# how to understand syllogisms_ 5 steps - wikihow

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• 7/29/2019 How to Understand Syllogisms_ 5 Steps - WikiHow

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3/28/13 How to Understand Syllogisms: 5 steps - wikiHow

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Diagramatic depiction of subject, predicate,

and middle terms in syllogisms

How to Understand Syllogisms

A syllogism is a logical argument composed of

three parts: the major premise, the minor premise,and the conclusion inferred from the premises.The following steps will help you understandsyllogisms.

Know the basic structure of syllogisms. A syllogism has three parts: major premise,minor premise, and conclusion. Each part is composed of two categorical terms, linked inthe form "Some/all A is/are [not] B." Each of the premises has one term in common with theconclusion: the major term in the major premise, which forms the predicate of theconclusion, and the minor term in the minor premise, which forms the subject of theconclusion. The categorical term in common in the premises is called the "middle term". Forexample:

Major premise: All birds are animals.Minor premise: All parrots are birds.Conclusion: All parrots are animals.

In this example, "animal" is the major term and predicate of the conclusion, "parrot" is theminor term and subject of the conclusion, and "bird" is the middle term.

Think of each term as representing a category. For example, "animal" is a categorycomposed of everything that can be described as an animal.

Understand each part is expressed as "Some/all/no A is/are [not] B," with fourpossible variation. The universal affirmative (symbolized as A) is expressed as "all Ais/are B," abbreviated as AaB. The universal negative (symbolized as E) is expressed as"no A is/are B," abbreviated as AeB. Theparticular affirmative (symbolized as I) isexpressed as "some A is/are B," abbreviated as AiB. Theparticular negative (symbolizedas O) is expressed as "some A is/are not B," abbreviated as AoB.

Determine the figure of the syllogism. Depending on whether the middle term serves

as subject or predicate in the premises, a syllogism may be classified as one of fourpossible figures:

First figure: The middle term serves as subject in the major premise and predicate inthe minor premise. Thus, first figure take the form:

Major premise: M-P..........e.g., "All birds are animals"Minor premise: S-M..........e.g., "All parrots are birds"Conclusion:......S-P..........e.g., "All parrots are animals".

Second figure: The middle term serves as predicate in the major premise andpredicate in the minor premise. Thus, first figure take the form:

Major premise: P-M..........e.g., "No foxes are birds"Minor premise: S-M..........e.g., "All parrots are birds"Conclusion:......S-P..........e.g., "No parrots are foxes".

Third figure: The middle term serves as subject in the major premise and subject in

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the minor premise. Thus, first figure take the form:

Major premise: M-P..........e.g., "All birds are animals"Minor premise: M-S..........e.g., "All birds are mortals"Conclusion:......S-P..........e.g., "Some mortals are animals".

Fourth figure: The middle term serves as predicate in the major premise and subjectin the minor premise. Thus, first figure take the form:

Major premise: P-M..........e.g., "No birds are cows"Minor premise: M-S..........e.g., "All cows are animals"Conclusion:......S-P..........e.g., "Some animals are not birds".

Determine whether a given syllogism is valid: by checking to see if it fits into one ofthe valid forms of syllogism for the given figure. A syllogism is valid if and only if theconclusion necessarily follows the premises, i.e., if the premises are true, the conclusionmust be true. Although there are 256 possible forms (4 possible variations (a, e, i, o) foreach part, three parts (major premise, minor premise, conclusion), and four figures, so4*4*4*4=256) of syllogism, only 19 of them are valid. The valid forms for each figure isgiven below, with their mnemonic names (each containing three vowels specifying the formof the part (a, e, i, o) in order of major premise, minor premise, conclusion):

First figure has 4 valid forms: Barbara, Ce larent, Darii, Ferio

Barbara (AAA): for example,All birds are animals.All parrots are birds.All parrots are animals.

Ce larent (EAE): for example,

No birds are foxes.All parrots are birds.No parrots are foxes.

Darii (AII): for example,All dogs are animals.Some mammals are dogs.Some mammals are animals.

Ferio (EIO): for example,No dogs are birds.Some mammals are dogs.Some mammals are not birds.

Second figure has 4 valid forms: Cesare, Camestres, Festino, Baroco

Cesare (EAE): for example,No foxes are birds.

All parrots are birds.No parrots are foxes.

Camestres (AEE): for example,All foxes are animals.No trees are animals.No trees are foxes.

Festino (EIO): for example,No restaurant food is healthy.Some recipes are healthy.Some recipes are not restaurant foods.

Baroco (AOO): for example,All liars are evil-doers.Some doctors are not evil-doers.Some doctors are not liars.

Third figure has 6 valid forms: *Darapti, Disamis, Datisi, Fe lapton, Bocardo, Ferison

Darapti (AAI): for example,All men are fallible.All men are animals.Some animals are fallible.

Disamis (IAI): for example,Some books are precious.All books are perishable.Some perishable things are precious.

Datisi (AII): for example,All books are imperfect.Some books are informative.Some informative things are imperfect.

Fe lapton (EAO): for example,Thank Our

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No snakes are good to eat.All snakes are animals.Some animals are not good to eat.

Bocardo (OAO): for example,Some websites are not helpful.All websites are internet resources.Some internet resources are not helpful.

Ferison (EIO): for example,No lepers are allowed to enter the church.All lepers are human.Some humans are not allowed to enter the church.

Fourth figure has 5 valid forms: Bramantip, Camenes, Dimaris, Fesapo, Fresison

Bramantip (AAI): for example,All pigs are unclean.All unclean things are best avoided.Some things that are best avoided are pigs.

Camenes (AEE): for example,All trees are plants.No plants are birds.No birds are trees.

Dimaris (IAI): for example,Some evil doers are lawyers.All lawyers are human.Some humans are evil doers.

Fesapo (EAO): for example,

No meals are free.All free things are desirable.Some desirable things are not meals.

Fresison (EIO): for example,No dogs are birds.Some birds are pets.Some pets are not dogs.

Understand the distribution of terms. A categorical term is said to be distributed if all

individual members of that category are accounted for, for example, in "all men are mortal",the term "men" is distributed because every member belonging to that category is accountedfor, in this case, as mortal. Note how each of the four variations distributes (or not) the terms:

In "All A are B" propositions, the subject (A) is distributed.

In "No A are B" propositions, both the subject (A) and the predicate (B) are distributed.

In "Some A are B" propositions, neither the subject nor the predicate are distributed.

In "Some A are not B" propositions, the predicate (B) is distributed.

Drawing out or visualising Venn Diagrams can help in understanding distribution of terms indetermining whether a given syllogism is valid or not.

The universal affirmative (A) is represented as one circle (the subject) entirely withinanother circle (the predicate).

The universal negative (E) is represented as two mutually exclusive, non-overlappingcircles.

The particulars (I, O) are represented as two intersecting circles, each with area incommon and area not in common with the other.

There is another way to mark up Venn Diagrams when solving problems of categoricalsyllogisms: instead of using them in the purely set-theoretical manner described above(also known as "Euler Circles").

Draw three intersecting circles and use shading to indicate absence (or impossibility),leave blank to indicate "no knowledge", and a small '+' sign to indicate presence.

Now a valid categorical statement will have one of four forms:

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