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| ==Origin== | | ==Origin== |
− | [https://nordan.daynal.org/wiki/index.php?title=English#ca._1100-1500_.09THE_MIDDLE_ENGLISH_PERIOD Middle English] ''corolarie'', from Late Latin ''corollarium'', from [[Latin]], [[money]] paid for a garland, gratuity, from [http://en.wikipedia.org/wiki/Corolla_%28chaplet%29 corolla] | + | [https://nordan.daynal.org/wiki/index.php?title=English#ca._1100-1500_.09THE_MIDDLE_ENGLISH_PERIOD Middle English] ''corolarie'', from Late Latin ''corollarium'', from [[Latin]], [[money]] paid for a garland, gratuity, from [https://en.wikipedia.org/wiki/Corolla_%28chaplet%29 corolla] |
− | *[http://en.wikipedia.org/wiki/14th_century 14th Century] | + | *[https://en.wikipedia.org/wiki/14th_century 14th Century] |
| ==Definitions== | | ==Definitions== |
| *1: a [[proposition]] inferred [[immediately]] from a proved proposition with little or no additional [[proof]] | | *1: a [[proposition]] inferred [[immediately]] from a proved proposition with little or no additional [[proof]] |
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| :b : something that incidentally or naturally accompanies or [[parallels]] | | :b : something that incidentally or naturally accompanies or [[parallels]] |
| ==Description== | | ==Description== |
− | In [[mathematics]] a '''corollary''' typically follows a [http://en.wikipedia.org/wiki/Theorem theorem]. The use of the term ''corollary'', rather than [[proposition]] or theorem, is intrinsically [[subjective]]. Proposition B is a corollary of proposition A if B can readily be [[deduced]] from A or is self-evident from its [[proof]], but the [[meaning]] of readily or self-evident varies depending upon the [[author]] and [[context]]. The importance of the corollary is often considered secondary to that of the initial theorem; B is unlikely to be termed a corollary if its mathematical [[consequences]] are as significant as those of A. Sometimes a corollary has a [[proof]] that explains the derivation; sometimes the derivation is considered to be self-evident. | + | In [[mathematics]] a '''corollary''' typically follows a [https://en.wikipedia.org/wiki/Theorem theorem]. The use of the term ''corollary'', rather than [[proposition]] or theorem, is intrinsically [[subjective]]. Proposition B is a corollary of proposition A if B can readily be [[deduced]] from A or is self-evident from its [[proof]], but the [[meaning]] of readily or self-evident varies depending upon the [[author]] and [[context]]. The importance of the corollary is often considered secondary to that of the initial theorem; B is unlikely to be termed a corollary if its mathematical [[consequences]] are as significant as those of A. Sometimes a corollary has a [[proof]] that explains the derivation; sometimes the derivation is considered to be self-evident. |
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− | In [[medicine]], corollary sometimes refers to using older, more narrow [[spectrum]] [http://en.wikipedia.org/wiki/Antibiotic antibiotics] whenever possible. This is to avoid an increase in [http://en.wikipedia.org/wiki/Drug_resistance drug resistance]. | + | In [[medicine]], corollary sometimes refers to using older, more narrow [[spectrum]] [https://en.wikipedia.org/wiki/Antibiotic antibiotics] whenever possible. This is to avoid an increase in [https://en.wikipedia.org/wiki/Drug_resistance drug resistance]. |
| *Peirce on corollarial and theorematic reasonings | | *Peirce on corollarial and theorematic reasonings |
− | [http://en.wikipedia.org/wiki/Charles_Sanders_Peirce Charles Sanders Peirce] held that the most important division of kinds of [[deductive]] reasoning is that between corollarial and theorematic. He [[argued]] that, while finally all [[deduction]] depends in one way or another on mental [[experimentation]] on schemata or diagrams, still in corollarial deduction "it is only [[necessary]] to [[imagine]] any case in which the premisses are true in order to [[perceive]] immediately that the conclusion holds in that case," whereas theorematic deduction "is deduction in which it is necessary to [[experiment]] in the [[imagination]] upon the image of the premiss in order from the result of such experiment to make corollarial deductions to the [[truth]] of the conclusion." He held that corollarial deduction matches [http://en.wikipedia.org/wiki/Aristotle Aristotle]'s conception of direct [[demonstration]], which Aristotle regarded as the only thoroughly [[satisfactory]] demonstration, while theorematic deduction (A) is the kind more prized by [[mathematicians]], (B) is peculiar to mathematics,[1] and (C) involves in its course the introduction of a [http://en.wikipedia.org/wiki/Lemma_(mathematics) lemma] or at least a definition uncontemplated in the thesis (the [[proposition]] that is to be proved); in remarkable cases that definition is of an abstraction that "ought to be supported by a proper postulate.". | + | [https://en.wikipedia.org/wiki/Charles_Sanders_Peirce Charles Sanders Peirce] held that the most important division of kinds of [[deductive]] reasoning is that between corollarial and theorematic. He [[argued]] that, while finally all [[deduction]] depends in one way or another on mental [[experimentation]] on schemata or diagrams, still in corollarial deduction "it is only [[necessary]] to [[imagine]] any case in which the premisses are true in order to [[perceive]] immediately that the conclusion holds in that case," whereas theorematic deduction "is deduction in which it is necessary to [[experiment]] in the [[imagination]] upon the image of the premiss in order from the result of such experiment to make corollarial deductions to the [[truth]] of the conclusion." He held that corollarial deduction matches [https://en.wikipedia.org/wiki/Aristotle Aristotle]'s conception of direct [[demonstration]], which Aristotle regarded as the only thoroughly [[satisfactory]] demonstration, while theorematic deduction (A) is the kind more prized by [[mathematicians]], (B) is peculiar to mathematics,[1] and (C) involves in its course the introduction of a [https://en.wikipedia.org/wiki/Lemma_(mathematics) lemma] or at least a definition uncontemplated in the thesis (the [[proposition]] that is to be proved); in remarkable cases that definition is of an abstraction that "ought to be supported by a proper postulate.". |
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| [[Category: Logic]] | | [[Category: Logic]] |
| [[Category: Mathematics]] | | [[Category: Mathematics]] |