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Apr 8, 2014 · Scientific reduction became an important topic in the philosophy of science within the context of a general interest in the unity of science, and it was inspired by specific cases of what seemed to be successful reductions.
Aug 13, 2018 · A proof (also known as a deduction or derivation) \ (\cD\) is a tree of sequents satisfying the conditions that (i) the topmost sequents of \ (\cD\) are logical axioms and (ii) every sequent in \ (\cD\) except the lowest one is an upper sequent of an inference whose lower sequent is also in \ (\cD\).
Jun 13, 2024 · Reduction, in syllogistic, or traditional, logic, method of rearranging the terms in one or both premises of a syllogism, or argument form, to express it in a different figure; the placement of the middle, or repeated, term is altered, usually to a preferred pattern.
- The Editors of Encyclopaedia Britannica
Jan 26, 2024 · One of the oldest solutions is to introduce a new proof method, traditionally called “reductio ad absurdum”, which means a reduction to absurdity. This method is also often called an “indirect proof” or “indirect derivation”.
Reduction. Consider a pair of reductive claims, one scientific, the other more philosophical: Facts about whether a physical object is alive reduce to facts about its chemical structure. Facts about what causes what reduce to facts about what happens, together with facts about the fundamental laws of nature that govern what happens.
Reductio ad absurdum is a mode of argumentation that seeks to establish a contention by deriving an absurdity from its denial, thus arguing that a thesis must be accepted because its rejection would be untenable. It is a style of reasoning that has been employed throughout the history of mathematics and philosophy from classical antiquity onwards.
Aug 17, 2021 · In formal systems of number theory formulated in the sequent calculus, the induction rule plays a central role. It can be eliminated from proofs of sequents of a certain elementary form: every proof of an atomic sequent can be transformed into a “simple” proof.
