XPost: alt.fan.rush-limbaugh, can.politics, alt.politics.liberalism
XPost: alt.politics.democrats, alt.politics.usa.republican
On Fri, 15 Sep 2023 09:55:46 -0700 (PDT),
edell@post.com says...
The superintendent is right. This is about what is right and what is
wrong, so the question is why do liberals want pornographic materials
in our schools?
A better question is why do kids get easy access to, or "accidentally stumble upon," porn on the net? Who is letting them get away with that? Like, parents maybe too busy to screen their kids' online activities? Time to throw computers out of homes.
Reductio ad absurdum
In logic, reductio ad absurdum (Latin for "reduction to absurdity"), also known as argumentum ad absurdum (Latin for "argument to absurdity") or apagogical arguments, is the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to absurdity or contradiction. This argument form traces back to Ancient Greek philosophy and has been used throughout history in both formal mathematical and philosophical reasoning, as well as in debate. The equivalent formal rule is known as negation introduction. A related mathematical proof technique is called proof by contradiction.
Examples
The "absurd" conclusion of a reductio ad absurdum argument can take a range of forms, as these examples show:
The Earth cannot be flat; otherwise, since the Earth is assumed to be finite in extent, we would find people falling off the edge.
There is no smallest positive rational number because, if there were, then it could be divided by two to get a smaller one.
The first example argues that denial of the premise would result in a ridiculous conclusion, against the evidence of our senses. The second example is a mathematical proof by contradiction (also known as an indirect proof), which argues that the denial of the premise would result in a logical contradiction (there is a "smallest" number and yet there is a number smaller than it).
Greek philosophy
Reductio ad absurdum was used throughout Greek philosophy. The earliest example of a reductio argument can be found in a satirical poem attributed to Xenophanes of Colophon (c. 570 - c. 475 BCE). Criticizing Homer's attribution of human faults to the gods, Xenophanes states that humans also believe that the gods" bodies have human form. But if horses and oxen could draw, they would draw the gods with horse and ox bodies. The gods cannot have both forms, so this is a contradiction. Therefore, the attribution of other human characteristics to the gods, such as human faults, is also false.
Greek mathematicians proved fundamental propositions using reductio ad absurdum. Euclid of Alexandria (mid-4th - mid-3rd centuries BCE) and Archimedes of Syracuse (c.?287 - c.?212 BCE) are two very early examples.
The earlier dialogues of Plato (424-348 BCE), relating the discourses of Socrates, raised the use of reductio arguments to a formal dialectical method (elenchus), also called the Socratic method. Typically, Socrates" opponent would make what would seem to be an innocuous assertion. In response, Socrates, via a step-by-step train of reasoning, bringing in other background assumptions, would make the person admit that the assertion resulted in an absurd or contradictory conclusion, forcing him to abandon his assertion and adopt a position of aporia.
The technique was also a focus of the work of Aristotle (384-322 BCE), particularly in his Prior Analytics where he referred to it as "demonstration to the impossible", 62b).
Another example of this technique is found in the sorites paradox, where it was argued that if 1,000,000 grains of sand formed a heap, and removing one grain from a heap left it a heap, then a single grain of sand (or even no grains) forms a heap.
Buddhist philosophy
Much of Madhyamaka Buddhist philosophy centers on showing how various essentialist ideas have absurd conclusions through reductio ad absurdum arguments (known as prasa?ga, "consequence" in Sanskrit). In the Mulamadhyamakakarika, Nagarjuna's reductio ad absurdum arguments are used to show that any theory of substance or essence was unsustainable and therefore, phenomena (dharmas) such as change, causality, and sense perception were empty (sunya) of any essential existence. Nagarjuna's main goal is often seen by scholars as refuting the essentialism of certain Buddhist Abhidharma schools (mainly Vaibhasika) which posited theories of svabhava (essential nature) and also the Hindu Nyaya and Vaise?ika schools which posited a theory of ontological substances (dravyatas).
Principle of non-contradiction
Aristotle clarified the connection between contradiction and falsity in his principle of non-contradiction, which states that a proposition cannot be both true and false. That is, a proposition Q {\displaystyle Q} Q and its negation
Q {\displaystyle \lnot Q} {\displaystyle \lnot Q} (not-Q) cannot both be true. Therefore, if a proposition and its negation can both be derived logically from a premise, it can be concluded that the premise is false. This technique, known as indirect proof or proof by contradiction, has formed the basis of reductio ad absurdum arguments in formal fields such as logic and mathematics.
