Aristotelian logic, also known as syllogistic logic, 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. Logic (from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, but coming to mean thought or reason) is most often said to be the study of arguments, although the exact definition of logic is a matter of controversy amongst philosophers (see below). ... Aristotle, marble copy of bronze by Lysippos. ... Prior Analytics is Aristotles work on deductive reasoning, part of his Organon, the organ of logical and scientific methods. ... De Interpretatione or Hermeneutics (Peri Hermeneias) is a work of the ancient Greek philosopher Aristotle, mainly on the philosophy of language. ... Traditional logic, also known as term logic, is a loose term for the logical tradition that originated with Aristotle and survived broadly unchanged until the advent of modern predicate logic in the late nineteenth century. ...

Aristotle's logical system

Aristotle recognised four kinds of quantified sentences, each of which contain a subject and a predicate: See subject (grammar) for the linguistic definition of subject. ... In mathematics, a predicate is a relation. ...

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

• Univ. Affirm: Written SaP (a comes from a-fir-mo, latin for to affirm, we take the first vowel, since it's universal)
• Univ. Neg: Written SeP (e comes from ne-go, latin for to deny, we take the first vowel, since it's universal)
• Part. Affirm: Written SiP (i comes from a-fir-mo, latin for to affirm, we take the second vowel, since it's particular)
• Part. Neg Written SoP (o comes from ne-go, latin for to deny, we take the second vowel, since it's particular)

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: In traditional logic, a syllogism is an inference in which one proposition (the conclusion) follows of necessity from two others (known as premises). ... The Middle Ages formed the middle period in a traditional schematic division of European history into three ages: the classical civilization of Antiquity, the Middle Ages, and modern times, beginning with the Renaissance. ...

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

Barbara comes from the three sentences used:

 MaP SaM ----- SaP 

At first glance, this may seem the same as:

 SaM MaP ----- SaP 

However, it is not so. The predicate must be given by the first premise, the subject by the second says a law of Logic. So it would be correct to write:

 SaM MaP ----- PaS 

A syllogism can, furthermore fall in one of the following patterns:

 I I I III I V M?P | P?M | M?P | P?M S?M | S?M | M?S | M?S 

For each there are several valid Modes. To check for validity, we see if the terms that are distributed. To be distributed means to be either:

 1) Subject of a Universal Premise (SaP ; SeP) 2) Predicate of a negative Premise (Sep ; SoP) 

Lastly, a premise can be obverted of converted to fall to a specific valid case. Convertion is, mainly switching terms.

Sap = PiS

SiP = PiS

SeP = PoS

SoP = Ø

Obvertion is, mainly negating the Predicate.

SaP = Se-P

SiP = So-P

SeP = Sa-P

SoP = Ø

Due to technical limitations we cannot display the nagated term as it should be. It's not S?-P, It's S?P, but the P has a line over it.

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 OR square of Boetsius lists all these logical entailments. Implication or entailment is used in propositional logic and predicate logic to describe a relationship between two sentences or sets of sentences. ... The Square of Opposition is a term from the study of Aristotelian logic or Term Logic in which the logical relationship between various types of sentences is spelled out: For any subject S and predicate P, these rules are supposed to apply: At least one of the universal statements must...

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.

References

• I. M. Bocheński, I. M., 1951. Ancient Formal Logic. North-Holland, Amsterdam.
• Louis Couturat, 1961. La Logique de Leibniz. Georg Olms Verlagsbuchhandlung, Hildesheim.
• Hammond and Scullard, 1992. The Oxford Classical Dictionary. Oxford University Press, ISBN 0198691173.
• Jan Lukasiewicz, 1951. Aristotle's Syllogistic, from the Standpoint of Modern Formal Logic. Clarendon Press, Oxford.
• Parry and Hacker, 1991. Aristotelian Logic. State University of New York Press, Albany.
• Terence Parsons, 1999. 'Traditional Square of Opposition'. Article at the Stanford Encyclopedia of Philosophy.
• Lynn E. Rose, 1968. Aristotle's Syllogistic. Clarence C. Thomas, Springfield.
• Robin Smith, 2004. 'Aristotle's Logic'. Article at the Stanford Encyclopedia of Philosophy.

The title given to this article is incorrect due to technical limitations. ... The Stanford Encyclopedia of Philosophy (hereafter SEP) is a free online encyclopedia of philosophy run and maintained by Stanford University. ... The Stanford Encyclopedia of Philosophy (hereafter SEP) is a free online encyclopedia of philosophy run and maintained by Stanford University. ...

External references

• James Evans' A summary of the Organon. Class notes.
• The Internet Encyclopedia of Philosophy: Aristotle.
• Fred Sommers and the New syllogistic