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The Simple Categorical Syllogism

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BASIC STRUCTURE• MAJOR TERM

– is the predicate of the conclusion– it must occur in the conclusion and in one of the

premises

• Example:Every animal is mortal;

but every dog is an animal;

therefore, every dog is mortal.

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BASIC STRUCTURE• MINOR TERM

– is the subject of the conclusion– it must occur in the conclusion and in the premise in

which the major term does not occur– it is often introduced by the adversative conjunction

“but”

• Example:Every animal is mortal;

but every dog is an animal;

therefore, every dog is mortal.

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BASIC STRUCTURE• MIDDLE TERM

– it occurs in each of the premises but not in the conclusion

– it is the medium through which the major and minor terms are united in the affirmative syllogism, and separated in the negative syllogism

• Example:Every animal is mortal;

but every dog is an animal;

therefore, every dog is mortal.

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BASIC STRUCTURE• as opposed to the middle term, the minor and

major terms are called the EXTREMES.• the major terms frequently has major or greatest

extension (mortal)• the minor term receives its name from the fact

that it often has minor or least extension (dog)• the middle term has medium or intermediate

extension

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GENERAL RULES

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a. The Rules of the Terms(Number and Arrangement)

1. There must be three terms and only three – the major term, the minor term, and the middle term.

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a. The Rules of the Terms(Number and Arrangement)

1. There must be three terms and only three – the major term, the minor term, and the middle term. the necessity of having only three terms follows from

the very nature of a categorical syllogism, in which a minor and a major terms are united or separated through the intermediacy of a third term, the middle term

the terms must have exactly the same meaning and must be used in exactly the same way in each occurrence

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a. The Rules of the Terms(Number and Arrangement)

1. There must be three terms and only three – the major term, the minor term, and the middle term. a term that has a different meaning in each

occurrence is equivalent to two terms the syllogism might commit a fallacy called “Fallacy of

Four Terms” we must be especially on guard against ambiguous

middle terms, otherwise the syllogism commits the “Fallacy of Amphiboly”

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a. The Rules of the Terms(Number and Arrangement)

1. There must be three terms and only three – the major term, the minor term, and the middle term.

Example:Men must eat;

but the picture on the wall is a man;

therefore, the picture on the wall must eat.

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a. The Rules of the Terms(Number and Arrangement)

2. Each term must occur in two propositions. The major term must occur in the conclusion, as predicate, and in one of the premises, which is therefore called the major premise. The minor term must occur in the conclusion as subject, and in the other premise, which is therefore called the minor premise. The middle term must occur in both premises but not in the conclusion

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a. The Rules of the Terms(Number and Arrangement)

the function of the middle term is to act as a common term of comparison, which is performed in the premises

the middle term has no function to do and no rightful place in the conclusion

the fallacy is called “Fallacy of Misplaced Middle Term”

EXAMPLE:Every kiwi is a bird;

but some birds are bipeds;

therefore, some birds are kiwis and bipeds.

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a. The Rules of the Terms(Quantity of Extension)

3. The major and minor terms may not be universal (or distributed) in the conclusion unless they are universal in the premise.

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a. The Rules of the Terms(Quantity of Extension)

3. The major and minor terms may not be universal (or distributed) in the conclusion unless they are universal in the premise. the reason for this rule is that we may not conclude

about all the inferiors of the term if the premise have given us information about only some of them

the conclusion is an effect of the premises and must therefore be contained in them implicitly; but all are not necessarily contained in some – at least not by virtue of the form of argumentation alone

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a. The Rules of the Terms(Number and Arrangement)

violation of this rule is called either “extending a term” or an “illicit process of a term”

to go from a particular to universal is forbidden – just as in the square of opposition; but to go from universal to particular is permissible

EXAMPLE:All dogs are mammals;

but no men are dogs;

therefore, no men are animals

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a. The Rules of the Terms(Quantity of Extension)

4. The middle term must be universal, or distributed, at least once.

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a. The Rules of the Terms(Quantity of Extension)

4. The middle term must be universal, or distributed, at least once. the reason for this rule is that when the middle term is

particular in both premises it might stand for a different portion of its extension in each occurrence and thus be equivalent to two terms, and therefore fail to fulfill its function of uniting or separating the minor and major terms

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a. The Rules of the Terms(Quantity of Extension)

4. The middle term must be universal, or distributed, at least once.

EXAMPLE:A dog is an animal;

but a cat is an animal;

therefore, a cat is a dog.

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b. The Rules of the Proposition(Quality of the Proposition)

5. If both premises are affirmative, the conclusion must be affirmative.

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b. The Rules of the Proposition(Quality of the Proposition)

5. If both premises are affirmative, the conclusion must be affirmative. the reason for this rule is that affirmative premises

either unite the minor and major terms, or else do not bring them into relationship with one another at all – as when there is an undistributed middle

in neither case may the major term be denied of the minor term

hence, to get a negative conclusion you must have one – and only one – negative premise

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b. The Rules of the Proposition(Quality of the Proposition)

5. If both premises are affirmative, the conclusion must be affirmative.

EXAMPLE:All sin is detestable;

but some pretense is sin;

therefore, some pretense is not detestable.

