33:
935:
183:'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.
227:. 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
353:
In 13.5, Nagarjuna wishes to demonstrate consequences of the presumption that things essentially, or inherently, exist, pointing out that if a "young man" exists in himself then it follows he cannot grow old (because he would no longer be a "young man"). As we attempt to separate the man from his
94:
and has been used throughout history in both formal mathematical and philosophical reasoning, as well as in debate. Formally, the proof technique is captured by an axiom for "Reductio ad
Absurdum", normally given the abbreviation RAA, which is expressible in
432:) 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
354:
properties (youth), we find that everything is subject to momentary change, and are left with nothing beyond the merely arbitrary convention that such entities as "young man" depend upon.
267:, 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.
426:
403:
981:
87:, is the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to absurdity or contradiction.
976:
905:
953:
878:
515:
915:
888:
718:
655:
127:
The Earth cannot be flat; otherwise, since the Earth is assumed to be finite in extent, we would find people falling off the edge.
105:) and it is sometimes named to make this connection clear. It is a consequence of the related mathematical proof technique called
138:
The first example argues that denial of the premise would result in a ridiculous conclusion, against the evidence of our senses (
532:
Pasti, Mary. Reductio Ad
Absurdum: An Exercise in the Study of Population Change. United States, Cornell University, Jan., 1977.
314:) of any essential existence. Nāgārjuna's main goal is often seen by scholars as refuting the essentialism of certain Buddhist
971:
382:
347:
295:
735:
535:
Daigle, Robert W.. The
Reductio Ad Absurdum Argument Prior to Aristotle. N.p., San Jose State University, 1991.
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arguments are used to show that any theory of substance or essence was unsustainable and therefore, phenomena (
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146:(also known as an indirect proof), which argues that the denial of the premise would result in a
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510:
264:
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385:, which states that a proposition cannot be both true and false. That is, a proposition
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because such a number would have to not be divisible by two, which is impossible.
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Howard-Snyder, Frances; Howard-Snyder, Daniel; Wasserman, Ryan (30 March 2012).
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42:
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Aristotle clarified the connection between contradiction and falsity in his
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150:(there is a "smallest" number and yet there is a number smaller than it).
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206:
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948:
794:. Department of Mathematics and Computer Science, Clark University
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310:) such as change, causality, and sense perception were empty (
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where he referred to it as demonstration to the impossible (
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argument can take a range of forms, as these examples show:
186:
Greek mathematicians proved fundamental propositions using
338:
schools which posited a theory of ontological substances (
855:
New York: Columibia
University Press. 2005, pgs. 225-263.
171:
argument can be found in a satirical poem attributed to
99:. This axiom is the introduction rule for negation (see
736:"The reductio ad absurdum argument prior to Aristotle"
411:
391:
605:
Collins
English Dictionary – Complete and Unabridged
821:. The Metaphysics Research Lab, Stanford University
198:(c. 287 – c. 212 BCE) are two very early examples.
904:Ferguson, Thomas Macaulay; Priest, Graham (2016).
762:"Reductio ad Absurdum - Definition & Examples"
420:
397:
263:Another example of this technique is found in the
372:And because an old man does not grow old either.
260: "demonstration to the impossible", 62b).
713:(5th ed.). McGraw-Hill Higher Education.
234:The technique was also a focus of the work of
69:for "reduction to absurdity"), also known as
8:
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437:
216:
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36:
215:arguments to a formal dialectical method (
205:(424–348 BCE), relating the discourses of
27:Argument that leads to a logical absurdity
410:
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910:. Oxford University Press. p. 146.
864:
526:The Fundamental Wisdom of the Middle Way
142:). The second example is a mathematical
634:The Internet Encyclopedia of Philosophy
544:
505:Hyde, Dominic; Raffman, Diana (2018).
369:Because a young man does not grow old.
330:(essential nature) and also the Hindu
286:ideas have absurd conclusions through
194:(mid-4th – mid-3rd centuries BCE) and
623:
621:
294:, "consequence" in Sanskrit). In the
7:
679:
677:
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577:"Definition of REDUCTIO AD ABSURDUM"
366:Something different does not change.
