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Topic: Reductio ad absurdum

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	Reductio ad Absurdum [Internet Encyclopedia of Philosophy]
		Reductio ad absurdum is a mode of argumentation that seeks to establish a contention by deriving an absurdity from its denial, thus arguing that a thesis must be accepted because its rejection would be untenable.
		The first of these is reductio ad absurdum in its strictest construction and the other two cases involve a rather wider and looser sense of the term.
		A classic instance of reductio reasoning in Greek mathematics relates to the discovery by Pythagoras - disclosed to the chagrin of his associates by Hippasus of Metapontum in the fifth century BC - of the incommensurability of the diagonal of a square with its sides.
	www.iep.utm.edu /r/reductio.htm (2568 words)

	NationMaster - Encyclopedia: Reductio Ad Absurdum (Site not responding. Last check: )
		Reductio ad absurdum is also often used to describe an argument where a conclusion is derived in the belief that everyone (or at least those being argued against) will accept that it is false or absurd.
		The argument from ignorance, also known as argumentum ad ignorantiam (appeal to ignorance [1]) or argument by lack of imagination, is a logical fallacy in which it is claimed that a premise is true only because it has not been proven false, or that a premise is false only because...
		In mathematical logic, the reductio ad absurdum is represented as: Mathematical logic is a subfield of mathematics that is concerned with formal systems in relation to the way that they encode intuitive concepts of mathematical objects such as sets and numbers, proofs, and computation.
	www.nationmaster.com /encyclopedia/Reductio-Ad-Absurdum (2366 words)

	Kids.Net.Au - Encyclopedia > Reductio ad absurdum
		Reductio ad absurdum (from Latin reduced to an absurdity) is type of logical argument, also known as proof by contradiction.
		Although it is quite freely used in mathematical proofs, not every school of mathematical thought accepts reductio ad absurdum arguments as universally valid.
		In symbolic logic, the reductio ad absurdum is represented as:
	www.kids.net.au /encyclopedia-wiki/re/Reductio_ad_absurdum (599 words)

	Reference.com/Encyclopedia/Reductio ad absurdum
		Reductio ad absurdum is also often used to describe an argument where a conclusion is derived in the belief that everyone (or at least those being argued against) will accept that it is false or absurd.
		Mathematical proofs are sometimes constructed using reductio ad absurdum, by first assuming the opposite of the theorem the presenter wishes to prove, then reasoning logically from that assumption until presented with a contradiction.
		When reductio ad absurdum is in error, it is because of a fallacy in the reasoning used to arrive at the contradiction, not the act of reduction itself.
	www.reference.com /browse/wiki/Apagogical_argument (1614 words)

	REDUCTIO AD HITLERUM : Encyclopedia Entry
		The term reductio ad Hitlerum (sometimes rendered reductio ad Hitlerem)—whimsical Latin for "reduction to Hitler"—was originally coined by University of Chicago professor and ethicist Leo Strauss.
		The reductio ad Hitlerum fallacy is of the form "Adolf Hitler (or the Nazi party) supported X; therefore X must be evil".
		For example, a reductio ad Stalinum could assert that corporal punishment of wayward children is necessary because Josef Stalin enacted its abolition, or that atheism is a dangerous philosophy because Stalin was an atheist.
	www.bibleocean.com /OmniDefinition/Reductio_ad_Hitlerum (759 words)

	Worldcon 2005 UK - Friday Night Play
		Reductio Ad Absurdum were asked by Interaction to present a brand new show for the Worldcon.
		The usual Reductio cast of three was augmented to eight in an attempt to fill the huge stage and share the blame.
		Reductio Ad Absurdum was formed in 1995 to perform Dune, or the Sand of Music at Intersection, the previous Glasgow Worldcon.
	www.interaction.worldcon.org.uk /progplay.htm (653 words)

