Reductio ad absurdum


Reductio ad absurdum (Latin: "reduction to the absurd") is a form of argument in which a proposition is disproven by following its implications to a logical but absurd consequence.(1) A particular kind of reductio ad absurdum, in its strictest sense, is proof by contradiction (also called indirect proof) where an assumption is proven false because it leads to a contradiction (for example a proposition of the form ‘p and not-p’).

Legal and everyday use

Some legal usage, and some common usage, depends on a much wider definition of reductio ad absurdum than proof by contradiction, where it is argued a proposition should be rejected because it has merely undesirable (though perhaps not actually self-contradictory) consequences. In a strict logical sense, this might be reductio ad incommodum rather than ad absurdum - since in formal logic, 'absurdity' applies only to impossible self-contradiction.(2) Reductio ad absurdum applied to ad coelum is, in this case, claiming that ad coelum is saying something that it is not. The reductio ad absurdum above argues only against taking ad coelum to its fullest extent.)It is only in everyday usage that this could acceptably be called a reductio ad absurdum."Reductio ad absurdum" is a logical rebuttal that takes a proposition to its logical extremes and examines the veracity of the conclusions the proposition implies in those extremes.In the case of the ad coelum example above, it is simply reductio ad absurdum being applied to an originally flawed reductio ad absurdum argument where the extremes were not rational for the original proposition.

See also

• Devil's advocate

References

1. WEB,weblink The Internet Journal of Philosophy, Reductio ad absurdum, Nicholas Rescher, 21 July 09,



2. For example, consider the proposition Cuius est solum eius est usque ad coelum et ad inferos (literally: 'for whoever owns the soil, it is theirs up to Heaven and down to Hell'). This is also known as ad coelum. A legal reductio ad absurdum argument against the proposition might be:

   Suppose we take this proposition to a logical extreme. This would grant a land owner rights to everything in a cone from the center of the earth to an infinite distance out into space, and whatever was inside that cone, including stars and planets. It is absurd that someone who purchases land on earth should own other planets, therefore this proposition is wrong.

   (This is a straw man fallacy if it is used to prove that the practical legal use of "ad coelum" is wrong, since ad coelum is only actually ever used to delineate rights in cases of tree branches that grow over boundary fences, mining rights, etc.WEB, Definition of Land Chapt. 2, OUP UK,weblink "The owner’s rights extend to such a height as is reasonably necessary for the ordinary use and enjoyment of the land. In Baron Bernstein of Leigh v Skyviews and General Ltd [1978] QB 479, Griffith J stated that it was necessary to balance the rights of an owner to enjoy the land against the rights of the general public to take advantage of all that 'science now offers in the use of airspace'."

{{logic-stub}}البرهان بنقض الفرض(zh-min-nan:Hoán-chèng-hoat)Давядзенне да абсурдуReductio ad absurdumReducció a l'absurdDůkaz sporemAbsurd (logik)Reductio ad absurdumVastuväiteline tõestusΕις άτοπον απαγωγήReducción al absurdoPruvo per disputoبرهان خلفRaisonnement par l'absurde귀류법Pembuktian melalui kontradiksiNiðursöllun í fáránleikaDimostrazione per assurdoהוכחה בדרך השלילהReductio ad absurdumReductio ad absurdumBewijs uit het ongerijmde背理法Reductio ad absurdumDowód nie wprostProva por contradiçãoArgumentum ad absurdumДоказательство от противногоReductio ad absurdumDôkaz sporomDokaz s protislovjemСвођење на контрадикцијуReductio ad absurdumReductio ad absurdumIndirekt bevisReductio ad absurdumДоведення від супротивного(zh-yue:反證法)反證法

home | about | policy | newsfeed