Aristotelian logic

Aristotelian logic, also known as syllogistic, is the particular type of logic 
created by Aristotle, primarily in his works Prior Analytics and De 
Interpretatione. It later developed into what became known as traditional 
logic or term logic.

Aristotle recognised four kinds of quantified sentences, each of which contain 
a subject and a predicate:

    * Universal affirmative: Every S is a P.
    * Universal negative: No S is a P.
    * Particular affirmative: Some S is a P.
    * Particular negative: Not every S is a P.

There are various ways to combine such sentences into syllogisms, both valid 
and invalid. In Mediaeval times, students of Aristotelian logic classified 
every possibility and gave them a name. For example, the Barbara syllogism is 
as follows:

    * Every X is a Y.
    * Every Y is a Z.
    * Therefore, every X is a Z.

Aristotle also recognised the various immediate entailments that each type of 
sentence has. For example, the truth of a universal affirmative entails the 
truth of the corresponding particular affirmative, and the falsity of the 
corresponding universal negative and particular negative. The square of 
opposition lists all these logical entailments.

Famously, Aristotelian logic runs into trouble when one or more of the terms 
involved is empty (has no members). For example, under Aristotelian logic, 
"all trespassers will be prosecuted" implies the existence of at least one 
trespasser.

The influence of the Organon

Aristotle's works on logic, (collectively called the Organon), are the only 
significant works of Aristotle that were never "lost"; all his other books 
were "lost" from his death, until rediscovered in the 11th century.

The Organon was not always popular during the Hellenistic era. Stoic logic 
was predominant, with the work of Chrysipus (none of whose work has 
survived).

In the 8th century the Scholastics, in non-Arab Europe, studied and promoted 
the study of logic based on the Organon. One of the greatest Scholastics was 
Dominican monk Albertus Magnus (1206–1280), the teacher of Thomas 
Aquinas (1226–1274).

The books of Aristotle were available in the Arab Empire and were studied by 
Islamic and Jewish scholars, including Rabbi Moses Maimonides (1135–1204) 
and Muslim Judge Ibn Rushd (1126 - 1198); both lived in Cordoba, Spain. Cordoba 
had 70 libraries, one of them with over 40,000 volumes; the two largest 
libraries in non-Arab Europe each had only 2,000 volumes. Thomas Aquinas used 
the writings and comments of Aristotle ("the philosopher"), Albert, 
Maimonides ("the Rabbi") and Ibn Rushd ("the commentator") and many others.

Immanuel Kant thought that there was nothing else to invent after the work 
of Aristotle, and a famous logic historian called Carl Prantl claimed that 
any logician who said anything new about logic was "confused, stupid or 
perverse." These examples illustrate the general tendency during the period 
between the 13th century and the 19th century to accept without question the 
work of Aristotle. He had already become known by the Scholastics (medieval 
Christian scholars) as "The Philosopher." The dogmatism created by the 
Scholastics in favor of Aristotle took a long time to disappear.

Aristotelian logic has lost most of its reputation as the one only correct 
logic. Gottlob Frege and Bertrand Russell criticized the work of Aristotle 
and showed its many limitations. They helped remove the positive prejudice 
associated with the work of Aristotle. Today logicians who study modern 
logic respect the Aristotelian logic in the sense of its great early 
accomplishment.        

History

Aristotle "says that `on the subject of reasoning' he `had nothing else on 
an earlier date to speak about'" (Bochenski, 1951). However, Plato reports 
that syntax was thought of before him, by Prodikos of Keos, who was concerned 
by the right use of words. Logic seems to have emerged from dialectics, the 
earlier philosophers used concepts like reductio ad absurdum as rule when 
discussing, but never understood its logical implications. Even Plato had 
difficulties with logic. Although he had the idea of constructing a system 
for deduction, he was never able to construct one. Instead, he relied on 
his dialectic, which was a confusion between different sciences and methods 
(Bochenski, 1951). Plato thought that deduction would simply follow from 
premises, so he focused on having good premises so that the conclusion would 
follow. Later on, Plato realised that a method for obtaining the conclusion
 would be beneficial. Plato never obtained such a method, but his best 
 attempt was published in his book Sophist, where he introduced his division
  method (Rose, 1968).

Analytics and the Organon

What we call today Aristotelian logic, Aristotle himself would have labelled
 analytics. The term logic he reserved to mean dialectics. Most of 
 Aristotle's  work is probably not authentic, since it was most likely edited 
 by students and later lecturers. The logical works of Aristotle were compiled 
 into six books at about the time of Christ:

   1. Categories
   2. On Interpretation
   3. Prior Analytics
   4. Posterior Analytics
   5. Topics
   6. On Sophistical Refutations

The order of the books (or the teahings from which they are composed) is not 
certain, but this list was derived from analysis of Aristotle's writings. There 
is one volume of Aristotle's concerning logic not found in the Organon, namely 
the fourth book of Metaphysics. (Bochenski, 1951).

Modal logic

Aristotle is also the creator of syllogisms with modalities (modal logic). 
The word modal refers to the word `modes', explaining the fact that modal 
logic deals with the modes of truth. Aristotle introduced the qualification 
of necessarily and possibly premises. He constructed a logic which helped in 
the evaluation of truth but which was very difficult to interpret. 
(Rose, 1968).