CATEGORICAL SYLLOGISM

INTRODUCTIONthe mere analysis of the of the S and P or direct observation will not disclose their judgment.

The mind compares the two certain ideas with the third idea to which is familiar

INTRODUCTION

AGREE

IDEA 1

IDEA 2

IDEA 3

INTRODUCTION

DISAGREE

IDEA 1

IDEA 2

IDEA 3

OR

INTRODUCTION• MEDIATE INFERENCE

– we derive conclusion from two or more premise

• MEDIATION of the THIRD IDEA

MEDIATE INFERENCE

a process of the mind in which from the agreement or disagreement of 2 ideas with a third idea we infer their agreement or disagreement with each other

EXAMPLE

All animal is mortal.

But every dog is an animal.

Therefore, every dog is mortal.

THE SYLLOGISM

IDEA : TERM

JUDGEMENT : PROPOSITION

MEDIATE INFERENCE : ARGUMENTATION

THE SYLLOGISM

• ARGUMENTATION – a discourse which logically deduces one proposition from the others

• SYLLOGISM

SYLLOGISM

An argumentation in which, from two known propositions that contain a common idea, and one at least of which is universal, a third proposition, different from the two propositions, follow with necessity.

(Timbreza, 1992)

SYLLOGISMis a kind of logical argument in which one proposition (the conclusion) is inferred from two or more others (the premises) of a certain form.

(Merriam-Webster Dictionary)

CATEGORICAL SYLLOGISM

is a piece of deductive, mediate inference which consists of three categorical propositions, the first two which are premises and the third is the conclusion

It contains exactly three terms, each of which occurs in exactly two of the constituent propositions.

EXAMPLE

All fish swim.(Major Premise)

Every shark is a fish.(Minor Premise)

Therefore every shark swim.

(Conclusion)

STRUCTURES OF A CATEGORICAL SYLLOGISM

Three Propositions:

1. Major Premise

2. Minor Premise

3. Conclusion

Three terms:

1. Major term (P)

2. Minor term (S)

3. Middle term (M)

THREE PROPOSITIONS

MAJOR PREMISE:

is the one wherein the major term (P) is compared to the middle term (M)

universal class

not challenged and assumed to be true

MINOR PREMISE:

is the one wherein the minor term (S) is compared to the middle term (M)

less universal class

THREE PROPOSITIONS

CONCLUSION:

is the new truth arrived at , the result of reasoning, wherein the agreement or disagreement between the minor term (S) and the major term (P) is enunciated or expressed.

THREE TERMS

MAJOR TERM (P):

• compared to the middle term in a major premise

• more universal class

• predicate of the conclusion

MINOR TERM (S):

• compared to the middle term in a minor premise

• less universal class

• subject of the conclusion

THREE TERMSMIDDLE TERM:

term of comparison

appears twice in the premise but NEVER in the conclusion

EXAMPLE

All fish (M) are sea creatues (P).

(Major Premise)

Every shark (S) is a fish (M).

(Minor Premise)

Therefore every shark (S) are sea creatures (P).

(Conclusion)

EXERCISE

_________ All mammals (_) have lungs (_).

_________ All whales (_) have lungs (_).

_________ Therefore, all whales (_) are

mammals(_).

EXERCISE

A land and water dwellers are called amphibians.

All salamanders are land and water dwellers.

All salamanders are amphibians.

TO SUMMARIZE

All M is P – Major premise

All is S is M – Minor premise

Therefore, all S is P - Conclusion

General Axioms (Principles) of the

Syllogism

Prepared by:

Agnes Baculi, Rn

Geinah R. Quiñones, RN

1. Principle of Reciprocal Identity

If two terms agree (or are identical) with a third term, then they are identical with each other.

M is P.S is M. ∴ S is P.

M agrees with P.

S agrees with M.

∴ S agrees with P.

Example:

A dog is an animal.

A hound is a dog.

∴ a hound is an animal.

2. Principle of Reciprocal Non-Identity

If two terms, one of which is identical with a third, but the other of which is not, then they are not identical with each other.

P is M.S is not M. ∴ S is not P.

