Logic seems to have emerged from dialectics ; the earlier philosophers made frequent use of concepts like reductio ad absurdum in their discussions, but never truly understood the logical implications.

Euclid stipulated this so that he could construct a reductio ad absurdum proof that the two numbers ' common measure is in fact the greatest.

Ethical issues like designed babies and human cloning have also given rise to controversies between and among scientists and bioethicists, especially in the light of past abuses with eugenics ( see reductio ad hitlerum ).

By reductio ad absurdum, Bastiat argued that the national trade deficit was an indicator of a successful economy, rather than a failing one.

Abelard in his Dialectica made an argument against the idea that the copula can express existence based on a reductio ad absurdum.

Although the number of individuals sincerely espousing solipsism has been small, it is not uncommon for one philosopher to accuse another's arguments of entailing solipsism as an unwanted consequence, in a kind of reductio ad absurdum.

Jacobi used the term to characterize rationalism and in particular Immanuel Kant's " critical " philosophy in order to carry out a reductio ad absurdum according to which all rationalism ( philosophy as criticism ) reduces to nihilism, and thus it should be avoided and replaced with a return to some type of faith and revelation.

Friedrich Heinrich Jacobi ( 1743 – 1819 ), characterized rationalism, and in particular Immanuel Kant's " critical " philosophy in order to carry out a reductio ad absurdum according to which all rationalism ( philosophy as criticism ) reduces to nihilism, and thus it should be avoided and replaced with a return to some type of faith and revelation.

Proof by contradiction is also known as indirect proof, apagogical argument, proof by assuming the opposite, and reductio ad impossibilem.

It is a particular kind of the more general form of argument known as reductio ad absurdum.

Schrödinger did not wish to promote the idea of dead-and-alive cats as a serious possibility ; quite the reverse, the paradox is a classic reductio ad absurdum.

Zeno's arguments are perhaps the first examples of a method of proof called reductio ad absurdum also known as proof by contradiction.

Constructivism and intuitionism are realistic about objects that can be explicitly constructed, but reject the use of the principle of the excluded middle to prove existence by reductio ad absurdum.

* challenge ( or even refute ) a prevailing theory, often involving the device known as reductio ad absurdum, ( as in Galileo's original argument, a proof by contradiction ),

One way to proceed — the Socratic method — is to show that a given hypothesis ( with other admissions ) leads to a contradiction ; thus, forcing the withdrawal of the hypothesis as a candidate for truth ( see reductio ad absurdum ).

Although the number of individuals sincerely espousing solipsism has been small, it is not uncommon for one philosopher to accuse another's arguments of entailing solipsism as an unwanted consequence, in a kind of reductio ad absurdum.

For example, as a consequence of this the form of proof known as reductio ad absurdum is suspect.

His best-known work is the Mūlamadhyamakakārikā, in which he used the reductio ad absurdum to show the non-substantiality of the perceived world.

The name is derived from prasanga, or reductio ad absurdum arguments, rather than svatantra-anumana, or independent syllogisms.

The argument by reductio ad absurdum is as follows: If there was nothing preventing a system from achieving higher throughput ( i. e., more goal units in a unit of time ), its throughput would be infinite — which is impossible in a real-life system.

In particular, Strauss argued that Plato's myth of the Philosopher king should be read as a reductio ad absurdum, and that philosophers should understand politics, not in order to influence policy but to ensure philosophy's autonomy from politics.

Of note, official and ex-officio contributors to American political dialogue often engage, with notable success, in reductio ad ridiculum as a rhetorical device.

The Law of Jante is related to other reductio ad absurdum products of alienation.

Such was and is the reductio ad absurdum of nationalism in its territorial version, although this was not fully demonstrated until the 1940s.

For example, if a bounded differentiable function f defined on a closed interval in the real line has a single critical point, which is a local minimum, then it is also a global minimum ( use the intermediate value theorem and Rolle's theorem to prove this by reductio ad absurdum ).