	Reductio ad Absurdum [Internet Encyclopedia of Philosophy]
		Reductio ad absurdum is a mode of argumentation that seeks to establish a contention by deriving an absurdity from its denial, thus arguing that a thesis must be accepted because its rejection would be untenable.
		The first of these is reductio ad absurdum in its strictest construction and the other two cases involve a rather wider and looser sense of the term.
		A classic instance of reductio reasoning in Greek mathematics relates to the discovery by Pythagoras - disclosed to the chagrin of his associates by Hippasus of Metapontum in the fifth century BC - of the incommensurability of the diagonal of a square with its sides.
	www.utm.edu /research/iep/r/reductio.htm (2568 words)

	Reductio ad absurdum (Site not responding. Last check: )
		A recent, fairly well-known example of reductio ad absurdum is Bobby Henderson's notion of the Flying Spaghetti Monster, used to parody efforts by creationists and believers in intelligent design to teach such theories in science classes, instead of or in addition to evolution.
		His argument is that, given the arguments used by creationists and supporters of intelligent design, his lighthearted theory that a flying spaghetti monster created the world has an equally legitimate claim to a place in the science curriculum.
		In mathematical logic, the reductio ad absurdum is represented as:
	en.askmore.net /Reductio_ad_absurdum.htm (1557 words)

	[No title]
		The reductio ad absurdum of the open borders policy proposed by the more extreme and irresponsible of the compassion-peddlers is a huge movement of capital and talent from poor countries to rich countries.
		Reductio ad absurdum is a logical tactic which consists of assuming the negation of the thing you want to prove, and then showing that thatassumption leads to a direct contradiction.
		The reductio ad absurdum of Krugman’s argument is a media organization that receives its funding from the government is freer from government influence than those media organizations that are merely regulated by the government.
	www.lycos.com /info/reductio-ad-absurdum.html (490 words)

	Reductio Ad Absurdum – The Consequences of an Argument : ChristianCourier.com
		Reductio Ad Absurdum – The Consequences of an Argument
		One format the Lord occasionally used is known as ad hominem, a Latin expression meaning, “to the man.” This line of argument is not designed to establish positive truth; rather, it is a form of refutation whereby the inconsistency of error is exposed.
		Many are familiar with a bizarre teaching that has come to be known as the “A.D. 70 doctrine.” Popularized by Max King and a small cluster of his zealots, this theory alleges that all Bible prophecy was fulfilled by A.D. 70, the year in which Jerusalem was destroyed by the Romans.
	www.christiancourier.com /archives/reductioAdAbsurdum.htm (1684 words)

	"reductio ad absurdum", by Lin Charlston -- HOW2 (Site not responding. Last check: )
		The artist's book 'reductio ad absurdum' is a facsimile of my improvised writing on the nature of time.
		I begin with the assertion that time is the only reality, but the argument develops into a personal response to the tyranny of mechanical time and concludes that the constraints of time are an illusion.
		In 'reductio ad absurdum' I have included non-linguistic features observed in other notebooks such as leaving the verso of the pages blank for later use, cut-away pages and further entries starting from the back page.
	www.asu.edu /pipercwcenter/how2journal/current/bookarts/charlston.html (357 words)

	Reductio ad Hitlerum - Biocrawler (Site not responding. Last check: )
		The term Reductio ad Hitlerum (fake Latin for "reduction to Hitler") was originally coined by University of Chicago Classics professor and ethicist Leo Strauss.
		The phrase comes from the more well-known logical argument, reductio ad absurdum.
		The "reductio ad Hitlerum" fallacy is a special case of the genetic fallacy, of the form "Adolf Hitler, or the Nazi party, supported X, therefore X must be evil".
	www.biocrawler.com /encyclopedia/Reductio_ad_Hitlerum (236 words)

	PlanetMath: terms from foreign languages used in mathematics (html version)
		a fortiori, a priori, ad absurdum, ad infinitum, Ansatz, cf., confer, doh, eigen, espace, et al., et alii, étale, étalé, e.g., exempli gratia, ibid., ibidem, i.e., id est, inter alia, logarithmus binaris, binary logarithm, logarithmus generalis, general logarithm, logarithmus naturalis, natural logarithm, loc.
		I would like to point out that being active in PM helps me. Adding entries helps cement mathematical concepts in my mind, and it also gives me practice using TeX, at which I was somewhat rusty a month ago.
		One thing that I hope will happen is that people are able to access information that will help them understand mathematical concepts, give them ideas for how to explain mathematics (especially important in the case of teachers), and stimulate their curiosity in higher mathematics and/or fields of mathematics with which they might not be familiar.
	www.planetmath.org /encyclopedia/ReductioAdAbsurdum.html (858 words)

