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- 1 Method to the madness
- 2 paradox ?????.......
- 3 The Paradox of Abraham
- 4 Impossible Directive
- 5 "VIGILANCE PARADOX"
- 6 This article appears to contradict itself
- 7 Sports Paradox
- 8 Definition
- 9 To technical?
- 10 Example given of howlers (Paradox) - alternate solution
- 11 Weed Paradox
- 12 Curry's paradox unresolved?
- 13 This is wrong
- 14 Russell's paradox, naive set theory and sources
- 15 Dialetheic paradoxes
- 16 "Appears to contradict itself": confusing and wrong definition
- 17 Anything is Possible paradox
- 18 "Is the answer to this question 'No'?"
Method to the madness
Well in a previous scene Polonius suggested to the Queen that true madness can only be defined as nothing but being mad, so in this scene he mentions another element (method) which corrupts his definition. That's not really what I mean though, which is that the aside in which he says there is a method in the madness served to reinforce the charade to the audience. There is no paradox because he wasn't mad, and paradoxes rely on definitional rigidity. 126.96.36.199 (talk) 12:51, 5 January 2011 (UTC)
if a man created a worm hole,by which he could go only 1hr back in time,goes through it and killed his own past,simply asking what would happen. ronitd 13:31, 3 June 2011 (UTC) — Preceding unsigned comment added by Ronitd (talk • contribs)
If a man could create a worm-hole and went back in time 1 hour, he would erase the last hour, and also erase when he went into the worm-hole, so in effect he never went back in time.Flight Risk (talk) 18:31, 11 December 2013 (UTC)
The Paradox of Abraham
Søren Kierkegaards "Fear and Trembling" brings the religious and ethical paradox of faith/belief through Abrahams willingness to sacrifice his son Isaac, whom he loves, to God. I would just recommend this book to anyone who finds an unresolved paradox interesting. What makes Abraham above the ethical, and so not a contemplating murderer? — Preceding unsigned comment added by 188.8.131.52 (talk) 13:13, 4 June 2011 (UTC)
How would one classify an impossible directive, like one that we see all the time ...
This is a test. Please ignore this message.
If I ignore this message, I am acknowledging it. If I respond to it, I am ignoring it. Thus, it's a directive that is impossible to follow. I'd guess that this is some sort of paradox. WHPratt (talk) 19:06, 7 July 2011 (UTC)
If you respond to the message, you are not ignoring it, but what it says (the directive). Even ignoring it is a response. Kenneyw (talk) 11:06, 20 January 2012 (UTC)
Of course, the sender of the message wants the recipient to do nothing. Thus, the statement ought to read something like "This message is a test. Please do not take any action regarding it." However, the other form, a directive that directs that its directions be ignored is paradoxical. WHPratt (talk) 13:21, 17 May 2012 (UTC)
Just saw a sign today in my building: "THIS DOOR MUST REMAIN CLOSED AT ALL TIMES." As it's also labeled a Fire Exit, it obviously isn't secured. So, said door can be opened; it's just that, to comply with the directive, you mustn't do so. Not ever. However, it's a commonly used route to a main stairwell to the other floors, so what they really want to say is to "Keep this door closed except when you're using it." One might argue that a door that remains closed at all times isn't really a door at all, it's just part of the wall. WHPratt (talk) 14:12, 28 March 2013 (UTC)
Does anyone have any information on the history of the "Vigilance Paradox"? I heard about this paradox a few days back, and can't seem to track down what it is. It's very important that I find out.
This article appears to contradict itself
I'll leave it to some expert to classify, but a once-good pitcher having a very bad season once said "It takes a good pitcher to lose 20 games."
