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 [http://plato.stanford.edu/entries/paradox-stpetersburg/ external link] 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). -- User: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? User:Paullusmagnus 18:32, 26 Feb 2004 (UTC) <''end of copied text''> Sounds good to me. I'll do it. -- User:Cyan 18:44, 26 Feb 2004 (UTC) Does this need to be locked? User:PakaranUser talk: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? --User: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. User: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. --User:Camembert :Edit warriors get into edit wars as a matter of principle. The obscurity of the issue has nothing to do with it. -- User:Arvindn 07:54, 18 Mar 2004 (UTC) I'm ''really'' hoping for a reply from the involved parties. --User:Camembert :Perhaps you should leave a message for them on their respective talk pages. -- User:Cyan 19:45, 18 Mar 2004 (UTC) == 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 09:45, Jul 15, 2004 (UTC) == new pic == I like the new pic lots better, hoorah! User:Sam Spade http://en.wikipedia.org/w/wiki.phtml?title=User_talk:Sam_Spade&action=edit§ion=new Spade 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. User: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. User:Anthony DiPierro User:Anthony_DiPierro/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! User: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. --User: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? -- User: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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Paradox
:''For other meanings of "Paradox", see Paradox (disambiguation).'' [[Image:Boyle%27sSelfFlowingFlask.png|thumb|Robert Boyle's self-flowing flask fills itself in this diagram, but Perpetual motion do not exist.]] A paradox is an apparently true statement or group of statements that seems to lead to a contradiction or to a situation that defies intuition. Typically, either the statements in question do not really imply the contradiction; or the puzzling result is not really a contradiction; or the premises themselves are not all really true (or, cannot all be true together). The recognition of ambiguity, equivocations, and unstated assumptions underlying known paradoxes has often led to significant advances in science, philosophy and mathematics. The word ''paradox'' is often used interchangeably with ''contradiction''; but where a contradiction by definition cannot be true, many paradoxes do allow of resolution, though many remain unresolved or only contentiously resolved (such as Curry's paradox). Still more casually, the term is sometimes used for situations that are merely surprising (albeit in a distinctly "logical" manner) such as the Birthday Paradox. This is also the usage in economics, where a paradox is an unintuitive outcome of economic theory. The etymology of ''paradox'' can be traced back to the early Renaissance. Early forms of the word appeared in the late Latin ''paradoxum'' and the related Greek language ''paradoxon''. The word is composed of the preposition ''para'' which means "by way of", or "according to" conjoined to the noun stem ''doxa'', meaning "what is received". Compare orthodox (literally, "straight teaching") and heterodox (literally, "different teaching"). The liar paradox and other paradoxes were studied in medieval times under the heading ''insolubilia''. Common themes in paradoxes include direct and indirect self-reference, infinity, circular definitions, and confusion of levels of reasoning. Paradoxes which are not based on a hidden error generally happen at the fringes of context or language, and require extending the context (or language) to lose their paradox quality. In moral philosophy, paradox plays a particularly central role in debates on ethics. For instance, an ethical admonition to "love thy neighbor" is not just in contrast with, but in contradiction to an armed neighbor actively trying to kill you: if he or she succeeds, you will not be able to love him or her. But to preemptively attack them or restrain them is not usually understood as very loving. This might be termed an ethical dilemma. Another example is the conflict between an injunction not to steal and one to care for a family that you cannot afford to feed without stolen money. ==Types of paradoxes== W. V. Quine (1962) distinguished three classes of paradox: * A ''veridical paradox'' produces a result that appears absurd but is demonstrated to be true nevertheless. Thus, the paradox of Frederic's birthday in ''The Pirates of Penzance'' establishes the surprising fact that a person may be more than N years old on his Nth birthday. Likewise, Arrow's impossibility theorem involves behavior