Editing Corollary (section)

==Peirce's theory of deductive reasoning<!--'Peirce's theory of deductive reasoning' redirects here-->==
[[Charles Sanders Peirce]] held that the most important division of kinds of [[deductive reasoning]] 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,<ref name=minute>Peirce, C. S., from section dated 1902 by editors in the "Minute Logic" manuscript, ''[[Charles Sanders Peirce bibliography#CP|Collected Papers]]'' v. 4, paragraph 233, quoted in part in "[http://www.helsinki.fi/science/commens/terms/corollarial.html Corollarial Reasoning]" in the ''Commons Dictionary of Peirce's Terms'', 2003–present, Mats Bergman and Sami Paavola, editors, University of Helsinki.</ref> 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"

while in theorematic deduction:

"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."<ref>Peirce, C. S., the 1902 Carnegie Application, published in ''[[Charles Sanders Peirce bibliography#NEM|The New Elements of Mathematics]]'', Carolyn Eisele, editor, also transcribed by [[Joseph Morton Ransdell|Joseph M. Ransdell]], see <!-- NEXT TWO HYPHENS IN TEXT ARE NEEDED FOR BROWSER SEARCH AT LINKED SITE -->"From Draft A – MS L75.35–39" in [http://www.cspeirce.com/menu/library/bycsp/l75/ver1/l75v1-06.htm#m19 Memoir 19] (once there, scroll down).</ref>

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:

# The kind more prized by mathematicians
# Peculiar to mathematics<ref name="minute" /> 
# Involves in its course the introduction of a [[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."<ref>Peirce, C. S., 1901 manuscript "On the Logic of Drawing History from Ancient Documents, Especially from Testimonies', ''[[Charles Sanders Peirce bibliography#EP|The Essential Peirce]]'' v. 2, see p. 96. See quote in "[http://www.helsinki.fi/science/commens/terms/corollarial.html Corollarial Reasoning]" in the ''Commens Dictionary of Peirce's Terms''.</ref>