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# Corollary

A corollary ( or UK /kɒˈrɒləri/) is a statement that follows readily from a previous statement.

In mathematics a corollary typically follows a 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.

It is also known as a bonus result.

In medicine, corollary sometimes refers to using older, more narrow spectrum antibiotics whenever possible. This is to avoid an increase in drug resistance.

## Peirce on corollarial and theorematic reasonings

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,[1] 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."[2] 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,[1] 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.".[3]

## References

1. ^ a b 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 Commens Dictionary of Peirce's Terms, 2003–present, Mats Bergman and Sami Paavola, edtiors, University of Helsinki.
2. ^ 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 - MS L75.35-39" in Memoir 19 (once there, scroll down).
3. ^ 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.

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• Corollary — Cor ol*la*ry (k?r ?l l? r?; 277), n.; pl. {Corollaries} ( r?z). [L. corollarium gift, corollary, fr. corolla. See {Corolla}.] 1. That which is given beyond what is actually due, as a garland of flowers in addition to wages; surplus; something… …   The Collaborative International Dictionary of English

• corollary — I noun addition, adjunct, appurtenance, complement, correlation, correspondence, deduction, derivation, derived principle, logical sequence, offshoot, outcome, outgrowth, propinquity, sequent, supplement, syllogism II index adjunct Burton s Legal …   Law dictionary

• corollary — late 14c., from L.L. corollarium a deduction, consequence, from L. corollarium, originally money paid for a garland, hence gift, gratuity, something extra; and in logic, a proposition proved from another that has been proved. From corolla small… …   Etymology dictionary

• corollary — [n] conclusion, deduction aftereffect, analogy, consequence, culmination, effect, end, end product, induction, inference, issue, precipitate, result, sequel, sequence, upshot; concepts 230,410,529 …   New thesaurus

• corollary — ► NOUN (pl. corollaries) 1) a logical proposition that follows from one already proved. 2) a direct consequence or result. ► ADJECTIVE ▪ associated; supplementary. ORIGIN Latin corollarium money paid for a garland or chaplet; gratuity (later a… …   English terms dictionary

• corollary — [kôr′ə ler΄ē, kär′ə ler΄ē; ] Brit & often Cdn [, kə räl′ər ē] n. pl. corollaries [ME corolarie < LL corollarium, a deduction < L, orig., money paid for a garland, hence gift, gratuity < corolla: see COROLLA] 1. a proposition that follows …   English World dictionary

• corollary — noun /kɒˈrɒləri,ˈkɒrələri,ˈkɔɹəˌlɛɹi/ a) Something given beyond what is actually due; something added or superfluous. Finally getting that cracked window fixed was a nice corollary of redoing the whole storefont. b) Something which occurs a… …   Wiktionary

• corollary — n. a corollary to * * * [kə rɒl(ə)rɪ] a corollary to …   Combinatory dictionary

• corollary — co|rol|la|ry [kəˈrɔləri US ˈko:rəleri, ˈka: ] n plural corollaries formal [Date: 1300 1400; : Latin; Origin: corollarium money paid for a circle of flowers, something additional , from corolla circle of flowers ] something that is the direct… …   Dictionary of contemporary English

• corollary — [[t]kərɒ̱ləri, AM kɔ͟ːrəleri[/t]] corollaries N COUNT: oft with poss A corollary of something is an idea, argument, or fact that results directly from it. [FORMAL] The number of prisoners increased as a corollary of the government s determination …   English dictionary