Changes

==Origin==

==Origin==

[http://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]]

: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.

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.".

[[Category: Logic]]

[[Category: Logic]]

[[Category: Mathematics]]

[[Category: Mathematics]]