Difference between revisions of "Proof"
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| + | '''Proof''' is a firmly attested and evident objective fact, or a coherent set of facts, which cannot be refuted, often an inescapable conclusion based on undeniable [[evidence]]. Proofs have been set aside by [[logical fallacies]] and [[prejudice]]. | ||
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==Mathematical proof== | ==Mathematical proof== | ||
A mathematical proof is a step-by-step demonstration of the truth of a mathematical theorem. Proofs build on [[axiom]]s, which are statements that are assumed to be true without proof, as well as previously-proved [[theorem]]s. | A mathematical proof is a step-by-step demonstration of the truth of a mathematical theorem. Proofs build on [[axiom]]s, which are statements that are assumed to be true without proof, as well as previously-proved [[theorem]]s. | ||
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''Main article:'' [[Scientific evidence]] | ''Main article:'' [[Scientific evidence]] | ||
| − | Unlike the [[theorem]]s 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 in the same sense that a mathematical theorem is true. Therefore scientists never claim that their theories are [[fact]]s. Instead, science searches for theories that are not disproved by currently-known experimental observations. Insofar as theories are consistent with nature, they may serve as a guide to improve [[technology]] for example and can be considered as true in laymen's terms. | + | Unlike the [[theorem]]s 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 in the same sense that a mathematical theorem is true. Therefore, scientists never claim that their theories are [[fact]]s. Instead, science searches for theories that are not disproved by currently-known experimental observations. Insofar as theories are consistent with nature, they may serve as a guide to improve [[technology]] for example and can be considered as true in laymen's terms. |
A notable exception may be found in the field of biology, where educators and other proponents frequently contend that, "Evolution is a fact." | A notable exception may be found in the field of biology, where educators and other proponents frequently contend that, "Evolution is a fact." | ||
==Notable Quotes== | ==Notable Quotes== | ||
| − | *John L. Synge<ref name="Capria">{{cite book |author=Marco M. Capria, Aubert Daigneaut et al. |title=Physics Before and After Einstein |publisher=IOS Press |year=2005 |chapter=5. General Relativity: Gravitation as Geometry and the Machian Programme |pages=97, 114|isbn=1-58603-462-6 |url=www.dmi.unipg.it/~mamone/pubb/PBAE.pdf |quote=John L. Synge, who was the author of one of the classic reference books on relativity [101], wrote half a century after Einstein’s first formulation of general relativity: [...] when one examines some proofs in the Neo-cartesian spirit, too often they seem to dissolve completely away, leaving one in a state of wonder as to whether the author really thought he had proved something. Or is the reader stupid? It is hard to say. In any case I am still waiting for a rational treatment of the dynamics of the solar system according to Einstein’s theory [100, p. 14].}}</ref> | + | *John L. Synge:<ref name="Capria">{{cite book |author=Marco M. Capria, Aubert Daigneaut et al. |title=Physics Before and After Einstein |publisher=IOS Press |year=2005 |chapter=5. General Relativity: Gravitation as Geometry and the Machian Programme |pages=97, 114|isbn=1-58603-462-6 |url=http://www.dmi.unipg.it/~mamone/pubb/PBAE.pdf |quote=John L. Synge, who was the author of one of the classic reference books on relativity [101], wrote half a century after Einstein’s first formulation of general relativity: [...] when one examines some proofs in the Neo-cartesian spirit, too often they seem to dissolve completely away, leaving one in a state of wonder as to whether the author really thought he had proved something. Or is the reader stupid? It is hard to say. In any case I am still waiting for a rational treatment of the dynamics of the solar system according to Einstein’s theory [100, p. 14].}}</ref> |
<blockquote>''"...when one examines some proofs in the Neo-cartesian spirit, too often they seem to dissolve completely away, leaving one in a state of wonder as to whether the author really thought he had proved something. Or is the reader stupid? It is hard to say."''</blockquote> | <blockquote>''"...when one examines some proofs in the Neo-cartesian spirit, too often they seem to dissolve completely away, leaving one in a state of wonder as to whether the author really thought he had proved something. Or is the reader stupid? It is hard to say."''</blockquote> | ||
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| + | ==Biblical proof== | ||
| + | See [[Biblical inerrancy]] and [[Sola scriptura]]. | ||
== Legal Proof == | == Legal Proof == | ||
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{{Reflist}} | {{Reflist}} | ||
| − | == See | + | == See also == |
*[[Explanation in science]] | *[[Explanation in science]] | ||
| − | + | *[[Proof text]] | |
| − | [[ | + | [[Category:Mathematics]] |
| − | [[ | + | [[Category:Science]] |
| − | [[ | + | [[Category:Law]] |
| − | [[ | + | [[Category:Food and Drink]] |
Revision as of 19:42, July 24, 2016
Proof is a firmly attested and evident objective fact, or a coherent set of facts, which cannot be refuted, often an inescapable conclusion based on undeniable evidence. Proofs have been set aside by logical fallacies and prejudice.
Contents
Mathematical proof
A mathematical proof is a step-by-step demonstration of the truth 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 do not rely on contested fields of maths are sometimes called elementary proofs.
Scientific proof
Main article: Scientific evidence
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 in the same sense that a mathematical theorem is true. Therefore, scientists never claim that their theories are facts. Instead, science searches for theories that are not disproved by currently-known experimental observations. Insofar as theories are consistent with nature, they may serve as a guide to improve technology for example and can be considered as true in laymen's terms.
A notable exception may be found in the field of biology, where educators and other proponents frequently contend that, "Evolution is a fact."
Notable Quotes
- John L. Synge:[1]
"...when one examines some proofs in the Neo-cartesian spirit, too often they seem to dissolve completely away, leaving one in a state of wonder as to whether the author really thought he had proved something. Or is the reader stupid? It is hard to say."
Biblical proof
See Biblical inerrancy and Sola scriptura.
Legal Proof
In American courts, crimes are proved "beyond reasonable doubt" to a jury, based on the jury's own analysis of the admissible evidence. Other legal issues may be decided by clear and convincing evidence or by a preponderance of the evidence (more likely than not).
Baking
In baking, proofing is the process of letting a dough rise. The process of letting a sourdough starter (or sponge) feed and develop is also called proofing.
References
- ↑ Marco M. Capria, Aubert Daigneaut et al. (2005). "5. General Relativity: Gravitation as Geometry and the Machian Programme", Physics Before and After Einstein. IOS Press, 97, 114. ISBN 1-58603-462-6. “John L. Synge, who was the author of one of the classic reference books on relativity [101], wrote half a century after Einstein’s first formulation of general relativity: [...] when one examines some proofs in the Neo-cartesian spirit, too often they seem to dissolve completely away, leaving one in a state of wonder as to whether the author really thought he had proved something. Or is the reader stupid? It is hard to say. In any case I am still waiting for a rational treatment of the dynamics of the solar system according to Einstein’s theory [100, p. 14].”
