Editing History of logic (section)

===Aristotle===
{{Main article|Term logic}}
[[File:Aristotle Altemps Inv8575.jpg|thumb|160px|Aristotle]]
The logic of [[Aristotle]], and particularly his theory of the [[syllogism]], has had an enormous influence in [[Western thought]].<ref>See e.g. [http://plato.stanford.edu/entries/aristotle-logic/ Aristotle's logic], Stanford Encyclopedia of Philosophy</ref> Aristotle was the first logician to attempt a systematic analysis of [[logical syntax]], of noun (or ''[[terminology|term]]''), and of verb. He was the first ''formal logician'', in that he demonstrated the principles of reasoning by employing variables to show the underlying [[logical form]] of an argument.<ref>{{cite book |author-last=Sowa |author-first=John F. |title=Knowledge representation: logical, philosophical, and computational foundations |date=2000 |publisher=Brooks/Cole |isbn=0-534-94965-7 |location=Pacific Grove |pages=2 |oclc=38239202}}</ref> He sought relations of dependence which characterize necessary inference, and distinguished the [[Validity (logic)|validity]] of these relations, from the truth of the premises. He was the first to deal with the principles of [[Principle of contradiction|contradiction]] and [[Law of excluded middle|excluded middle]] in a systematic way.<ref name="Bochenski p. 63">Bochenski p. 63</ref> 
[[File:Aristoteles Logica 1570 Biblioteca Huelva.jpg|alt=Front cover of book, titled "Aristotelis Logica", with an illustration of eagle on a snake|240px|thumb|left|Aristotle's logic was still influential in the [[Renaissance]].]]

====The Organon====
His logical works, called the ''[[Organon]]'', are the earliest formal study of logic that have come down to modern times. Though it is difficult to determine the dates, the probable order of writing of Aristotle's logical works is:
* ''[[Categories (Aristotle)|The Categories]]'', a study of the ten kinds of primitive term.
* ''[[Topics (Aristotle)|The Topics]]'' (with an appendix called ''[[On Sophistical Refutations]]''), a discussion of dialectics.
* ''[[De Interpretatione|On Interpretation]]'', an analysis of simple [[categorical proposition]]s into simple terms, negation, and signs of quantity. 
* ''[[Prior Analytics|The Prior Analytics]]'', a formal analysis of what makes a [[syllogism]] (a valid argument, according to Aristotle).
* ''[[Posterior Analytics|The Posterior Analytics]]'', a study of scientific demonstration, containing Aristotle's mature views on logic.
[[File:Square of opposition, set diagrams.svg|thumb|180px|This diagram shows the contradictory relationships between [[categorical proposition]]s in the [[square of opposition]] of [[Term logic|Aristotelian logic]].]]
These works are of outstanding importance in the history of logic. In the ''Categories'', he attempts to discern all the possible things to which a term can refer; this idea underpins his philosophical work ''[[Metaphysics (Aristotle)|Metaphysics]]'', which itself had a profound influence on Western thought.

He also developed a theory of non-formal logic (''i.e.,'' the theory of [[logical fallacy|fallacies]]), which is presented in ''Topics'' and ''Sophistical Refutations''.<ref name="Bochenski p. 63"/>

''On Interpretation'' contains a comprehensive treatment of the notions of [[Square of opposition|opposition]] and conversion; chapter 7 is at the origin of the [[square of opposition]] (or logical square); chapter 9 contains the beginning of [[modal logic]].

The ''Prior Analytics'' contains his exposition of the "syllogism", where three important principles are applied for the first time in history: the use of variables, a purely formal treatment, and the use of an axiomatic system.