Difference between revisions of "Proof"
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Unlike the [[theorem | theorems]] of [[mathematics | mathematics]], [[science | science]] does not seek to prove that its [[theory | theories]] are true. Instead, the [[scientific method | scientific method]] seeks to check whether the predictions implied by a theory are observed in nature. Therefore, as philosopher of science [[Karl Popper | Karl Popper]] argued, science can only hope to show that a theory is false. But scientists recognize that science ''can never prove'' that a theory is true. Therefore scientists never claim that their theories are [[fact | facts]]. Instead, science searches for theories that are not disproved by currently-known facts. Insofar as theories are consistent with nature, they may serve as a guide to improve [[technology | technology]]. | Unlike the [[theorem | theorems]] of [[mathematics | mathematics]], [[science | science]] does not seek to prove that its [[theory | theories]] are true. Instead, the [[scientific method | scientific method]] seeks to check whether the predictions implied by a theory are observed in nature. Therefore, as philosopher of science [[Karl Popper | Karl Popper]] argued, science can only hope to show that a theory is false. But scientists recognize that science ''can never prove'' that a theory is true. Therefore scientists never claim that their theories are [[fact | facts]]. Instead, science searches for theories that are not disproved by currently-known facts. Insofar as theories are consistent with nature, they may serve as a guide to improve [[technology | technology]]. | ||
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Revision as of 10:14, March 14, 2007
Mathematical proof
A mathematical proof is a step-by-step demonstration of the truth or falsity of a mathematical theorem. Proofs build on axioms, which are statements that are assumed to be true without proof, as well as previously-proved theorems.
Several types of proofs are widely used, such as proof by contradiction and proof by induction. Proofs that rely only on certain simple forms of reasoning are sometimes called elementary proofs.
Andrew Schlafly cited the lack of a Wikipedia page on "elementary proof" as proof of bias in Wikipedia. Ironically, at that time Conservapedia did not even have a page on "proof".
Scientific proof
Unlike the theorems of mathematics, science does not seek to prove that its theories are true. Instead, the scientific method seeks to check whether the predictions implied by a theory are observed in nature. Therefore, as philosopher of science Karl Popper argued, science can only hope to show that a theory is false. But scientists recognize that science can never prove that a theory is true. Therefore scientists never claim that their theories are facts. Instead, science searches for theories that are not disproved by currently-known facts. Insofar as theories are consistent with nature, they may serve as a guide to improve technology.
