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Reductio ad absurdum, painting by John Pettie exhibited at the Royal Academy in 1884. In logic, reductio ad absurdum (Latin for "reduction to absurdity"), also known as argumentum ad absurdum (Latin for "argument to absurdity") or apagogical arguments, is the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to absurdity or contradiction.
Zeno's arguments may then be early examples of a method of proof called reductio ad absurdum, also known as proof by contradiction. Thus Plato has Zeno say the purpose of the paradoxes "is to show that their hypothesis that existences are many, if properly followed up, leads to still more absurd results than the hypothesis that they are one."
The heart of the dialogue opens with a challenge by Socrates to the elder and revered Parmenides and Zeno. Employing his customary method of attack, the reductio ad absurdum, Zeno has argued that if as the pluralists say things are many, then they will be both like and unlike; but this is an impossible situation, for unlike things cannot be like, nor like things unlike.
Derived from reductio ad absurdum. reductio ad infinitum: leading back to the infinite: An argument that creates an infinite series of causes that does not seem to have a beginning. As a fallacy, it rests upon Aristotle's notion that all things must have a cause, but that all series of causes must have a sufficient cause, that is, an unmoved mover.
Scientists also use thought experiments when particular physical experiments are impossible to conduct (Carl Gustav Hempel labeled these sorts of experiment "theoretical experiments-in-imagination"), such as Einstein's thought experiment of chasing a light beam, leading to special relativity. This is a unique use of a scientific thought ...
To disprove opposing views about reality, he wrote a series of paradoxes that used reductio ad absurdum arguments, or arguments that disprove an idea by showing how it leads to illogical conclusions. [12] Furthermore, Zeno's philosophy makes use of infinitesimals, or quantities that are infinitely small while still being greater than zero. [14]
But if it is impossible, its denial, ~(~B → B), is a logical truth. Aristotelian syllogisms (as opposed to Boolean syllogisms) appear to be based on connexive principles. For example, the contrariety of A and E statements, "All S are P," and "No S are P," follows by a reductio ad absurdum argument similar to the one given by Aristotle.
Reductio ad absurdum, reducing to an absurdity, is a method of proof in polemics, logic and mathematics, whereby assuming that a proposition is true leads to absurdity; a proposition is assumed to be true and this is used to deduce a proposition known to be false, so the original proposition must have been false.