of voting systems that is surprising but all too true. * A ''falsidical paradox'' establishes a result that not only appears false but actually is false; there is a fallacy in the supposed demonstration. The various invalid proofs (e.g. that 1 = 2) are classic examples, generally relying on a hidden division by zero. Another example would be the Horse paradox. * A paradox which is in neither class may be an ''antinomy'', which reaches a self-contradictory result by properly applying accepted ways of reasoning. For example, the Grelling-Nelson paradox points out genuine problems in our understanding of the ideas of truth and description. ==List of paradoxes== Quine's classification, of course, is useful only once a paradox has a clear resolution. That question is treated on the page for each individual paradox; the following are grouped thematically. ===Logic (except mathematical)=== * Paradox of entailment: Inconsistent premises always make an argument valid. * Raven paradox (or Hempel's Ravens): Observing a red apple increases the likelihood of all ravens being black. * Horse paradox: All horses are the same colour. * Unexpected hanging paradox: The day of the hanging will be a surprise, so it can't happen at all, so it will be a surprise. * Barber paradox: The barber who shaves all men who don't shave themselves, and no-one else. (A close relative of Russell's paradox.) * Richard's paradox: We appear to be able to use simple English to define a decimal expansion in a way which is self-contradictory. ====Semantic paradoxes==== These form a well-known (and well-studied) class having in common that any permissible assignment of semantic value (truth, reference) to an expression immediately implies the assignment of a different value. * Berry paradox: What is "The first number not nameable in under ten words"? (And hasn't it just been named in nine?) * Curry's paradox: "If I'm not mistaken, the world will end in a week." * Epimenides paradox: A Cretan says "All Cretans are liars". * Grelling-Nelson paradox: Is the word "heterological", meaning "not applicable to itself," a heterological word? * Liar paradox: "This sentence is false." * Quine's liar paradox: "Yields a falsehood when appended to its own quotation." * Russell's paradox: Does the set of all those sets that do not contain themselves contain itself? * The Y combinator in the lambda calculus and combinatory logic has been called the paradoxical combinator since it is related to the self-referential antinomies. ====Vagueness==== * Ship of Theseus/George Washington's axe: When every component of the ship has been replaced at least once, is it still the same ship? * Sorites paradox: At what point does a heap stop being a heap as I take away grains of sand? Alternately, at what point does someone become bald? ===Mathematics and statistics=== Monty_Hall_problem:_which_door_do_you_choose?">Image:Monty-hall.png|thumb|right|The Monty Hall problem: which door do you choose? * Apportionment paradox: Some systems of apportioning representation can have unintuitive results ** Alabama paradox ** New states paradox ** Population paradox * Will Rogers phenomenon: the mathematical concept of an average, whether defined as the mean or median, leads to apparently paradoxical results - for example, it is possible that moving an entry from Wikipedia to Wiktionary would increase the average entry length on both sites * Berkson's paradox * Bertrand's paradox (probability): Different common-sense definitions of randomness give quite different results. * Birthday paradox: What is the chance that two people in a room have the same birthday? * Borel's paradox: Conditional probability density functions are not invariant under coordinate transformations. * Elevator paradox: Elevators can seem to be mostly going in one direction, as if they were being manufactured in the middle of the building and being disassembled on the roof and basement. * Hodgson's paradox: the ratio of two Gaussian random variables has neither mean nor variance. * Richard's paradox: A complete list of definitions of real numbers doesn't exist. * Monty Hall problem: An unintuitive consequence of conditional probability. * Simpson's paradox: An association in sub-populations may be reversed in the population. It appears that two sets of data separately support a certain hypothesis, but, when considered together, they support the opposite hypothesis. * Sleeping beauty paradox: One half or one third? news://rec.puzzles cannot agree on a probability. * Statistical paradox: It is quite possible to draw wrong conclusions from correlation. For example, towns with a larger number of churches generally have a higher crime rate — because both result from higher population. A professional organization once found that economists with a Doctor