# GetWiki

*Corollary*

ARTICLE SUBJECTS

being →

database →

ethics →

fiction →

history →

internet →

language →

linux →

logic →

method →

news →

policy →

purpose →

religion →

science →

software →

truth →

unix →

wiki →

ARTICLE TYPES

essay →

feed →

help →

system →

wiki →

ARTICLE ORIGINS

critical →

forked →

imported →

original →

Corollary

[ temporary import ]

**please note:**

- the content below is remote from Wikipedia

- it has been imported raw for GetWiki

**corollary**({{IPAc-en|Ëˆ|k|É’r|É™|ËŒ|l|É›r|i}} {{respell|KORR|É™|lerr|ee}}, {{IPAc-en|uk|k|É’|Ëˆ|r|É’|l|É™r|i}} {{respell|korr|OL|É™r|ee}}) is a statement that follows readily from a previous statement.

## Overview

In mathematics, a corollary is a theorem connected by a short proof to an existing theorem.BOOK, Wolfram, Stephen, A New Kind of Science, Wolfram Media, Inc., 2002, 1176, 1-57955-008-8, 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 be readily deduced from

*A*or is self-evident from its proof. 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 self-evident.

## Peirce's theory of deductive reasoning

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,Peirce, C. S., from section dated 1902 by editors in the "Minute Logic" manuscript,*Collected Papers*v. 4, paragraph 233, quoted in part in "Corollarial Reasoning" in the

*Commons Dictionary of Peirce's Terms*, 2003â€“present, Mats Bergman and Sami Paavola, editors, University of Helsinki. still in corollarial deduction "it is only necessary to imagine any case in which the premises 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 premise in order from the result of such experiment to make corollarial deductions to the truth of the conclusion."Peirce, C. S., the 1902 Carnegie Application, published in

*The New Elements of Mathematics*, Carolyn Eisele, editor, also transcribed by Joseph M. Ransdell, see "From Draft A â€“ MS L75.35â€“39" in Memoir 19 (once there, scroll down). He held that corollarial deduction matches 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, and (C) involves in its course the introduction of a 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."Peirce, C. S., 1901 manuscript "On the Logic of Drawing History from Ancient Documents, Especially from Testimonies',

*The Essential Peirce*v. 2, see p. 96. See quote in "Corollarial Reasoning" in the

*Commens Dictionary of Peirce's Terms*.

## See also

{{wiktionary}}- Lemma (mathematics)
- Toyota Corolla
- Porism
- Lodge Corollary to the Monroe Doctrine
- Roosevelt Corollary to the Monroe Doctrine

## Notes

{{Reflist}}## References

- {{MathWorld|urlname=Corollary|title=Corollary}}
*corollary*at dictionary.com- Chambers's Encyclopaedia. Volume 3, Appleton 1864, p. 260 ({{Google books|6WIMAAAAYAAJ|online copy|page=260}})

**- content above as imported from Wikipedia**

- "

- time: 10:47pm EST - Thu, Jan 17 2019

- "

__Corollary__" does not exist on GetWiki (yet)- time: 10:47pm EST - Thu, Jan 17 2019

[ this remote article is provided by Wikipedia ]

LATEST EDITS [ see all ]

GETWIKI 09 MAY 2016

GETWIKI 18 OCT 2015

GETWIKI 20 AUG 2014

GETWIKI 19 AUG 2014

GETWIKI 18 AUG 2014

© 2019 M.R.M. PARROTT | ALL RIGHTS RESERVED