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b. The Rules of the Proposition(Quality of the Proposition)

6. If one premise is affirmative and the other negative, the conclusion must be negative.

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b. The Rules of the Proposition(Quality of the Proposition)

6. If one premise is affirmative and the other negative, the conclusion must be negative. the reason for this rule is that the affirmative premise

unites the middle term with one of the extremes, and the negative premise separates the middle term from the other extreme

two things, of which the one is identical with a third thing and the other is different from that same third thing, cannot be identical, with one another

if a syllogism with a negative premise concludes at all, it must conclude negatively

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b. The Rules of the Proposition(Quality of the Proposition)

6. If one premise is affirmative and the other negative, the conclusion must be negative.

EXAMPLE:Dogs are not centipedes;

but hounds are dogs;

therefore, hounds are not centipedes.

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b. The Rules of the Proposition(Quality of the Proposition)

7. If both premises are negative – and not equivalently affirmative – there is no conclusion at all.

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b. The Rules of the Proposition(Quality of the Proposition)

7. If both premises are negative – and not equivalently affirmative – there is no conclusion at all. to fulfill its function of uniting or separating the minor

and the major terms, the middle term must itself be united with at least one of them

if both premises are negative, the middle term is denied of each of the extremes and we learn nothing about the relationship of the extremes toward one another

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b. The Rules of the Proposition(Quality of the Proposition)

7. If both premises are negative – and not equivalently affirmative – there is no conclusion at all. the fallacy committed is “Fallacy of Exclusive

Premises”

EXAMPLE:A stone is not an animal;

but a dog is not a stone;

therefore, a dog is not an animal.

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b. The Rules of the Proposition(Quantity of the Proposition)

8. At least one premise must be universal.

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b. The Rules of the Proposition(Quantity of the Proposition)

8. At least one premise must be universal. possible pairs of particular premises; II, IO, OI, OO II premises do not contain a distributed term and

consequently they leave the middle term undistributed if a conclusion is drawn from IO or OI premises, it

must be negative, and thus the conclusion will distributed

OO, two negative premises; no conclusion

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b. The Rules of the Proposition(Quantity of the Proposition)

8. At least one premise must be universal.

EXAMPLES:

Undistributed Middle Illicit Major

Some M is P Some M is P

Some S is M Some S is not M

Some S is P Some S is not P

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b. The Rules of the Proposition(Quantity of the Proposition)

8. At least one premise must be universal.

EXAMPLES:

Undistributed Middle Illicit Major

Some M is not P Some P is not M

Some S is M Some S is M

Some S is not P Some S is not P

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b. The Rules of the Proposition(Quantity of the Proposition)

9. If a premise is particular, the conclusion must be particular. violation of this rule is called “Fallacy of Universal

Conclusion Drawn from Particular Premises”

Valid Valid

Major Premise P (Particular) U (Universal)

Minor Premise U (Universal) P (Particular)

Conclusion P (Particular) P (Particular)

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b. The Rules of the Proposition(Quantity of the Proposition)

9. If a premise is particular, the conclusion must be particular.

Invalid Invalid

Major Premise P (Particular) U (Universal)

Minor Premise U (Universal) P (Particular)

Conclusion U (Universal) U (Universal)

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b. The Rules of the Proposition(The Existential Import of the Proposition)

10.The actual real existence of a subject may not be asserted in the conclusion unless it has been asserted in the premises.

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b. The Rules of the Proposition(The Existential Import of the Proposition)

10.The actual real existence of a subject may not be asserted in the conclusion unless it has been asserted in the premises. the reason for this rule is the general principle that

nothing may ever be asserted in the conclusion that has not been asserted implicitly in the premises

The Expository Syllogism: differs from an ordinary syllogism in that its middle

term is singular in both premises it is not an inference at all in the strictest sense of the

word but rather an appeal to experience

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b. The Rules of the Proposition(The Existential Import of the Proposition)

10.The actual real existence of a subject may not be asserted in the conclusion unless it has been asserted in the premises.The Expository Syllogism: as its name suggests, it “exposes” a truth to the

senses by setting an example before the mind it is useful for refuting A and E propositions by

establishing their contradictories

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b. The Rules of the Proposition(The Existential Import of the Proposition)

10.The actual real existence of a subject may not be asserted in the conclusion unless it has been asserted in the premises.The Expository Syllogism:

EXAMPLE: (A) All woods float.

This does not float;

but this is wood;

therefore, not all woods float.

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b. The Rules of the Proposition(The Existential Import of the Proposition)

10.The actual real existence of a subject may not be asserted in the conclusion unless it has been asserted in the premises.The Expository Syllogism:

EXAMPLE: (B) No Greek was a philosopher.

Socrates was a philosopher;

but Socrates was a Greek;

therefore, some Greek was a philosopher.