P agrees with M.S does not agree

with M. ∴ S does not agree

with P.

Example:

Nuclear-powered submarines are not commercial vessels.

All nuclear-powered submarines are warships.

∴ warships are not commercial vessels.

3. Dictum de Omni (The Law of All)

What is affirmed of a logical class may also be affirmed of its logical member.

P

M

S

Formula:1. P is affirmed of M.

But M is affirmed of S.

Hence, P may also be affirmed of S.

2. Circle M is inside circle P.

But circle S in inside circle M.

Therefore, circle S is inside circle P.

Formula:

3. M is part of P.

But S is a part of M.

Therefore, S is also a part of P.

4. Circle P contains circle M.

But circle M contains circle S.

Therefore, circle P also contains circle S.

Example:All terriers are mammals.

Terriers are dogs.

Therefore, all dogs are mammals.Mamm

als

Dogs

Terrier

4. Dictum de Nullo (The Law of None)

What is denied of a logical class is also denied of its logical member.

What is denied universally of a term is also denied of each of all referents of that term.

Example:Graduate students are voters.

No person under eighteen years of age is a voter.

Therefore, graduate students are not under eighteen years of age.

Under eighteen years of age

Voters

Graduate

students

Eight General Syllogistic Rules

I. Rules on the Terms1. There must be only three terms in the

syllogism.

2. Neither the major nor the minor term may be distributed in the conclusion, if it is undistributed in the premises.

3. The middle term must not appear in the conclusion.

4. The middle term must be distributed at least once in the premises.

Eight General Syllogistic Rules

II. Rules on the Premises5. Only an affirmative conclusion can be

drawn from two affirmative premises.

6. No conclusion can be drawn from two negative premises.

7. If one premise is particular, the conclusion must also be particular; if one premise is negative, the conclusion must be negative.

8. No conclusion can be drawn from two particular premises.

Rule 1: There must be only three terms in the syllogism.

Terms:

-Minor Term (S)

-Major Term (P)

-Middle Term (M)

Fallacy of Four Terms

occurs when a syllogism has four (or more) terms rather than the requisite three.

All M is P.All S is R.

∴ all S is P.

Example:

All academicians are egotists.

Susan is someone who works in a university.

Therefore, Susan is an egotist.

Fallacy of Ambiguous Middle

Sound travels very fast.

His knowledge of law is sound.

Therefore, his knowledge of law travels very fast.

Rule 2: Neither the major nor the minor term may be distributed in

the conclusion, if it is undistributed in the premises.

2 Parts of the rule:

a)Major term must not become universal in the conclusion if it is only particular in the major premise.

b)Minor term must not become universal in the conclusion if it is only particular in the minor premise.

Fallacy of Illicit Process

2 Kinds:

a) Fallacy of Illicit Major

b) Fallacy of Illicit Minor

Fallacy of Illicit Major

Committed if and only if the major term (P) becomes universal in the conclusion while it is only particular in the major premise.

Example:

All Texans are Americans.

No Californians are Texans.

Therefore, no Californians are Americans.

Mu Pp

A- All Texans are Americans.

Su Mu

E- No Californians are Texans.

Su Pu

E- Therefore, no Californians are Americans.

Fallacy of Illicit Minor

Minor term becomes universal in the conclusion while it is only particular (undistributed) in the minor premise.

Example:

All animal rights activists are vegans.

All animal rights activists are humans.

Therefore, all humans are vegans.

Mu Pp

A- All animal rights activists are vegans.

Mu Sp

A- All animal rights activists are humans.

Su Pu

A- Therefore, all humans are vegans.

Rule 3: The middle term must not appear in the

conclusion.

Example:

All tables have four legs

All dogs have four legs

Therefore all dogs and tables have four legs.

Rule 4: The middle term must be distributed at least once in the

premises.

Middle term must be used as least once as universal in any of the premises.

It must be shown in the premises that at least all members or referents of the middle term are identical or not identical with all the members or referents of either the minor or the major term.

Example:

Contradictories are opposites.

Black and white are opposites.