	Reductio Ad Absurdum
		Reductio ad absurdum is the process by which an hypothesis is proved by showing the opposite to be impossible.
		It is clearly impossible for a number to be both even and odd, so the square root of two must not be "some ratio of whole numbers".
		The term reductio ad absurdum actually comes from Medieval Latin and basically means "reduction to absurdity".
	www.indepthinfo.com /articles/reductio-ad-absurdum.shtml (342 words)

	Tutorial- Reductio ad Absurdum
		Conditional proof (CP) can be used to prove a conditional statement by making an assumption that is used to derive a consequent which, in turn, justifies a conditional conclusion.
		The Latin phrase means a reduction to absurdity or contradiction; the technique is to show that if we accept the premises of an argument, but deny the conclusion, we contradict ourselves.
		The reductio ad absurdum technique is to take the negation of the conclusion, add it as an assumption (just as in conditional proof), and then from the premises and that assumption, derive a contradiction--a statement of the form p
	www.wwnorton.com /college/phil/logic3/ch13/reductio.htm (403 words)

	CATHOLIC ENCYCLOPEDIA: Zeno of Elea
		There were, it seems, several discourses, in each of which he made a supposition, or hypothesis, and then proceeded to show the absurd consequences that would follow.
		This is now known as the method of indirect proof, or reductio ad absurdum, and it appears to have been used first by Zeno.
		Aristotle in his "Physics" has preserved the arguments by which Zeno tried to prove that motion is only apparent, or that real motion is an absurdity.
	www.newadvent.org /cathen/15756b.htm (332 words)

	Reductio ad Hitlerum - Education - Information - Educational Resources - Encyclopedia - Music
		The term Reductio ad Hitlerum was originally coined by University of Chicago Classics professor and ethicist Leo Strauss.
		The "reductio ad Hitlerum" fallacy is a special case of the genetic fallacy, of the form "Adolf Hitler, or the Nazi party, supported X, therefore X must be evil".
		The fallacious nature of this argument is best illustrated by identifying "X" as something that Adolf Hitler or his minions did support but is not considered evil, setting X = "vegetarianism" or X = "breathing in and out".
	www.music.us /education/R/Reductio-ad-Hitlerum.htm (347 words)

	The Ayn Rand Institute: Reductio ad Totalitarianism
		Critics first imagined fast-food litigation as a "reductio ad absurdum"--a reduction to absurdity--of the lawsuits against tobacco companies.
		The problem with the "reductio ad absurdum" argument, one of my philosophy teachers once warned me, is that your opponent may simply embrace the logical end result of his ideas--no matter how absurd it is. And that's exactly what is happening now.
		The anti-fast-food suits are a logical extension of the premise behind the anti-tobacco suits: the denial of individual responsibility.
	www.aynrand.org /site/News2?JServSessionIdr006=mq5tuqxyz1.app14b&page=NewsArticle&id=7436 (853 words)

	Reductio Ad Absurdum
		Proof by reductio ad absurdum (from Latin words meaning "reducing to an absurdity") is an interesting and useful technique.
		Here's another simple example of reductio ad absurdum, which Euclid used to prove the infinitude of primes.
		Thus, no matter how large a finite set of primes we have, we can always prove that there is a prime that is not in the set, and therefore there are infinitely many primes.
	www.cpax.org.uk /maths/reductio.php (556 words)

	Reductio ad absurdum - Definition, explanation
		In each case, B has used a reduction to the absurd to argue his or her point.
		Among some people, there is a misconception that reductio ad absurdum just means "a silly argument".
		In the above, p is the proposition we wish to prove; and S is a set of statements which are given as true — these could be, for example, the axioms of the theory we are working in, or earlier theorems we can build upon.
	www.calsky.com /lexikon/en/txt/r/re/reductio_ad_absurdum.php (938 words)

