Editing Syllogism (section)

{{Short description|Type of logical argument that applies deductive reasoning}}
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A '''syllogism''' ({{langx|grc|συλλογισμός}}, ''syllogismos'', 'conclusion, inference') is a kind of [[Argument|logical argument]] that applies [[deductive reasoning]] to arrive at a [[Logical consequence|conclusion]] based on two [[proposition]]s that are asserted or assumed to be true.

[[File:Socrates_Louvre.jpg|thumb|"Socrates" at the Louvre]]
In its earliest form (defined by [[Aristotle]] in his 350 BC book ''[[Prior Analytics]]''), a deductive syllogism arises when two true premises (propositions or statements) validly imply a conclusion, or the main point that the argument aims to get across.<ref>{{Cite book|last=Lundberg|first=Christian|title=The Essential Guide to Rhetoric|publisher=Bedford/St.Martin's|year=2018|pages=38}}</ref> For example, knowing that all men are mortal (major premise), and that [[Socrates]] is a man (minor premise), we may validly conclude that Socrates is mortal. Syllogistic arguments are usually represented in a three-line form: 
	
<blockquote><poem>All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.<ref>John Stuart Mill, ''A System of Logic, Ratiocinative and Inductive, Being a Connected View of the Principles of Evidence, and the Methods of Scientific Investigation'', 3rd ed., vol. 1, chap. 2 (London: John W. Parker, 1851), 190.</ref></poem></blockquote>In antiquity, two rival syllogistic theories existed: [[Term logic|Aristotelian syllogism]] and [[Stoic logic|Stoic syllogism]].<ref name=":0" /> From the [[Middle Ages]] onwards, ''categorical syllogism'' and ''syllogism'' were usually used interchangeably. This article is concerned only with this historical use. The syllogism was at the core of historical deductive reasoning, whereby facts are determined by combining existing statements, in contrast to [[inductive reasoning]], in which facts are predicted by repeated observations.

Within some academic contexts, syllogism has been superseded by [[First-order logic|first-order predicate logic]] following the work of [[Gottlob Frege]], in particular his ''[[Begriffsschrift]]'' (''Concept Script''; 1879). Syllogism, being a method of valid logical reasoning, will always be useful in most circumstances, and for general-audience introductions to logic and clear-thinking.<ref>Hurley, Patrick J. 2011. ''A Concise Introduction to Logic''. Cengage Learning. {{ISBN|9780840034175}}</ref><ref>Zegarelli, Mark. 2010. ''Logic for Dummies''. John Wiley & Sons. {{ISBN|9781118053072}}.</ref>