The point is not, of course, that losing games is a good thing, but that only a pitcher of proven ability will get the chance to get that many decisions. If the team didn't have confidence in him, they'd stop using him well before 20 losses. WHPratt (talk) 18:56, 29 November 2011 (UTC)
Another. Discussing the wisdom of Yogi Berra on the talk page for his article, I recalled this story: someoned is asking Yogi for an opinion about organized Little League baseball. He told about his youth in the summer time, how he and his friends would rise early and play softball all morning, eat a sandwich under a tree, then play hardball until it got dark, really dark. All day, every day. In Little League, he noted, you play two innings and they have to take you out and put in another kid. Why, he said, you can't even learn to strike out in that amount of time. This suggests that in attaining mastery of some subject, even the negative things, like striking out properly have to be learned. One can imagine there are lots of variants on this theme. I suspect that Yogi may be a source of more paradoxes as well. WHPratt (talk) 14:34, 31 January 2012 (UTC)
- Yes, I agree. This page demonstrates a clear problem that I see on Wikipedia quite often. It is dominated by the overtly-rational, "left-brain"-oriented way of knowing that suggests that all things can be resolved through direct logic and clear description. It has a connection to analytic philosophy and some weird sort of Physicalism that seeks to deny that some things exist. If a paradox is a contradiction, it has a link to an aporia, in the sense that puzzlement and confusion may lead to ideas and perceptions that simply contradict and cannot be resolved. That's it. But, to accept this irreconcilability is not enough.
- Accepting that some things cannot be resolved, requires what Keats suggested, that we must to be able to "stand comfortably in uncertainty, Mystery, doubt" within his definition of Negative capability. Here, and elsewhere on Wikipedia, there is tendency to deny that there any "uncertainty, Mystery, doubt" in the world, but only our failure to think rationally or clearly enough about it. I would argue that is a problem not with the world, or with rationality, but a problem with the human mind.
- The human mind needs to know and does not like not knowing, thus we have a tendency to turn away from mystery and doubt and pretend it does not exist. Thus, the paradox is described as merely as a "confusion" or "tautology" and not contradiction that perhaps, cannot be reconciled. Edunoramus (talk) 15:36, 10 March 2012 (UTC)
- Here's the former lede on the article, when it was a featured article on Wikipedia back in 2004: "A paradox is an apparently true statement that seems to lead to a logical self-contradiction, or to a situation that contradicts common intuition. The identification of a paradox based on seemingly simple and reasonable concepts has often led to significant advances in science, philosophy and mathematics. In moral philosophy, paradox plays a particularly central role in debates on ethics, particularly in the form of ethical dilemmas. Common themes in paradoxes include direct and indirect self-reference, infinity, circular definitions, and confusion of levels of reasoning." Edunoramus (talk) 15:56, 10 March 2012 (UTC)
- There are at least four definitions of paradox that are quite popular in philosophy. They come from William Lycan (from his 2010 "What, exactly, is a paradox?"), Roy Sorensen (from his 2003 "A Brief History of the Paradox"), John Corcoran (from his 1989 "Argumentations and Logic"), and W.V.O. Quine (from his 1966 "The Ways of Paradox"). Any one of them would benefit the article quite a bit. They all have the commonality of a paradox arising when there is a surprising juxtaposition of (seeming) truth-values of statements. Being this general, it is incorrect to say that paradoxes in science and mathematics need to be distinguished from paradoxes in philosophy (though, perhaps it is helpful to distinguish between deductive paradoxes and inductive ones). In fact, most of the paradoxes which have been very influential in philosophy come from physics (e.g. Zeno's paradoxes, grandfather paradox, EPR paradox) and foundations of mathematics (e.g. Russell's Paradox, Lowenheim-Skolem Paradox). — Preceding unsigned comment added by 184.108.40.206 (talk) 19:01, 5 April 2012 (UTC)
- It would then seem prudent to split this page further to explain the idiosyncratic variance between what is expected and the end result, as this seems to be the core issue that has sprung up around paradox
- "Patrick Hughes outlines three laws of the paradox:" it says. I'm a bit puzzled as to why "This statement is false" appears three separate times. I can't find the original, presumably three laws but it does seem plausible to simplify this portion of the text to remove the superfluous. Mizusajt (talk) 17:45, 22 June 2012 (UTC)
It can give you a head ache but with a little reading I think it makes sense.
Example given of howlers (Paradox) - alternate solution
Slightly past half-way down the section, Logical paradox, is an example given in which a father and son are driving down the road. The surgeon does not have to be the boy's mother for the story to be non-contradictory. I suggest that the "father" mentioned at the beginning of the story might be referring to the boy's father, as in priest, in which case the boy can have two fathers without the story being contradictory.
Christopher, Salem, OR (talk) 08:37, 26 May 2013 (UTC)
Is there any classification known as a Weed Paradox (or some similar term)?