	The Law of the Excluded Middle
		This is a method of proof: to prove a statement A, take a contrary hypothesis, reason from this to an absurdity, conclude (by consistency) that the contrary hypothesis is false, whence (by completeness) that A is true.
		Now, reductio is deeply entrenched in the corpus of mathematical knowledge: with the standard definition of continuity, reductio is required in most proofs that a function is continuous - to give but one example.
		Fortunately, many uses of the law of reductio can be avoided - typically by replacing some axioms and definitions with ones which reductio would render equivalent, but which actually imply the things we want without needing negation; and frequently the result proved is similarly one which reductio would render equivalent to the result originally proved.
	www.chaos.org.uk /~eddy/math/found/reductio.html (1234 words)

	absurdum A Bookmarks
		Simplistic viewConcord Monitor, NH - 44 minutes agoNext, the bulk of your argument combined "straw man" with reductio ad absurdum.
		What do writers read?Charlotte Observer, NC - Feb 16, 2007"Lists, unless grocery shopping lists, are truly a reductio ad absurdum." (Her selections, which she says she provided "just so you'll give it a rest,"...
		Why the IPCC bomb was a dudHuffington Post, NY - Feb 6, 2007This is something of a reductio ad absurdum of the deep conviction among progressives that "getting the facts out" is the primary challenge around climate...
	www.iaswww.com /ODP/Bookmarks/A/absurdum (281 words)

	2nd Refutation of the Reductio ad Absurdum Argument for a Pauline Papacy
		Reductio ad absurdum arguments only succeed when they start with the actual premises of the argument being criticized.
		The reductio ad absurdum only succeeds if the counter-arguments are based on fact as well; this gives them their "punch" and effectiveness as rhetoric and argumentation.
		Since a reductio advanced against your own belief or position will begin with a statement of your belief as a premiss, you must either attack the logic of the argument presented or you must be ready to endorse the conclusion.
	ic.net /~erasmus/RAZ353.HTM (14767 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal (Site not responding. Last check: )
		The following is a trickier reduction, but one which is stronger from the philosophical point of view because it does not rely on A's accepting that C's opinion is wrong:
		He says that if all his friends who had previously jumped off cliffs reported it to have been an enjoyable and worthwhile experience, and in the absence of evidence to the contrary, he would indeed follow suit: "A better question would be, 'If everyone wore clothes, would you do it?'"
		The procedure is to show that assuming p leads to a logical contradiction.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=reductio_ad_absurdum (1249 words)

	The Enneagram Institute Discussion Board - Sociopaths
		I think it goes this way: someone proves wrong P with a reductio ad absurdum that ends to Q; the modus tollens in order to prove that P doesn't actually lead to Q, therefore it's valid.
		Doesn't a reductio ad absurdum that proves not P, by definition, start with P and end with not P i.e.
		Reductio ad absurdum is a method of proof whereby one assumes the opposite of what one is trying to prove and then shows that this leads to a contradiction, thus proving that the opposite of the opposite (i.e.
	www.enneagraminstitute.com /forum/topic.asp?TOPIC_ID=12453&whichpage=7 (4801 words)

	HU250 Short Cut Method
		First, we need to say what reductio ad absurdum is. It is a argumentative strategy to attack a thesis, hypothesis, suggestion, etc. In other words, you are trying to show that some statement is false.
		When we use the short cut method, we first assume the argument is invalid, which is the hypothesis H, and then fill in truth values for statement letters that this assumption forces.
		If we are forced into a contradiction, we use reductio ad absurdum to infer that H is false (i.e, the argument is valid).
	www.hu.mtu.edu /~wsewell/hu250/shortcut.htm (802 words)

	Math Forum Discussions (Site not responding. Last check: )
		as the protypical) reductio ad absurdum proof is merely clutter.
		proof of the theorem as a whole is a reductio ad absurdum.
		reductio ad absurdum that G is not equal to A, B or C. You could even
	www.mathforum.com /kb/message.jspa?messageID=4161656&tstart=0 (2257 words)

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