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954:Internet Encyclopedia of Philosophy
819:Stanford Encyclopedia of Philosophy
516:Stanford Encyclopedia of Philosophy
442:arguments in formal fields such as
238:(384–322 BCE), particularly in his
686:"Reductio Ad Absurdum in Argument"
412:
90:This argument form traces back to
25:
528:, Oxford: Oxford University Press
933:
81:for "argument to absurdity") or
982:Theorems in propositional logic
660:A Concise Introduction to Logic
363:A thing itself does not change.
282:centers on showing how various
654:DeLancey, Craig (2017-03-27),
553:"Reductio ad absurdum | logic"
383:principle of non-contradiction
377:Principle of non-contradiction
130:There is no smallest positive
1:
938:The dictionary definition of
119:The "absurd" conclusion of a
877:Ziembiński, Zygmunt (2013).
324:) which posited theories of
165:. The earliest example of a
977:Latin philosophical phrases
788:"Euclid's Elements: Book I"
251:ἡ εἰς τὸ ἀδύνατον ἀπόδειξις
1013:
734:Daigle, Robert W. (1991).
436:, has formed the basis of
250:
813:Bobzien, Susanne (2006).
656:"8. Reductio ad Absurdum"
524:Garfield, Jay L. (1995),
346:Example from Nāgārjuna's
201:The earlier dialogues of
883:. Springer. p. 95.
92:Ancient Greek philosophy
840:Hyde & Raffman 2018
581:www.merriam-webster.com
557:Encyclopedia Britannica
519:(Summer 2018 ed.).
421:{\displaystyle \lnot Q}
949:"Reductio ad absurdum"
630:"Reductio ad absurdum"
607:(12th ed.), 2014
601:"reductio ad absurdum"
438:
434:proof by contradiction
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196:Archimedes of Syracuse
173:Xenophanes of Colophon
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144:proof by contradiction
108:proof by contradiction
73:argumentum ad absurdum
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972:Latin logical phrases
907:A Dictionary of Logic
853:Nagarjuna in Context.
786:Joyce, David (1996).
742:. San Jose State Univ
662:, Open SUNY Textbooks
472:List of Latin phrases
462:Argument from fallacy
423:
400:
148:logical contradiction
102:negation introduction
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18:Reductio ad absurdium
684:Nordquist, Richard.
439:reductio ad absurdum
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348:Mūlamadhyamakakārikā
304:reductio ad absurdum
296:Mūlamadhyamakakārikā
290:arguments (known as
288:reductio ad absurdum
209:, raised the use of
192:Euclid of Alexandria
188:reductio ad absurdum
161:was used throughout
159:Reductio ad absurdum
121:reductio ad absurdum
84:apagogical arguments
61:reductio ad absurdum
38:Reductio ad absurdum
280:Buddhist philosophy
271:Buddhist philosophy
223:), also called the
97:propositional logic
711:The Power of Logic
628:Nicholas Rescher.
477:Mathematical proof
457:Appeal to ridicule
418:
395:
140:empirical evidence
51:
792:Euclid's Elements
507:"Sorites Paradox"
446:and mathematics.
405:and its negation
398:{\displaystyle Q}
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175:(c. 570 – c. 475
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768:. 2014-05-18
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987:Madhyamaka
966:Categories
825:August 22,
772:2021-08-31
746:August 22,
695:2019-11-27
666:2021-08-31
586:2019-11-27
562:2019-11-27
540:References
482:Prasangika
321:Vaibhasika
316:Abhidharma
277:Madhyamaka
992:Arguments
690:ThoughtCo
413:¬
340:dravyatas
336:Vaiśeṣika
300:Nāgārjuna
236:Aristotle
492:Strawman
450:See also
327:svabhava
292:prasaṅga
275:Much of
219:elenchus
212:reductio
207:Socrates
168:reductio
115:Examples
639:21 July
513:(ed.).
499:Sources
308:dharmas
49:in 1884
914:
887:
717:
229:aporia
509:. In
444:logic
428:(not-
332:Nyāya
312:sunya
246:Greek
203:Plato
181:Homer
79:Latin
67:Latin
55:logic
912:ISBN
885:ISBN
827:2012
800:2017
748:2012
715:ISBN
641:2009
613:2016
358:13:5
334:and
257:lit.
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302:'s
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