Categorical Syllogism-MCM

Hum021( Intro to Logic and Critical Thinking

1. Categorical Syllogism
ROY D. PERFUMA
HUM021 ( LOGIC AND CRITICAL THINKING)

2. Learning Outcomes
uAt the end of the session, students are expected to:
1.Differentiate deductive from inductive type of argument by creating examples of
both.
2.Create categorical syllogisms based on the four figures (Praising Hands)
3.Construct a valid categorical syllogism by recognizing the 19 valid moods.
4.Apply reduction methods by answering exercises
5.Interpret reduction of categorical syllogism by enumerating each process
6.Construct reduced categorical syllogisms through written exercises

3. Quality, Quantity and Distribution of
Terms
PROPOSITION Letter
Name
Quantity Quality Terms
Distributed
All S are P A UniversalAffirmative S
NoS are P E Universal Negative S andP
Some S are P I ParticularAffirmative None
Some S are not P O Particular Negative P

4. Categorical Syllogism
I. INTRODUCTION
What is Syllogism
uAn 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)
uis 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)

5. Categorical Syllogism
What is a categorical syllogism?
It is kind of a mediate deductive argument, which is composed of
three standard form categorical propositions that uses only three
distinct terms.
Example
All politicians are good in rhetoric.
All councilors are politicians.
Therefore, all councilors are good in rhetoric.

6. Categorical Syllogism
II. RULES FOR MAKING VALID CATEGORICAL SYLLOGISMS
1. A valid categorical syllogism only has three terms: the major,
the minor, and the middle term

7. Categorical Syllogism
Example
All politicians are sociable people.
All councilors are politicians.
Therefore, all councilors are sociable people.

8. Categorical Syllogism
The major term is predicate of the conclusion. It appears in
the Major Premise (which is usually the first premise).
The minor term is the subject of the conclusion. It appears in
the Minor Premise (which is usually the second premise).
The middle term is the term that connects or separates other
terms completely or partially.

9. CATEGORICAL PROPOSITION
Fallacy of Four Terms
occurs when a syllogism has four (or more) terms rather than the requisite
three.
Example:
All academicians are egotists. All M is P
Susan is someone who works in a university. All S is R
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Therefore, Susan is an egotist. All S is P

10. Categorical Syllogism
II. RULES FOR MAKING VALID CATEGORICAL SYLLOGISMS
2. Each term of a valid categorical syllogism must occur in two propositions of
the argument.
Example:
All politicians are sociable people.
All councilors are politicians.
Therefore, all councilors are sociable people.
Politicians –occurs in the first and second premise.
Sociable People –occurs in the first premise and conclusion.
Councilors –occurs in the second premise and conclusion.

11. Categorical Syllogism

12. Categorical Syllogism
II. RULES FOR MAKING VALID CATEGORICAL SYLLOGISMS
3.If a Term is Distributed in the conclusion, then it must be
distributed in a Premise.

13. Categorical Syllogism
FALLACY OF ILLICIT MAJOR
Example:
All horses are animals. A M(d) are S(u)
Some dogs are not horses. O S(u) are not M(d)
Some dogs are not animals. O S(u) are not P(d)

14. Categorical Syllogism
FALLACY OF ILLICIT Minor
Example:
All tigers are mammals A P(d) are M(u)
All mammals are animals A M(d) are S(u)
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All animals are tigers A S(d) are P(u)

15. CATEGORICAL PROPOSITION
Fallacy of Ambiguous Middle
Example:
Sound travels very fast.
His knowledge of law is sound.
Therefore, his knowledge of law travels very fast.

16. Categorical Syllogism
II. RULES FOR MAKING VALID
CATEGORICAL SYLLOGISMS
4. The middle term in a valid categorical
syllogism must be distributed in at least
one of its occurrence.

17. Categorical Syllogism
II. RULES FOR MAKING VALID CATEGORICAL SYLLOGISMS
FALLACY OF UNDISTRIBUTED MIDDLE:
Example 1.
Some animals are pigs. IM (undistributed) are P( undistributed)
All cats are animals. A S (distributed) are M (undistributed)
Some cats are pigs. I. S (undistributed) are P( undistributed)
Some gamblers are cheaters. I. M (undistributed) are P(undistributed)
Some Filipinos are gamblers. I S ( undistributed) are M(undistributed)
Some Filipinos are cheaters. I. S. ( undistributed) are P(undistributed)

18. Categorical Syllogism

19. Categorical Syllogism

20. Categorical Syllogism
5. In a valid categorical syllogism, if both premises are
affirmative, then the conclusion must be affirmative.
Ex.
All risk-takers are gamblers. (A)
Some Filipinos are gamblers. (I)
Some Filipinos are risk-takers. (I)

21. Categorical Syllogism

22. Categorical Syllogism
6. In a valid categorical syllogism, if one premise is affirmative
and the other negative, the conclusion must be negative
Example.
No computer is useless. (E)
All ATM are computers. (A)
No ATM is useless. (E)

