Imported from: wikipedia
Reductio ad absurdum (Latin: "reduction to the absurd") is a form of argument in which a proposition is disproven by following its implications logically to an absurd consequence
A common species of reductio ad absurdum is proof by contradiction (also called indirect proof) where a proposition is proven true by proving that it is impossible for it to be false. For example, if A is false, then B is also false; but B is true, therefore A cannot be false and therefore A is true.
Consider the following statement, attributed to physicist Niels Bohr: "The opposite of every great idea is another great idea." If this statement is true, then it would certainly qualify as a great idea - it would automatically lead to a corresponding great idea for every great idea already in existence. But if the statement itself is a great idea, its opposite ("the opposite of every great idea is not a great idea") must also be a great idea. Taken to its logical conclusion, the statement contradicts itself, being both true and untrue.[2]
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.[1]
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.[3] 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: 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.
Reductio Ad Absurdum in Euclid's Elements
In his Elements, Book III Proposition 5, Euclid demonstrates that if two circles cut one another, they do not have the same center. He begins by assuming that the opposite is true, that two circles may cut one another and have the same center. He then shows that if this happen, the radius of one circle would be both equal to and less than the radius of the other, which is impossible.
Reductio Ad Absurdum in Popular Culture
In an episode of the American TV series The Big Bang Theory, Sheldon refers to a Reductio Ad Absurdum of Leonard's. It is a misuse of the term, which he defines as "The logical fallacy of extending someone's argument to ridiculous proportions and then criticizing the result." The fallacy he describes is actually an Appeal to Ridicule.
No comments:
Post a Comment