See also
Appeal to ridicule
Argument from fallacy
Contraposition
List of Latin phrases
Mathematical proof
Prasangika
Slippery slope
Strawman
Sources
Hyde, Dominic; Raffman, Diana (2018). "Sorites Paradox". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy (Summer 2018 ed.).
Pasti, Mary. Reductio Ad Absurdum: An Exercise in the Study of Population Change. United States, Cornell University, Jan., 1977.
Daigle, Robert W.. The Reductio Ad Absurdum Argument Prior to Aristotle. N.p., San Jose State University, 1991.
References
^ "Reductio ad absurdum | logic". Encyclopedia Britannica. Retrieved 2019-11- 27.
^ "Definition of REDUCTIO AD ABSURDUM". www.merriam-webster.com. Retrieved 2019-11-27.
^ "reductio ad absurdum", Collins English Dictionary - Complete and Unabridged (12th ed.), 2014, retrieved October 29, 2016
^ Jump up to: a b Nicholas Rescher. "Reductio ad absurdum". The Internet Encyclopedia of Philosophy. Retrieved 21 July 2009.
^ DeLancey, Craig (2017-03-27), "8. Reductio ad Absurdum", A Concise Introduction to Logic, Open SUNY Textbooks, retrieved 2021-08-31
^ Jump up to: a b c Nordquist, Richard. "Reductio Ad Absurdum in Argument". ThoughtCo. Retrieved 2019-11-27.
^ Howard-Snyder, Frances; Howard-Snyder, Daniel; Wasserman, Ryan (30 March 2012). The Power of Logic (5th ed.). McGraw-Hill Higher Education. ISBN 978- 0078038198.
^ Daigle, Robert W. (1991). "The reductio ad absurdum argument prior to Aristotle". Master's Thesis. San Jose State Univ. Retrieved August 22, 2012.
^ "Reductio ad Absurdum - Definition & Examples". Literary Devices. 2014-05-18. Retrieved 2021-08-31.
^ Joyce, David (1996). "Euclid's Elements: Book I". Euclid's Elements. Department of Mathematics and Computer Science, Clark University. Retrieved December 23, 2017.
^ Bobzien, Susanne (2006). "Ancient Logic". Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab, Stanford University. Retrieved August 22, 2012.
^ Hyde & Raffman 2018.
^ Wasler, Joseph. Nagarjuna in Context. New York: Columibia University Press. 2005, pgs. 225-263.
^ Ziembinski, Zygmunt (2013). Practical Logic. Springer. p. 95. ISBN 978- 9401756044.
^ Ferguson, Thomas Macaulay; Priest, Graham (2016). A Dictionary of Logic. Oxford University Press. p. 146. ISBN 978-0192511553.
External links
The dictionary definition of per impossibile at Wiktionary
"Reductio ad absurdum". Internet Encyclopedia of Philosophy.
Categories:
Latin logical phrasesLatin philosophical phrasesTheorems in propositional logicMadhyamakaArgumentsPyrrhonism
http://plato.stanford.edu/entries/logic-ancient/#NonModSyl http://scholarworks.sjsu.edu/cgi/viewcontent.cgi?article=1228 &context=etd_theses
http://www.iep.utm.edu/reductio/ http://www.thefreedictionary.com/reductio+ad+absurdum http://www.utm.edu/research/iep/r/reductio.htm https://books.google.com/books?id=2Q5nDAAAQBAJ&q="principle+of+non- contradiction"&pg=PT146
https://books.google.com/books?id=LOfsCAAAQBAJ&q="principle+of+non- contradiction"&pg=PA95
https://en.wikipedia.org/w/index.php? title=Reductio_ad_absurdum&action=edit§ion=5
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https://en.wikipedia.org/wiki/Appeal_to_ridicule https://en.wikipedia.org/wiki/Argument_from_fallacy https://en.wikipedia.org/wiki/Contraposition https://en.wikipedia.org/wiki/Edward_N._Zalta https://en.wikipedia.org/wiki/File:Wiktionary-logo-en-v2.svg https://en.wikipedia.org/wiki/ISBN_(identifier)
