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In many cases, a corollary corresponds to a special case of a larger theorem, which makes the theorem easier to use and apply, even though its importance is generally considered to be secondary to that of the theorem. In particular,
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Peirce also held that corollarial deduction matches
Aristotle's conception of direct demonstration, which Aristotle regarded as the only thoroughly satisfactory demonstration, while theorematic deduction is:
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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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is that between corollarial and theorematic. He argued that while all deduction ultimately depends in one way or another on mental experimentation on schemata or diagrams, in corollarial deduction:
235:"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."
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which is incidentally proved while proving another proposition; it might also be used more casually to refer to something which naturally or incidentally accompanies something else.
203:. A corollary might have a proof that explains its derivation, even though such a derivation might be considered rather self-evident in some occasions (e.g., the
229:"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"
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of less importance which can be readily deduced from a previous, more notable statement. A corollary could, for instance, be a
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Peirce, C. S., 1901 manuscript "On the Logic of
Drawing History from Ancient Documents, Especially from Testimonies',
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is unlikely to be termed a corollary if its mathematical consequences are as significant as those of
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Secondary statement which can be readily deduced from a previous, more notable statement
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Peirce, C. S., from section dated 1902 by editors in the "Minute Logic" manuscript,
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Cut the knot: Sample corollaries of the
Pythagorean theorem
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Peirce, C. S., the 1902 Carnegie
Application, published in
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500:, Carolyn Eisele, editor, also transcribed by
249:Involves in its course the introduction of a
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434:. Vol. 3. Appleton. 1864. p. 260.
477:v. 4, paragraph 233, quoted in part in "
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243:The kind more prized by mathematicians
215:Peirce's theory of deductive reasoning
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529:Commens Dictionary of Peirce's Terms
483:Commons Dictionary of Peirce's Terms
191:or is self-evident from its proof.
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232:while in theorematic deduction:
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523:v. 2, see p. 96. See quote in "
497:The New Elements of Mathematics
179:is a corollary of proposition
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187:can be readily deduced from
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508:(once there, scroll down).
333:"Definition of COROLLARY"
309:"Definition of corollary"
565:Mathematical terminology
431:Chambers's Encyclopaedia
361:dictionary.cambridge.org
337:www.merriam-webster.com
246:Peculiar to mathematics
446:"Mathwords: Corollary"
381:"Mathwords: Corollary"
290:to the Monroe Doctrine
220:Charles Sanders Peirce
525:Corollarial Reasoning
479:Corollarial Reasoning
410:mathworld.wolfram.com
520:The Essential Peirce
404:Weisstein, Eric W.
288:Roosevelt Corollary
264:Lemma (mathematics)
224:deductive reasoning
205:Pythagorean theorem
502:Joseph M. Ransdell
313:www.dictionary.com
207:as a corollary of
450:www.mathwords.com
385:www.mathwords.com
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406:"Corollary"
357:"COROLLARY"
274:Proposition
168:proposition
159:mathematics
147:proposition
32:mathematics
18:Corollaries
575:Statements
559:Categories
455:2019-11-27
415:2019-11-27
390:2019-11-27
366:2019-11-27
342:2019-11-27
318:2019-11-27
295:References
88:-ə-lair-ee
527:" in the
506:Memoir 19
481:" in the
163:corollary
40:corollary
570:Theorems
258:See also
153:Overview
281:to the
173:theorem
143:theorem
141:) is a
269:Porism
138:-ər-ee
251:lemma
183:, if
36:logic
134:kər-
86:KORR
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171:or
157:In
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