Is reductio ad absurdum proof by contradiction?
There is in mathematics a powerful method of proof known as “reductio ad absurdum” (Latin phrase: “reducing to absurdity”) or commonly referred to as “proof by contradiction”. Its reasoning is based on the fact that given a mathemati- cal statement S, either S is true or else not-S (negation of S) is true.
How do you do reductio ad absurdum?
By pushing the premises and conclusions to their logical limits or likewise strengthening your own argument by showing the opposite push to its logical limits will also result in an absurdity.
What is reductio ad absurdum and how can it be used to argue against relativism?
The most common responses to relativism come in the form of what is called a reductio ad absurdum—a form of argument meant to disprove a view by showing us the difficult or absurd (hence the name) conclusions that the view being responded to would lead to.
What is a reductio ad absurdum argument 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, 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.
How do you prove a contradiction?
To prove something by contradiction, we assume that what we want to prove is not true, and then show that the consequences of this are not possible. That is, the consequences contradict either what we have just assumed, or something we already know to be true (or, indeed, both) – we call this a contradiction.
What is the role of contradiction and consistency in this technique?
Contradiction and Consistency. We say that a statement, or set of statements is logically consistent when it involves no logical contradiction. A logical contradiction is the conjunction of a statement S and its denial not-S.
What does the term reductio ad absurdum mean?
Definition of reductio ad absurdum
1 : disproof of a proposition by showing an absurdity to which it leads when carried to its logical conclusion. 2 : the carrying of something to an absurd extreme.
What does reductio ad absurdum translate to?
reductio ad absurdum in American English
(rɪˈdʌktiˌoʊ æd æbˈsɜrdəm ; rɪˈdʌkʃiˌoʊ ) Latin. Logic. the proof of a proposition by showing its opposite to be an obvious falsity or self-contradiction, or the disproof of a proposition by showing its consequences to be impossible or absurd.
What is another term for reductio ad absurdum?
Reductio Ad Absurdum synonyms
In this page you can discover 4 synonyms, antonyms, idiomatic expressions, and related words for reductio ad absurdum, like: disproof, reduction, ridicule and reductio.