https://en.wikipedia.org/wiki/Internet_Encyclopedia_of_Philosophy https://en.wikipedia.org/wiki/List_of_Latin_phrases https://en.wikipedia.org/wiki/Mathematical_proof https://en.wikipedia.org/wiki/Prasangika https://en.wikipedia.org/wiki/Reductio_ad_absurdum#CITEREFHydeRaffman2018 https://en.wikipedia.org/wiki/Reductio_ad_absurdum#cite_ref-13 https://en.wikipedia.org/wiki/Reductio_ad_absurdum#cite_ref-2 https://en.wikipedia.org/wiki/Reductio_ad_absurdum#cite_ref-3 https://en.wikipedia.org/wiki/Reductio_ad_absurdum#cite_ref-5 https://en.wikipedia.org/wiki/Reductio_ad_absurdum#cite_ref-7 https://en.wikipedia.org/wiki/Reductio_ad_absurdum#cite_ref-9 https://en.wikipedia.org/wiki/Reductio_ad_absurdum#cite_ref-:0_1-0 https://en.wikipedia.org/wiki/Reductio_ad_absurdum#cite_ref-:1_6-0 https://en.wikipedia.org/wiki/Reductio_ad_absurdum#cite_ref-:1_6-1 https://en.wikipedia.org/wiki/Reductio_ad_absurdum#cite_ref-:1_6-2 https://en.wikipedia.org/wiki/Reductio_ad_absurdum#cite_ref-Bobzien_11-0 https://en.wikipedia.org/wiki/Reductio_ad_absurdum#cite_ref-Daigle_8-0 https://en.wikipedia.org/wiki/Reductio_ad_absurdum#cite_ref-Euclid_10-0 https://en.wikipedia.org/wiki/Reductio_ad_absurdum#cite_ref- FOOTNOTEHydeRaffman2018_12-0
https://en.wikipedia.org/wiki/Reductio_ad_absurdum#cite_ref-Ferguson1_15-0 https://en.wikipedia.org/wiki/Reductio_ad_absurdum#cite_ref-IEP_4-0 https://en.wikipedia.org/wiki/Reductio_ad_absurdum#cite_ref-IEP_4-1 https://en.wikipedia.org/wiki/Reductio_ad_absurdum#cite_ref-Ziembinski_14-0 https://en.wikipedia.org/wiki/Slippery_slope https://en.wikipedia.org/wiki/Special:BookSources/978-0078038198 https://en.wikipedia.org/wiki/Special:BookSources/978-0192511553 https://en.wikipedia.org/wiki/Special:BookSources/978-9401756044 https://en.wikipedia.org/wiki/Stanford_Encyclopedia_of_Philosophy https://en.wikipedia.org/wiki/Straw_man https://en.wiktionary.org/wiki/reductio_ad_absurdum https://literarydevices.net/reductio-ad-absurdum/ https://mathcs.clarku.edu/~djoyce/elements/bookI/propI6.html https://milnepublishing.geneseo.edu/concise-introduction-to-logic/chapter/8- reductio-ad-absurdum/
https://plato.stanford.edu/entries/sorites-paradox/ https://www.britannica.com/topic/reductio-ad-absurdum https://www.merriam-webster.com/dictionary/reductio+ad+absurdum https://www.thoughtco.com/reductio-ad-absurdum-argument-1691903
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Holier-than-thou LIBERAL Canadians, think they're soooo superior when it comes to slavery, because they "ended" it (not really) a mere 30 years earlier.
Canada "ended" slavery a mere 30 years before Lincoln wrote the "Emancipation Proclamation".
HOW does that make Canada ANY "better" or different? It doesn't.
Canada's Shameful, Modern-Day Slave Trade
https://torontosun.com/2012/02/10/canadas-shameful-modern-day-slave- trade/wcm/2e410af6-9dc4-4ef7-bc3e-821a5970ed41
Colonial Canada Had Slavery For More Than 200 Years. And Yes, It Still Matters Today
More Canadians Say Racism Is A "Serious Problem" Today Than 1 Year Ago
Canada Urged To Open Its Eyes To Systemic Racism In Wake Of Police Violence
Racism In Canada Is Ever-Present, But We Have A Long History Of Denial
Majority (60%) See Racism as a Serious Problem in Canada Today, Up 13 points Since Last Year
Nearly a Third of Canadians (28%) Say They Have Personally Experienced Racism in the Past Year - 24 July 2020
https://www.ipsos.com/en-ca/majority-60-see-racism-serious-problem-canada- today-13-points-last-year
Canada's Enduring Legacy Of Power, Politics And Racism
https://theclarion.ca/politicslaw/canadians-no-less-racist-than-americans/
75 Per Cent of Canadians Polled, Say Royal Canadian Mounted Police Has Systemic Racism Issue
Systemic Racism In The Royal Canadian Mounted Police Force
https://www.citynews1130.com/2020/07/11/study-canadians-agree-rcmp-systemic- racism/
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