Modus Barbara

Modus Barbara is a logical conclusion ( syllogism ) of a certain form. The name "Barbara" comes from the Latin word for this syllogism. The sequence of the three vowels "a" in the index word means that both prerequisites and the conclusion are affirmative and generally valid ( all quantified , but not negated ). ("A" is the first vowel of the Latin "affirmare", which can be translated as "affirmative".)

The following example shows the form of the Barbara mode: (on the right in predicate logic )

All people (M) are mortal (S) All Greeks (G) are people (M) It follows All Greeks (G) are mortal (S)

${\displaystyle \forall x(Mx\rightarrow Sx)}$ ${\displaystyle \forall x(Gx\rightarrow Mx)}$ It follows ${\displaystyle \forall x(Gx\rightarrow Sx)}$

The above representation is the coding of Petrus Hispanus . The mode Barbara was represented by Aristotle in its original form with premises in a different order and then has similarity to the chain connection for the special case n = 3.

See also

• Transitive relation
• Other traditional conclusions:
  • Mode tollendo tollens
  • Modus ponendo ponens
  • Modus ponendo tollens
  • Mode tollendo ponens

Web links

• Aristotle's syllogistics

Individual evidence

1. ↑ NI Kondakow: Dictionary of Logic . Ed .: Erhard Albrecht, Günter Asser. 1st edition. VEB Bibliographisches Institut Leipzig, Leipzig 1978, p. 72 .
2. ↑ Aristotle: An.pr. A4 25b37b-26a2, 26a23-28, perfect syllogisms (axioms)