of Philosophy actually had a lower average salary than those with a Bachelor of Science — but this was found to be due to the fact that those with a Doctor of Philosophy worked in academia, where salaries are generally lower. This is also called a spurious relationship. * Low birth weight paradox: Low birth weight babies have a higher mortality rate, babies of smoking mothers have lower average birth weight, babies of smoking mothers have a higher mortality rate, but low birth weight babies of smoking mothers have a lower mortality rate than other low birth weight babies. * Two-envelope paradox: Given two envelopes, one of which contains twice as much money as the other, the benefit seems always to lie in switching from one to the other. ====Infinity==== * Burali-Forti paradox: If the ordinal numbers formed a set, it would be an ordinal number which is smaller than itself. * Galileo's paradox: Though most numbers are not squares, there are no more numbers than squares. (See also Cantor, Cantor's diagonal argument) * Hilbert's paradox of the Grand Hotel: If a hotel with infinitely many rooms is full, it can still take in more guests. * Monty Hell problem: Positive daily profits yield zero assets in the (infinite) limit. * Skolem's paradox: countable infinite models of Axiomatic set theory contain uncountable infinite sets. ====Geometry and topology==== * Banach-Tarski paradox: Cut a ball into 5 pieces, re-assemble the pieces to get two balls, both of equal size to the first. * Gabriel's Horn or Torricelli's trumpet: A simple object with finite volume but infinite surface area. Also, the Mandelbrot set and various other fractals have finite area, but infinite perimeter. * Hausdorff paradox: There exists a countable subset C of the sphere S such that S\C is equidecomposable with two copies of itself. * Smale's paradox: A sphere can, topologically, be turned inside out. ===Psychology, action, and practical reason=== * Abilene paradox: People can make decisions based not on what they actually want to do, but on what they think that other people want to do, with the result that everybody decides to do something that nobody really wants to do, but only what they thought that everybody else wanted to do. * Buridan's ass: How can a rationality choice be made between two outcomes of equal value? * Control paradox: Man can never be free of control, for to be free of control is to be controlled by oneself. * Paradox of hedonism: When one pursues happiness itself, one is miserable; but, when one pursues something else, one achieves happiness. * Newcomb's paradox: How do you play a game against an omniscient opponent? * Kavka's toxin puzzle: Can one ''intend'' to drink the nondeadly toxin, if the intention is the only thing needed to get the reward? * Socratic Paradox: One can never knowingly choose the lesser good or willingly do the wrong thing. * Cursed Friend: If one is cursed into hurting one’s friends by just being with them, can one still be a friend and seek the other's company? * Paradox of Denial: How can one accept oneself as one is, if one is not the way one thinks one should be? Yet, how does one effectively change oneself without accepting oneself as one is, and working from that? * Hypocritical paradox: I hate hypocrites, but one thing I hate even more is intolerant hypocrites. ===Physics=== * Braess' paradox: Sometimes adding extra capacity to a network can reduce overall performance. * Carroll's paradox: the angular momentum of a stick should be zero, but isn't * D'Alembert's paradox: An viscosity liquid produces no drag. * Denny's paradox: Surface-dwelling arthropods (such as the water strider) should not be able to propel themselves horizontally. * Einstein-Podolsky-Rosen paradox: Can far away events influence each other in quantum mechanics? * Gibbs paradox: In an ideal gas, is entropy an extensive variable? * The GZK paradox: High-energy cosmic rays have been observed which seem to violate the Greisen-Zatsepin-Kuzmin limit which is a consequence of special relativity. * Loschmidt's paradox: Why is there an inevitable increase in entropy when the physical law are T-symmetry? The time reversal symmetry of physical laws appears to allow the second law of thermodynamics to be broken. * Mpemba effect: Hot water can under certain conditions freeze faster than cold water, even though it must pass the lower temperature on the way to freezing. * Olbers' paradox Why is the night sky black if there is an infinity of stars? * Twin paradox: When the travelling twin returns, he's younger and older than his brother who stayed put. * Black hole information paradox * Supplee's paradox: the buoyancy of a relativistic object (such as a bullet) appears to change when the reference frame is changed from one in which the bullet is at rest to one in