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Types of syllogism1

Although there are infinitely many possible syllogisms, there are only a finite number of 

logically distinct types. We shall classify and enumerate them below. Note that the

syllogisms above share the same abstract form:

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[1] as follows.

The letters standing for the types of proposition (A, E, I, O) have been used since the

medieval Schools to form mnemonic names for the forms. The meaning of the letters is

given by the table:

code quantifier subject copula predicate type example

A All S are Puniversal

affirmativesAll humans are mortal.

E All S are not Puniversal

negatives

All humans are not

 perfect / No humans are

 perfect.

I Some S are P particular affirmatives

Some humans are healthy.

O Some S are not P  particular negatives Some humans are notclever.

(See Square of opposition for a discussion of the logical relationships between thesetypes of propositions.)

By definition, S is the subject of the conclusion, P is the predicate of the conclusion, M is

the middle term, the major premise links M with P and the minor premise links M with S.

However, the middle term can be either the subject or the predicate of each premise thatit appears in. This gives rise to another classification of syllogisms known as the figure.

The four figures are:

 Figure 1 Figure 2 Figure 3 Figure 4

Major premise: M–P P–M M–P P–M

Minor premise: S–M S–M M–S M–S

Conclusion: S–P S–P S–P S–P

1 http://en.wikipedia.org/wiki/Syllogism

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Putting it all together, there are 256 possible types of syllogisms (or 512 if the order of 

the major and minor premises is changed, although this makes no difference logically).

Each premise and the conclusion can be of type A, E, I or O, and the syllogism can beany 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

syllogisms above are AAA-1.

Of course, the vast majority of the 256 possible forms of syllogism are invalid (theconclusion does not follow logically from the premises). The table below shows the valid

forms of syllogism. Even some of these are sometimes considered to commit the

existential fallacy, thus invalid. These controversial patterns are marked in italics.

 Figure 1 Figure 2 Figure 3 Figure 4

Barbar a Cesar e  Dar a pt i   Br amant i  p

Celar ent Camestr es Disamis Camenes

Dar ii Festino Datisi Dimar is

Fer io Bar oco  F el a pt on F e sa poBocardo Fr esison

Fer ison

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.

Barbara

All men are animals.

All animals are mortal.

All men are mortal.

Celarent

 No reptiles have fur.

All snakes are reptiles.

 No snakes have fur.

Darii

All kittens are playful.

Some pets are kittens.

Some pets are playful.

Ferio

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 No homework is fun.

Some reading is homework.

Some reading is not fun.

Cesare

 No healthy food is fattening.

All cakes are fattening.

 No cakes are healthy.

Camestres

All horses have hooves.

 No humans have hooves.

 No humans are horses.

Festino

 No lazy people pass exams.Some students pass exams.

Some students are not lazy.

Baroco

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

Some websites are not informative.

 Darapti 

All fruit is nutritious.All fruit is tasty.

Some tasty things are nutritious.

Disamis

Some mugs are beautiful.

All mugs are useful.

Some useful things are beautiful.

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.

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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.

Bocardo

Some cats have no tails.

All cats are mammals.

Some mammals have no tails.

Ferison

 No tree is edible.

Some trees are green.

Some green things are not edible.

 Bramantip

All apples in my garden are wholesome.

All wholesome fruit is ripe.

Some ripe fruit are apples in my garden.

Camenes

All coloured flowers are scented.

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

Dimaris

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

Some colourful birds are small.

Fesapo

 No humans are perfect.All perfect creatures are mythical.

Some mythical creatures are not human.

Fresison

 No competent people are people who always make mistakes.

Some people who always make mistakes are people who work here.

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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.

SUBALTERNS CONTRARIES

SUBCONTRARIES SUBALTERNS