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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."
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.
The dream hypothesis is also used to develop other philosophical concepts, such as Valberg's personal horizon: what this world would be internal to if this were all a dream. [56] Lucid dreaming is characterized as an idea where the elements of dreaming and waking are combined to a point where the user knows they are dreaming, or waking perhaps ...
More broadly, proof by contradiction is any form of argument that establishes a statement by arriving at a contradiction, even when the initial assumption is not the negation of the statement to be proved. In this general sense, proof by contradiction is also known as indirect proof, proof by assuming the opposite, [2] and reductio ad ...
In honor of her role in Francis Ford Coppola’s film “Megalopolis,” the performer took the stage at the 47th Kennedy Center Honors where she sang, “The Impossible Dream.”
The method of exhaustion typically required a form of proof by contradiction, known as reductio ad absurdum. This amounts to finding an area of a region by first comparing it to the area of a second region, which can be "exhausted" so that its area becomes arbitrarily close to the true area.
The metamathematical value of the principle of explosion is that for any logical system where this principle holds, any derived theory which proves ⊥ (or an equivalent form, ) is worthless because all its statements would become theorems, making it impossible to distinguish truth from falsehood.