which the fluid is at rest ===Philosophy=== * Fermi paradox: If there are many other sentient species in the Universe, then where are they? Shouldn't their presence be obvious? * Grandfather paradox: You time travel and kill your grandfather before he meets your grandmother which precludes your own conception and, therefore, you couldn't go back in time and kill your grandfather. * Mere addition paradox: Is a large population living barely tolerable lives better than a small happy population? * Nihilist paradox: If truth does not exist, the statement "truth does not exist" is a truth, thereby proving itself incorrect. * Omnipotence paradox: Can an omnipotent being create a rock too heavy to lift? Can an irresistible force move an unmovable object? * Predestination paradox: A man travels back in time and impregnates his great-great-grandmother. The result is a line of offspring and descendants, including the man's parent(s) and the man himself. Therefore, unless he makes the time-travel trip at all, he will never exist. * Epicurean paradox, or Problem of evil: The existence of evil is incompatible with the existence of an omnipotent and caring God. * Moore's paradox: "It's raining but I don't believe that it is." * Zeno's paradoxes: When you reach the turtle's spot, it has already advanced a bit, so you can never catch it. * Locudox - The opposite of a Paradox: First imagined by Portugese Mathematician Pedro Nunes. Given the human brain can describe a paradox it must be able to contain it, and the state where any given paradox ceases to display its inherent conflicting characteristics is decribed as a Locudox. ===Economics=== * Abilene paradox: A group of people often has to decide against its own interests. * Arrow's impossibility theorem/Voting paradox/Condorcet paradox: You can't have all the attributes of an ideal voting system at once. * Bertrand paradox (economics): Two players reaching a state of Nash equilibrium both find themselves with no profits. * Bird in the bush paradox: Why are people so risk-averse? * Diamond-water paradox Why is water cheaper than diamonds, when humans need water to survive, not diamonds? * Edgeworth paradox: with capacity constraints, there may not be an equilibrium. * Ellsberg paradox: A paradoxical result in experimental decision theory. * Giffen good: Can increasing the price of bread make poor people eat more of it? * Jevons paradox: Increases in efficiency lead to even larger increases in demand. * St. Petersburg paradox: People will only offer a modest fee for a reward of infinite value. ==References== * Quine, W. V. (1962). "Paradox". ''Scientific American'', April 1962, pp. 84–96. * Clarke, Michael (2002). ''Paradoxes from A to Z''. London: Routledge. ==See also== * Impossible object * Logical fallacy * Puzzle ==External links== *Open Directory Project: [http://www.dmoz.org/Society/Philosophy/Philosophy_of_Logic/Paradoxes/ Paradoxes] *[http://www.dpmms.cam.ac.uk/~wtg10/richardsparadox.html Definability paradoxes] *[http://plato.stanford.edu/entries/insolubles Insolubles] ''(at the [http://plato.stanford.edu Stanford Encyclopedia of Philosophy])'' Logic Paradoxes simple:Paradox
Paradox
---- 193.203.83.xxx for which Newcomb that paradox stands for. The American astronomer? user:XJamRastafire [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: *http://www.etext.org/Fiction/PurpleNotebook/ch442.html The Paradox of 'Freedom of Will' * http://sprott.physics.wisc.edu/pubs/paper251/paper251.htm *http://www.uchicago.edu/research/jnl-pub-cult/backissues/pc18/gladney.html *http://www.etext.org/Fiction/PurpleNotebook/ch442.html *http://www.counterpunch.org/jensen1012.html *http://www.animalfreedom.org/english/opinion/paradox.html *http://min.ecn.purdue.edu/~butta/ *http://www.newamerica.net/index.cfm?pg=article&pubID=18 *http://showcase.netins.net/web/paradox/box/014letgo.html *http://www.gvsu.edu/gened-tme12/ *http://www.dreamstrike.com/control.html *http://www.praxagora.com/stevet/netfuture/fwd/1998/2.html *http://www.geocities.com/~n4bz/feedbk.htm *http://www.geocities.com/~n4bz/gst/gst8.htm *http://www.geocities.com/Athens/4690/locke.html *http://www.geocities.com/Athens/Acropolis/9356/thesis/chap31.html *http://www.kuro5hin.org/comments/2001/11/18/141521/31?pid=34 *http://www.uh.edu/engines/epi1288.htm *http://hellomo.com/content/lose.control/content.html *http://www.gerrymcgovern.com/nt/1998/nt_1998_11_16_libertarian.htm *http://www.religiousstudies.co.uk/alevel/omnipot.htm *http://www.philosophypages.com/dy/s7.htm *http://www.sussex.ac.uk/Users/sefd0/bib/polphil.htm *http://www.nyu.edu/gsas/dept/politics/faculty/landa/LandaEarlyModernSyl.html *http://www.popecenter.org/clarion/2000/jul-aug/review.html *http://newtexts.com/newtexts/book.cfm?book_id=542 *http://www.inq7.net/vwp/2001/mar/25/vwp_1-1.htm *http://www.papers24-7.com/categories/161-005.html *http://www.phil.uga.edu/faculty/wolf/study1.htm *http://www.erraticimpact.com/~modern/html/modern_jean_jacques_rousseau.htm *http://www.westminster.edu/staff/brennie/group1/rousseaulink5.htm *http://www.interconnect.is.it/capitalism/first.html : Half of the links in above list are either dead or online-shops are link farms. So what's the idea of this? User: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.User: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. -- User: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 Gödel's incompleteness theorem demonstrate the limits of formal systems of number theory. User: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. -- User: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. User: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? User:Paullusmagnus 22:11, 1 Oct 2003 (UTC) : Give it a shot. The people who care are watching this page. -- User: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 User:Paullusmagnus (and User:Dandrake for finding a good structure to use)! User:Nanobug 02:46, 15 Oct 2003 (UTC) ::Ditto! User: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. User: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? User:Pakaran 19:51, 18 Oct 2003 (UTC) : It's probably just pre-emtive, waiting for someone to write the article. :-) User:Evercat 19:55, 18 Oct 2003 (UTC) :: Ok thanks. Then there was no such article? User:Pakaran 19:59, 18 Oct 2003 (UTC) : Apparently not. There's no indication that it ever existed (and was deleted). User: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 :) User: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? User: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. Albert 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 number 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. -- User:Cyan 06:07, 24 Jan 2004 (UTC) ------ Isn't Schrödinger's cat a scientific paradox? User: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. User: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? User: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 [http://plato.stanford.edu/entries/paradox-stpetersburg/ external link] 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). -- User: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? User:Paullusmagnus 18:32, 26 Feb 2004 (UTC) <''end of copied text''> Sounds good to me. I'll do it. -- User:Cyan 18:44, 26 Feb 2004 (UTC) Does this need to be locked? User:PakaranUser talk: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? --User: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. User: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. --User:Camembert :Edit warriors get into edit wars as a matter of principle. The obscurity of the issue has nothing to do with it. -- User:Arvindn 07:54, 18 Mar 2004 (UTC) I'm ''really'' hoping for a reply from the involved parties. --User:Camembert :Perhaps you should leave a message for them on their respective talk pages. -- User:Cyan 19:45, 18 Mar 2004 (UTC) == 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 09:45, Jul 15, 2004 (UTC) == new pic == I like the new pic lots better, hoorah! User:Sam Spade http://en.wikipedia.org/w/wiki.phtml?title=User_talk:Sam_Spade&action=edit§ion=new Spade 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. User: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. User:Anthony DiPierro User:Anthony_DiPierro/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! User: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. --User: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? -- User: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?
Paradox
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P
PA | PB | PC | PD | PE | PF | PG | PH | PI | PJ | PK | PL | PM | PN | PO | PR | PS | PT | PU | PW | PX | PY | PZ |Words begining with Paradox:
Paradox
Paradox
Paradox
Paradox01
Paradox2
Paradox2
Paradox3
Paradox460
Paradox76
Paradoxband
Paradoxes
Paradoxes
Paradoxes_of_Zeno
Paradoxian
Paradoxian
Paradoxic
Paradoxic
Paradoxical
Paradoxically
Paradoxical_combinator
Paradoxical_Escape
Paradoxical_intention
Paradoxical_reaction
Paradoxical_sleep
Paradoxist_distich
Paradoxist_distich
Paradoxography
Paradoxography
Paradoxornithidae
Paradoxurus_hermaphroditus
Paradoxx
Paradoxymoron
Paradox_(database)
Paradox_(disambiguation)
Paradox_(disambiguation)
Paradox_(software)
Paradox_Entertainment
Paradox_games
Paradox_Interactive
Paradox_Interactive
Paradox_of_entailment
Paradox_of_happiness
Paradox_of_hedonism
Paradox_of_hedonism
Paradox_of_the_heap
Paradox_of_the_heap
Paradox_of_thrift
Paradox_of_thrift
Paradox_Poetry
Paradox_Poetry.com
Paradox_sector
Paradox_theorem_prover
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