This led to a reductio ad absurdum with a chain of homunculi " all the way down ".

# REDIRECT reductio ad absurdum

In particular, Salmon is known for his development and defense of a reductio ad absurdum argument, using a sorites-like problem ( slippery slope ), against nearly universally accepted modal logic systems S4 and S5, which he argues commit " the fallacy of necessity iteration ," sanctioning the invalid inference from the observation that a proposition p is a necessary truth to the conclusion that it is a necessary truth that p is a necessary truth.

Further, a facetious " attack " on it was the first public writing of Samuel Johnson, whose A Complete Vindication of the Licensers of the English Stage feigns support for Walpole while it drives the censor's argument to reductio ad absurdum.

For example, a reductio ad Stalinum could assert that atheism is a dangerous philosophy because Stalin was an atheist for most of his life.

The phrase reductio ad Hitlerum is first known to have been used in an article written by University of Chicago professor Leo Strauss for " Measure: a critical journal " in Spring 1951 ; it was made famous in a book by the same author published in 1953 Natural Right and History, Chapter II:

The phrase was derived from the legitimate logical argument called reductio ad absurdum.

But, as so many other times, a court or hearing or board room was Franklin Gowen's special arena ; and by his charm, caustic sarcasm, a staggering array of baffling figures, and a key, fallacious reductio ad absurdum argument regarding the Laurel Run Improvement Company, the investigating legislators ' final report was fully in Gowen's favor.

The satire was, of course, not a vindication at all, but rather a reductio ad absurdum of the position for censorship.

Its storyline was a reductio ad absurdum projection of contemporary issues of the time, taken to extremes, and played poignantly during 1968 — an election year with many controversies ( the Vietnam War, the Draft, Civil Rights, the population explosion, rioting and assassinations, and the baby boomer generation coming of age ).

That nondual awareness is the only possible self-awareness is defended by a reductio argument.

A semantic proof of Tarski's theorem from Post's theorem is obtained by reductio ad absurdum as follows.

The proof of Tarski's undefinability theorem in this form is again by reductio ad absurdum.

Zeno, on the other hand, primarily employed the reductio ad absurdum, attempting to destroy the arguments of others by showing their premises led to contradictions ( Zeno's paradoxes ).

#: from ( 3 ) and ( 4 ) by reductio ad absurdum ( discharging assumption 2 )

The case ( c ) in the Bogoliubov and Shirkov classification corresponds to the quantum triviality in full theory ( beyond its perturbation context ), as can be seen by a reductio ad absurdum.

Critics of Chavez have ridiculed this ( reductio ad incommodum ) by ironically suggesting the use of a totuma to bathe ( although Chavez himself did not suggest this ).

The Eristic method allowed them to prove their ideas by disproving those of the one they were arguing with and therefore indirectly proving one's own point ( see reductio ad absurdum ).

The fallacious nature of reductio ad Hitlerum is easily illustrated by identifying X as something that Adolf Hitler or his supporters did promote but which is not considered unethical, such as painting, enjoying classical music, or owning dogs.

In 1991, Professor Michael André Bernstein alleged reductio ad Hitlerum over a full-page advertisement placed in The New York Times by the Lubavitch community, following the Crown Heights Riot, under the heading " This Year Kristallnacht Took Place on August 19th Right Here in Crown Heights.

The method of exhaustion typically required a form of proof by contradiction, known as reductio ad absurdum.

Plato often used " absurdity " to describe very poor reasoning, or the conclusion from adopting a position that is false and reasoning to a false conclusion, called an " absurdity " ( argument by reductio ad absurdum ).

A burlesque or lampoon in prose would imitate a despised author and quickly move to reductio ad absurdum by having the victim say things coarse or idiotic.

* Whereas Uncle Joe concludes his proof reductio ad absurdum, modern mathematicians would more commonly claim " proof by contradiction.