Many herbariums and botanical institutions maintain weed gardens, for the sake of completeness, and probably to support research on controlling these.
The defintion of "weed" usually centers about a plant that grows where is isn't wanted, where it shouldn't be growing.
So, a weed in a weed garden isn't a weed, as that's where weeds belong. Gather together enough weeds, and they cease being weeds. (Presumably, if a pretty flower pops up there, it gets removed.)
Curry's paradox unresolved?
I wonder what makes Curry's paradox unresolved. It seems to me that it is as much resolved as the Liars Paradox and in a similar way. This is also expressed in the Article for Curry's paradox. Mordoron (talk) 13:53, 31 October 2013 (UTC)
- "Curry's paradox can be formulated in any language supporting basic logic operations that also allows a self-recursive function to be constructed as an expression."
- To solve it, you have to give up either at least one basic logic operation or recursive statements. Either way, you get a pain in the ass. Same goes for the liar. Paradoctor (talk) 00:00, 1 November 2013 (UTC)
- Thank you. I agree with your statement. I take it you argue that in order to "resolve" the paradox we have to revert to using a natural language in which the paradox can not be formulated. This interpretation of the word "resolve" seems too strict to me. The use of the word "yet" is also misleading in my opinion. It infers that some future knowledge or understanding is lacking in order for us to resolve the paradox. Is that really possible in view of the above interpretation of "resolve"?
- In any case, it seems misleading to argue that Curry's paradox (and by the same logic Liar's) is "unresolved", where in the appropriate articles there are 3 paragraphs dedicated to the resolution (Curry's), and at least 6 great philosophers giving their resolution (Liar's). At the very least, I would change the sentence "Others, such as Curry's paradox, are not yet resolved." to "Others, such as Curry's paradox and Liar's paradox are examples that some sentences in natural language can not be consistently assigned a truth value" Mordoron (talk) 13:09, 8 November 2013 (UTC)
This is wrong
|“||'Nothing is Impossible', meaning that it is impossible for something to be impossible, thus contradicting itself.||”|
Nothing literally means "not a thing". So by definition, nothing is the absence of "something" (or more specifically all things that exist or are 'some thing'). So "nothing is impossible" is in fact not a self-contradicting statement, because it literally means "not a thing is impossible", which refers to physical existence. Any thing that exists is possible, by virtue of it's own existence. Nothing is the absence of existence and thus not "something". — Preceding unsigned comment added by 220.127.116.11 (talk) 03:59, 2 November 2013 (UTC)
- Nothing doesn't mean "not a thing". It means "no thing". Britmax (talk) 05:07, 2 November 2013 (UTC)
- Can you give me an example of nothing then? If nothing is "no thing" then what exactly is it? I don't see how the statement "No thing is impossible" could possibly imply that "something is impossible". "No thing" is the exact opposite of "some thing".
- This might seem pedantic, but it is an important distinction. Just because we use this phrase rather freely in everyday life does not mean that we can just equivocate "nothing" with "something" and subsequently argue that it is a self-contradicting statement. It might be a vacous statement, but that doesn't make it self-contradicting. — Preceding unsigned comment added by 18.104.22.168 (talk) 05:36, 2 November 2013 (UTC)
- Thank you.
- In the article about the exception paradox it is argued that "If everything is possible, then it is possible for anything to be impossible.", but this argument seems to be making the same categorical error.
- In one category we have the category of all things that are possible. In this specific case this would include all things, with no exception ("Everything is possible without exception"), the second category of things that are impossible would subsequently be empty. I don't see how you then get to "everything is impossible" which is the exact opposite of that statement. If everything was indeed possible, no thing would be impossible.
