Editing Term logic (section)

== Aristotle's system ==
[[Aristotle]]'s logical work is collected in the six texts that are collectively known as the ''[[Organon]]''. Two of these texts in particular, namely the ''[[Prior Analytics]]'' and ''[[On Interpretation]]'', contain the heart of Aristotle's treatment of judgements and formal [[inference]], and it is principally this part of Aristotle's works that is about term [[logic]]. Modern work on Aristotle's logic builds on the tradition started in 1951 with the establishment by [[Jan Lukasiewicz]] of a revolutionary paradigm.<ref>Degnan, M. 1994. Recent Work in Aristotle's Logic. Philosophical Books 35.2 (April, 1994): 81-89.</ref> Lukasiewicz's approach was reinvigorated in the early 1970s by [[John Corcoran (logician)|John Corcoran]] and [[Timothy Smiley]] – which informs modern translations of ''Prior Analytics'' by Robin Smith in 1989 and [[Gisela Striker]] in 2009.<ref>*Review of "Aristotle, Prior Analytics: Book I, Gisela Striker (translation and commentary), Oxford UP, 2009, 268pp., $39.95 (pbk), {{ISBN|978-0-19-925041-7}}." in the ''Notre Dame Philosophical Reviews'', [http://ndpr.nd.edu/review.cfm?id=18787 2010.02.02].</ref>

The ''Prior Analytics'' represents the first formal study of logic, where logic is understood as the study of arguments. An argument is a series of true or false statements which lead to a true or false conclusion.<ref>{{cite book |last1=Nolt |first1=John |last2=Rohatyn |first2=Dennis |title=Logic: Schaum's outline of theory and problems |page=1 |year=1988 |publisher=McGraw Hill |isbn=0-07-053628-7 }}</ref> In the ''Prior Analytics'', Aristotle identifies valid and invalid forms of arguments called [[syllogisms]]. A syllogism is an argument that consists of at least three sentences: at least two [[premise]]s and a conclusion. Although Aristotle does not call them "[[Categories (Aristotle)|categorical]] sentences", tradition does; he deals with them briefly in the ''Analytics'' and more extensively in ''[[On Interpretation]]''.<ref>{{cite book |author=Robin Smith |title=Aristotle: Prior Analytics |page=XVII }}</ref> Each proposition (statement that is a thought of the kind expressible by a declarative sentence)<ref>{{cite book |author=John Nolt/Dennis Rohatyn |title=Logic: Schaum's Outline of Theory and Problems |pages=274–275 }}</ref> of a syllogism is a categorical sentence which has a subject and a predicate connected by a verb. The usual way of connecting the subject and predicate of a categorical sentence as Aristotle does in ''On Interpretation'' is by using a linking verb e.g. P is S. However, in the Prior Analytics Aristotle rejects the usual form in favour of three of his inventions: 

*P belongs to S 
*P is predicated of S
*P is said of S 

Aristotle does not explain why he introduces these innovative expressions but scholars conjecture that the reason may have been that it facilitates the use of letters instead of terms avoiding the ambiguity that results in Greek when letters are used with the linking verb.<ref>{{cite book |last=Anagnostopoulos |first=Georgios |title=A Companion to Aristotle |page=33 |year=2009 |publisher=Wiley-Blackwell |isbn=978-1-4051-2223-8 }}</ref> In his formulation of syllogistic propositions, instead of the copula ("All/some... are/are not..."), Aristotle uses the expression, "... belongs to/does not belong to all/some..." or "... is said/is not said of all/some..."<ref>{{cite book |last=Patzig |first=Günther |title=Aristotle's theory of the syllogism |page=49 |year=1969 |publisher=Springer |isbn=978-90-277-0030-8 }}</ref> There are four different types of categorical sentences: universal affirmative (A), universal negative (E), particular affirmative (I) and particular negative (O).

*A	-	A belongs to every B
*E - A belongs to no B
*I	-	A belongs to some B
*O	-	A does not belong to some B

A method of symbolization that originated and was used in the Middle Ages greatly simplifies the study of the Prior Analytics.
Following this tradition then, let:

:a = belongs to every

:e = belongs to no

:i = belongs to some

:o = does not belong to some

Categorical sentences may then be abbreviated as follows:

:AaB = A belongs to every B (Every B is A)

:AeB = A belongs to no B (No B is A)

:AiB = A belongs to some B (Some B is A)

:AoB = A does not belong to some B (Some B is not A)

From the viewpoint of modern logic, only a few types of sentences can be represented in this way.<ref>{{cite book |title=The Cambridge Companion to Aristotle |pages=34–35 }}</ref>