Syllogism – Wikipedia

November 25, 2017



There are infinitely many possible syllogisms, but only 256 logically distinct types and only 24 valid types (enumerated below). A syllogism takes the form:

Major premise: All M are P.Minor premise: All S are M.Conclusion: All S are P.

(Note: M – Middle, S – subject, P – predicate. See below for more detailed explanation.)

The premises and conclusion of a syllogism can be any of four types, which are labeled by letters[12] as follows. The meaning of the letters is given by the table:

code quantifier subject copula predicate type example
A All S are P universal affirmative All humans are mortal.
E No S are P universal negative No humans are perfect.
I Some S are P particular affirmative Some humans are healthy.
O Some S are not P particular negative Some humans are not clever.

Putting it all together, there are 256 possible types of syllogisms (or 512 if the order of the major and minor premises is changed, though this makes no difference logically). Each premise and the conclusion can be of type A, E, I or O, and the syllogism can be any of the four figures. A syllogism can be described briefly by giving the letters for the premises and conclusion followed by the number for the figure. For example, the syllogism BARBARA below is AAA-1, or "A-A-A in the first figure".

Figure 1 Figure 2 Figure 3 Figure 4
Barbara Cesare Datisi Calemes
Celarent Camestres Disamis Dimatis
Darii Festino Ferison Fresison
Ferio Baroco Bocardo Calemos
Barbari Cesaro Felapton Fesapo
Celaront Camestros Darapti Bamalip