- This argument, again seems to making the same fallacy of equivocation, where the words possible and impossible are equivocated to mean the same thing, even though they mean the exact opposite. If everything is possible, no thing is impossible. There is no paradox there. 22.214.171.124 (talk) 18:56, 2 November 2013 (UTC)
Russell's paradox, naive set theory and sources
Among the problems we have is that the assertion that "Russell's paradox [...] showed that naive set theory was flawed." is, well, flawed. Firstly, the source cited appears to be an undergraduate dissertion which we would not normally regard as a reliable source: see WP:SCHOLARSHIP. Secondly the source states clearly that Russell found an inconsistency in Frege's axiomatic set theory. A later remark is "the (naïve) set theory of Frege leads to a contradiction". So the source, if reliable, only supports the claim that one particular naive set theory is flawed. The distinction between an axiomatic theory and a naive theory is not resolved. However, I suggest that what Russell's paradox showed was that a development of set theory in which sets are identified with properties is flawed, since the property "is not a member of itself" cannot (consistently) be identified with a set. Deltahedron (talk) 11:24, 11 May 2014 (UTC)
- Definitive improvement, you didn't have to justify it on my account. Paradoctor (talk) 12:01, 11 May 2014 (UTC)
I'm having trouble with these citations. I don't see how they support the claim that some religious teachings classify some paradoxes as dialetheias. I couldn't access the Graham book, but neither of the other sources mentions paradoxical statements as being considered both true and false at the same time. Please note that one of them must obtain independent of the other. Merely holding that a statement would be true iff it was false is simple logic, not a dialetheia. Paradoctor (talk) 15:12, 3 November 2014 (UTC)
- It's not all religion. There are multiple Eastern traditions. The South Asian traditions can be religious, in the Western sense (in fact one could argue that Western religious traditions stem from India). However the East Asian traditions have secular empire mixed up with them. It is part of Chinese literature that Empire is to be ruled by ritual ("You won the world on horseback, but you will lose it on horseback"— said the scholar-bureaucrat to the founder of the Han dynasty, meaning that appeal to rite is necessary to rule an empire peacefully, and not all rites are religious, for example, a rite of passage.). Perhaps I might email you p.334 of Graham. Failing that, might I recommend Joseph Needham Science and Civilisation in China (I admit it's 27 volumes and counting). Briefly, Chinese civilization is old, wise, and vital (capable of resilient response to change). So the formulations of the Mohists, 2200 years ago, were subsumed into the literature of China, long ago. --Ancheta Wis (talk | contribs) 17:43, 4 November 2014 (UTC)
- There are other sources of paradox:
- Ivan Niven (1959) Mathematics: a House built on Sand?,
- Galileo (1638) Two new sciences, his discovery of a hierarchy of infinities
- Mandate of heaven -- it's not 'divine right of kings', it's 'winner take all', after cutting the Gordian knot. After all, Aristotle was the teacher of the man who cut it. --17:43, 4 November 2014 (UTC)
"Appears to contradict itself": confusing and wrong definition
The article opens with the definitive claim that paradoxes appear to contradict themselves. That's inconsistent with some of the classic paradoxes in philosophy as well as examples the article proceeds to give. For instance, the Ship of Theseus story doesn't contradict itself at all--it just illustrates the paradoxical idea that two things can be identical while sharing none of the same parts. Similarly, Zeno's paradox that motion is impossible doesn't contradict itself. It just contradicts what seems to be the case, namely, that sometimes things move. The same goes with the Socratic paradoxes like everyone seeks the good and weakness of will is impossible.
The problematic definition seems to be uncritically lifted from general purpose dictionaries. That's probably not a good idea, given that the dominant use of paradox as a concept is technical, viz., in the sense used by philosophy and logic.126.96.36.199 (talk) 14:24, 27 January 2015 (UTC) (This post was edited to fix a mistake on 1/28. Same user, different IP:188.8.131.52 (talk) 17:56, 28 January 2015 (UTC))
pandion-enwiki 10/28/2015 14:43 EDT - here's a more complete definition: a statement or proposition that, despite sound (or apparently sound) reasoning from acceptable premises, leads to a conclusion that seems senseless, logically unacceptable, or self-contradictory. — Preceding unsigned comment added by Pandion~enwiki (talk • contribs) 18:43, 27 October 2015 (UTC)
Anything is Possible paradox
It can be explained simply as:
If anything is possible, then it could be false because it's possible.
"Is the answer to this question 'No'?"
This question has multiple answers. The paradoxical responses are "yes", "no", and all affirmative responses. However, we are not required to use them; we can use unsure responses, such as "I don't know". We can also use terms synonymous with "no", such as "it isn't".— Preceding unsigned comment added by 184.108.40.206 (talk) 23:24, 30 October 2015 (UTC)