23. Categorical Proposition
FALLACY OF DRAWING AN AFFIRMATIVE CONCLUSION FROM A NEGATIVE PREMISE
Example:
All crows are birds
Some wolves are not crows
Some wolves are birds
FALLACY OF DRAWING A NEGATIVE CONCLUSION FROM AFFIRMATIVE
PREMISES
All triangles are three-angled polygons
All three-angled polygons are three sided polygons
Some three-sided polygons are not triangles

24. Categorical Syllogism
7. No valid categorical proposition can have two negative
premises.
Example.
No country is leaderless. (E)
No ocean is a country. (E)
No ocean is leaderless. (E)

25. Categorical Syllogism
FALLACY OF EXCLUSIVE PREMISES
Example:
No fish are mammals E
Some dogs are not fish O
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Some dogs are not mammals. O

26. Categorical Syllogism
8. At least one premise must be universal in a valid
categorical syllogism.
Ex.
Some kids are music-lovers. (I)
Some Filipinos are kids. (I)
Some Filipinos are music-lovers. (I)

27. Categorical Syllogism
9. In a valid categorical syllogism, if a premise is particular, the
conclusion must also be particular.
All angels are winged-beings. (A)
Some creatures are angels (I)
Some creatures are winged-beings. (I)

28. Categorical Proposition
Existential Fallacy
If both premises are Universal, the conclusion cannot be
Particular
All mammals are animals. A. M are P
All tigers are mammals. AS are M
Some Tigers are animals. I S are P

29. Categorical Syllogism
10. In a valid categorical syllogism, the actual real existence of
a subject may not be asserted in the conclusion unless it
has been asserted in the premises.
Example
This wood floats.
That wood floats.
Therefore, all wood floats.

30. Categorical Syllogism
III. THE STANDARD FORMS OF A VALID CATEGORICAL SYLLOGISM
The logical form is the structure of the categorical syllogism as indicated
by its “figure” and “mood.”
“Figure” is the arrangement of the terms (major, minor, and middle) of the
argument.
“Mood” is the arrangement of the propositions by quantity and quality.

31. III. THE STANDARD FORMS OF A VALID
CATEGORICAL SYLLOGISM

32. III. THE STANDARD FORMS OF A VALID
CATEGORICAL SYLLOGISM
MOODS:
4 types of categorical propositions (A, E, I, O)
Each type can be used thrice in an argument.
There are possible four figures.
Calculation: There can be 256 possible forms of a categorical
syllogism.
But only 16 forms are valid.

33. III. THE STANDARD FORMS OF A VALID
CATEGORICAL SYLLOGISM

34. III. THE STANDARD FORMS OF A VALID
CATEGORICAL SYLLOGISM

35. III. THE STANDARD FORMS OF A VALID
CATEGORICAL SYLLOGISM

36. III. THE STANDARD FORMS OF A VALID
CATEGORICAL SYLLOGISM

37. Valid Syllogistic Forms
Figure 1 Figure 2 Figure3 Figure4
AAA AEE AAI AAA
AII AOO AII AEE
EAE EAE EOA EAO
EIO EIO EIO EIO
IAA IEE IAI IAI
OAO

38. PNEUMONICS FOR VALID MOODS
FIGURE 1
1.AbAkAfor AAA
2.mAkIsIgfor AII
3.mEnAnEfor EAE
4.gEmInOfor EIO
5.hInAnApfor IAA
FIGURE 2
1.mAchEtEfor AEE
2.AdObOfor AOO
3.mEnAnEfor EAE
4.gEmInOfor EIO
5.IrEnEfor IEE
FIGURE 3
1. mArAmIfor AAI
2. mAkIsIgfor AII
3. EnAnOfor EAO
4. gEmiNofor EIO
5. mIsAmIsfor IAI
6. dOnAtOfor OAO
FIGURE 4
1. AbAkAfor AAA
2. mAchEtEfor AEE
3. EnAnOfor EAO
4. gEmInOfor EIO
5. mIsAmIsfor IAI

39. Sample Drill
Identify the major, minor and middle terms,
and the mood and figure of each
1. No insect that eat mosquitos are insects that should be killed
All dragonflies are insects that eat mosquitos
Therefore, no dragonflies are insects that should be killed.
2.No environmentally produced diseases are inherited afflictions.
Some psychological disorders are not inherited afflictions
Therefore, some psychological disorders are environmentally
produced diseases

40. Sample Drill
RECONSTRUCT THE SYLLOGISTIC FORMS FROM THE
FOLLOWING COMBINATIONS OF MOOD AND FIGURE:
1.OAE -3
2.EIA –4
3.AII-3
4.IAE–1
5.AOO-2

41. Sample Drill
Construct the following syllogisms:
1.EIO-2
Major Term-Dogmatists
Minor Term –Theologians
Middle Term –scholars who encourage free thinking
E -No Dogmatists are scholars who encourage free thinking
I -Some theologians are scholars who encourage fee thinking
_______________________________________________________________
O –Some theologians are not dogmatists

42. Sample Drill
Construct the following syllogisms:
2.A valid syllogism having mood OAO -3 :
Major Term –Things capable of replicating by themselves
Minor Term -structures that invade cells
Middle Term -viruses
O -Some viruses are not things capable of replicating by themselves
A -All viruses are structures that invade cells
O -Some structures that invade cells are not things capable of replicating by
themselves