Syllogisms – Examples and Types

Although syllogisms seem like a form of verbal reasoning, they are in fact closer related to mathematical reasoning. So mostly they are classified as a form of logical reasoning. There are an infinite number of possible syllogisms, but there are only a finite number of logical types. In total there are 256 possible types of syllogisms (or 512 if the order of the major and minor premises is reversed, but this makes no difference logically).

Structure Syllogism

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

The premises and conclusion of a syllogism can be any of four types, which are labelled by letters A, E, I and O. For example the letter A stands for a premise or conclusion of the type:

“Universal Affirmatives” (A)

These are of the type “All S are P”. An example would be: “All humans are mortal”. The letter “E” is of the same category universal premises, but has the opposite meaning:

“Universal Negatives” (E)

These are of the type “No S are P” and would be on an opposite terms e.g. “No humans are perfect”. The letters A and E mean Everybody and nobody, that why they are called universal. The other type is called “Particular”. These are represented by the letters I and O. The letter I stand for the type:

“Particular Affirmatives” (I)

These are called a “Some S are P” , because they dont effect everybody, but just someone. The other type that is represented by the letter O stand then for:

“Particular Negatives” (O)

And of course belong to the type “”Some S are not P” Now we have explained all types and below follows a summary.

Summary

A	Universal Affermatives	All S are P	All humans are mortal
E	Universal Negatives	No S are P	No humans are perfect
I	Particular Affirmatives	Some S are P	Some humans are healthy
O	Particular Negatives	Some S are not P	Some humans are not clever

With the letters A, E, I or O only make a finite possibilties of syllogisms are possible where the conclusion can follow logically from the premisses. And with these letters you can give a code to each syllogism and helps you understand the basics of logical reasoning syllogisms. Each premise and the conclusion can be of type A, E, I or O, and the syllogism can be any of the four figures.

Syllogsms Example (AAA)

(A)    All animals are mortal.
(A)    All men are animals.
(A)    All men are mortal.

The syllogism above can be briefly described by the letters “AAA-1″. The major and minor premisse as the conclusion are of the type “universal affirmatives” represented by the letter “A”. Therefore the syllogism above is AAA-1.

The vast majority of the 256 possible types of syllogisms are invalid. This means that the conclusion does not follow logically from the premises. Valid types of syllogisms are shown below on the table and even some of these are sometimes considered to commit the existential fallacy, meaning they are invalid if they mention an empty category.

Valid Types of Syllogisms

Figure 1	Figure 2	Figure 3	Figure 4

Barbara	Cesare	Darapti	Bramantip
Celarent	Camestres	Disamis	Camenes
Darii	Festino	Datisi	Dimaris
Ferio	Baroco	Felapton	Fesapo
Bocardo	Fresison
Ferison

These controversial patterns are marked in italics. The letters A, E, I, O have been used since the medieval Schools to form mnemonic names for the forms as follows: Barbara stands for AAA, ‘Celarent’ for EAE etc. A sample syllogism of each type follows:

1. Barbara

All animals are mortal.
All men are animals.
All men are mortal.

2. Celarent

No reptiles have fur.
All snakes are reptiles.
No snakes have fur.

3. Darii

All kittens are playful.
Some pets are kittens.
Some pets are playful.

4. Ferio

No homework is fun.
Some reading is homework.
Some reading is not fun.

5. Cesare

No healthy food is fattening.
All cakes are fattening.
No cakes are healthy.

6. Camestres

All horses have hooves.
No humans have hooves.
No humans are horses.

7. Festino

No lazy students pass exams.
Some students pass exams.
Some students are not lazy.

8. Baroco

All informative things are useful.
Some websites are not useful.
Some websites are not informative.

9. Darapti

All fruit is nutritious.
All fruit is tasty.
Some tasty things are nutritious.

10. Disamis

Some mugs are beautiful.
All mugs are useful.
Some useful things are beautiful.

11. Datisi

All the industrious boys in this school have red hair.
Some of the industrious boys in this school are boarders.
Some boarders in this school have red hair.

12. Felapton

No jug in this cupboard is new.
All jugs in this cupboard are cracked.
Some of the cracked items in this cupboard are not new.

13. Bocardo

Some cats have no tails.
All cats are mammals.
Some mammals have no tails.

14. Ferison

No tree is edible.
Some trees are green.
Some green things are not edible.

15. Bramantip

All apples in my garden are wholesome.
All wholesome fruit is ripe.
Some ripe fruit are apples in my garden.

16. Camenes

All coloured flowers are scented flowers.
No scented flowers are grown indoors.
No flowers grown indoors are coloured flowers.

17. Dimaris

Some small birds live on honey.
All birds that live on honey are colourful birds.
Some colourful birds are small birds.

18. Fesapo

No humans are perfect creatures.
All perfect creatures are mythical creatures.
Some mythical creatures are not human.

19. Fresison

No competent people are people who always make mistakes.
Some people who always make mistakes are people who work here.
Some people who work here are not competent people.

Forms can be converted to other forms, following certain rules, and all forms can be converted into one of the first-figure forms.