∴ black and white are contradictories.

Pu Mp

Contradictories are opposites.

Su Mp

Black and white are opposites.

Su Pp

∴ black and white are contradictories.

Fallacy of Undistributed Middle

Arises when the middle term is not used at least once as universal in the premises.

RULES ON PREMISES

5. Only an affirmative conclusion can be drawn from affirmative premises

• The major term (P) and minor term (S) of both affirmative premises agree with the middle term.

• Hence, the conclusion must express agreement between the major term (P) and minor term (S).

EXAMPLE

Every carnivore is a meat-eater.

(affirmative)

A lion is a carnivore.

(affirmative)

Therefore, a Lion is a meat-eater.

(affirmative)

RULES ON PREMISES6. No conclusion can be drawn from

two negative premises

• If both the premises are negative, major term (P) and the minor term (S) disagree with the middle term, then the middle term cannot establish any relation between the major term (P) and the minor term (S)

FALLACY OF TWO NEGATIVES

No vegetables are fruits.

(negative)

All tomatoes are not vegetables.

(negative)

Therefore, all tomatoes are not fruits.

(negative)

RULES ON PREMISES

7. If one premise is particular, the conclusion must be particular; if the one premise is negative the conclusion must be negative.

• Only a portion of either the minor term (S) or major term (P) referents share something in common with the middle term.

FALLACY OF ILLICIT MINOR

All Spartans are Greek.

Some warriors are Spartans.

(particular)

Therefore, all warriors are Greek.

EXAMPLE

All Spartans are Greek.

Some warriors are Spartans.

Therefore, some warriors are Greek.

RULES ON PREMISES

if one of the premises is negative, then neither agrees with the middle term therefore they don’t agree with each other

negative propostion:

S is not P

EXAMPLE

No cube is round.

(negative)

A box is a cube.

Therefore a box is not round.

(negative)

RULES ON PREMISES8. No conclusion can be drawn from two

particular premises.

• THREE POSSIBILITIES:

a) either both are affirmative

b) both are negative

c) one is affirmative and the other is negative

THREE POSSIBILITIESa) either both are affirmative

• if both premises are particular affirmative then all four terms will be particular.

b) if both premises are particular negative no conclusion can be made.

THREE POSSIBILITIES

c) if either of the particular premises is negative then the syllogism will contain either a fallacy of illicit major or undistributed middle

FALLACY OF ILLICIT MAJOR

Some priests are Dominicans.

Some teachers are not priests.

Therefore, some teachers are not Dominicans.

FALLACY OF UNDISTRIBUTED MIDDLE

Some elephants are big.

Some boys are big.

Therefore some boys are elephants.

Figures and Moods of the Categorical Syllogism

Figure

Proper arrangement (position) of the middle term (M) with respect to the major term (P) and the minor term (S) in the premises.

4 Syllogistic Figures

1st Premi

se

M-p p-M   M-p p-M

2nd Premi

se

s-M s-M M-s M-s

Figure

1 2 3 4

Figure 1: The middle term is the subject of the major premise and

the predicate of the minor premise

Example:

M-p Some people are difficult to get along with.

s-M All Americans are people.

S-P Therefore, some Americans are difficult to get along with.

Figure 2: The middle term is the predicate of both

premises.Example:

p-M Registered students are members of this class.

s-M John is a member of this class.

S-P Therefore, John is a registered student.

MoodProper arrangement of the premises according to quantity and quality.

AAAA EEEE IIII OOOO

AEIO AEIO AEIO AEIO

Valid Moods of the Four Figures

Figure 1 AAA , EAE, AII, EIO

Figure 2 EAE, AEE, EIO, AOO

Figure 3 AAI, EAO, IAI, AII, OAO, EIO

Figure 4 AAI, AEE, IAI, EAO, EIO

Example:

A- All textbooks are books intended for careful study.

I- Some reference books are intended for careful study.

I- Therefore, some reference books are textbooks.

Example:

A- All criminal actions are wicked deeds.

A- All prosecutions for murder are criminal actions.

A- Therefore, all prosecutions for murder are wicked deeds.