categorical syllogism

Categorical SyllogismIn general a syllogism is a deductive argument consisting of two premises and one conclusion. A categorical syllogism is a special type of syllogism in which all three statements are categorical propositions.

Example:

No wealthy individuals are paupers.

All civic leaders are wealthy individuals.

Therefore, no civic leaders are paupers.3

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Categorical Syllogism

Standard Form of Syllogism

1. Quantifier

2. Quantifier

3. Quantifier

copula

copula

copula

{

{{

Major premise(contains major term )

Minor premise(contains minor term )

Conclusion

MinorTerm

MajorTerm

Categorical SyllogismNOTE: The requirements that premises and conclusion contain exactly three terms, each of which appears twice, need two qualifications:

Example:

No wealthy individuals are paupers.

All civic leaders are well to do individuals.

Therefore, no civic leaders are paupers.3

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(1) Argument containing more than three terms may qualify as a categorical syllogism if it can be translated into an equivalent argument having exactly three terms.

Well to do = wealthy

Hence, this qualifies as categorical syllogism.}

Categorical SyllogismNOTE: The requirements that premises and conclusion contain exactly three terms, each of which appears twice, need two qualifications:

Example:

God is love.

Love is blind.

Therefore, God is blind.1

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(2) Each of the three terms must be used in the same sense throughout the argument

There are four terms in the argument: “love” has two meanings.Hence, this does not qualify as categorical syllogism.

}

Categorical SyllogismA categorical syllogism is said to be in a standard form

when the following three conditions are met.

(1) All three statements are standard-form categorical propositions.

(2) The two occurrences of each term are identical.

(3) The major premise is listed first, the minor premise second, and the conclusion last.

Example:

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2All water colors are paintings.

Some water colors are masterpieces.

Hence, some paintings are masterpieces.

Not in standard form because premises are not listed in the right order.

All water colors are paintings.Some water colors are masterpieces.

Hence, some paintings are

masterpieces.

Standard form because premises are listed in the right order.


Figures: Attribute of the categorical syllogism that specifies the location of the middle term.

Figure. 1

--M --P

-- S --M

--S --P

Figure. 2 Figure. 3 Figure. 4

--P --M --M --P --P --M

-- S --M -- M --S --M --S

--S --P --S --P --S --P


Figures

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Categorical SyllogismRULES AND FALLACIES

Rule 1.

Fallacy:

Example:

A valid standard form categorical syllogism must contain exactly three terms each of which is used in the same sense through out the argument.

Four terms

All criminal actions are wicked deeds

All prosecutions for murder are criminal actions.

Hence, all prosecutions for murder are wicked deeds.

COPI AND COHEN:

In every categorical syllogism the conclusion asserts the relationships between two terms, the subject (minor term) and the predicate (major term)Such a conclusion can be justified only if the premises assert the relationship of each of those two terms to the same third term (middle term). If the premises fail to to do this consistently, the needed connection of the two terms in the conclusion cannot be established, and the argument will fail. So every valid categorical syllogism must involve three terms—no more no less. If more than three terms are involved the syllogism is invalid.


RULES AND FALLACIES

Rule 2.

Fallacy:

Example:

The middle terms must be distributed at least once.

Undistributed middle

All sharks are fish.

All salmon are fish.

All salmon are sharks.

COPI AND COHEN:

A term is distributed in a proposition when the proposition refers to all members of the class designated by the term. If the middle term is not distributed in at least one premise, the connection required by the conclusion cannot be made.


Rule 3.

Fallacy:

Example:

If a term is distributed in the conclusion, then it must be distributed in the premise

Illicit major; illicit minor

All horses are animals

Some dogs are not horses.

Some dogs are not animals All animals are tigers

All tigers are mammals

All mammals are animals

COPI AND COHEN:

To refer to all members of the class is to say more about the class than is said when only some of its members are referred to. Therefore, when a conclusion of a syllogism distributes a term that was undistributed in the premises, it says more about the term than the premises did. But a valid argument is one whose premises logically entails its conclusion, and for that to be true the conclusion must not assert any more than is asserted in the premises. A term that is asserted in the conclusion that is not distributed in the premises is therefore a sure mark that the conclusion has gone beyond its premises, has reached too far. The fallacy is that of illicit process.


RULES AND FALLACIES

Rule 4.

Fallacy:

Example:

Two negative premises are not allowed.

Exclusive premises

All fish are not mammals

Some dogs are not fish.

Some dogs are not mammals

COPI AND COHEN:

Any negative proposition (E or O) denies class inclusion; it asserts that all or some members of one class are excluded from the whole other class. But two premises asserting such exclusion cannot yield the linkage that the conclusion asserts, and therefore cannot yield a valid argument.


Rule 5.

Fallacy:

Example:

A negative premise requires a negative conclusion, and a negative conclusion requires a negative premise.

Drawing an affirmative conclusion from a negative premise or drawing a negative conclusion from affirmative premises

All crows are birds.

Some wolves are not crows.

Some wolves are birds.

All triangles are three-angled polygonAll three-angled polygons are three-sided polygons

Some three-sided polygons are not triangles.

COPI AND COHEN:

If the conclusion is affirmative, that is, if it asserts that one of the two classes, S and P, is wholly or partly contained in the other, it can only be inferred from premises that assert the existence of a third class that contains the first and is itself contained in the second. But class inclusion can only be stated by affirmative propositions. Therefore an affirmative conclusion can only follow from two affirmative premises.


Rule 6.

Fallacy:

Example:

If If both premises are universal, the conclusion cannot be particular.

Existential fallacy

All mammals are animalsAll tigers are mammals.

Some tigers are animals Some unicorns are animals.

All mammals are animalsAll unicorns are mammals

COPI AND COHEN:

In the Boolean interpretation of categorical propositions, universal propositions (A and E) have no existential import, but particular propositions (I and O) do have such import. Wherever the Boolean interpretation is supposed , a rule is needed that precludes the passage from premises that have no existential import to a conclusion that does have such import.

categorical syllogism

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