Based from the book : "Logic Made Simple for Filipinos" by Florentino Timbreza here is the summary made into powerpoint of Lesson 12: The Categorical Syllogism. It Includes: Introduction to categorical syllogism General Axioms of the Syllogism Eight Syllogistic Rules Figures and Moods of the Categorical Syllogism Examples in these slides are our own, there were no examples derived from the book.

1. CATEGORICAL
SYLLOGISM

2. INTRODUCTION
the 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

3. INTRODUCTION
IDEA 1 IDEA 2 IDEA 3



4. INTRODUCTION
IDEA 1 IDEA 2 IDEA 3

OR


5. INTRODUCTION
• MEDIATE INFERENCE –
we derive conclusion
from two or more
premise
• MEDIATION of
the THIRD IDEA

6. 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

7. EXAMPLE
All animal is mortal.
But every dog is an animal.
Therefore, every dog is mortal.

8. THE SYLLOGISM
IDEA : TERM
JUDGEMENT : PROPOSITION
MEDIATE INFERENCE :
ARGUMENTATION

9. THE SYLLOGISM
• ARGUMENTATION – a
discourse which
logically deduces one
proposition from the
others

10. 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)

11. SYLLOGISM
is 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)

12. 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.

13. EXAMPLE
All fish swim.
(Major Premise)
Every shark is a fish.
(Minor Premise)
Therefore every shark
swim.
(Conclusion)

14. STRUCTURES OF A CATEGORICAL
SYLLOGISM
Three Propositions: Three terms:
1. Major Premise 1. Major term (P)
2. Minor Premise 2. Minor term (S)
3. Conclusion 3. Middle term (M)

15. THREE PROPOSITIONS
MAJOR PREMISE: MINOR PREMISE:
is the one wherein the is the one wherein the minor
major term (P) is compared term (S) is compared to the
to the middle term (M) middle term (M)
less universal class
universal class
not challenged and
assumed to be true

16. 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.

17. THREE TERMS
MAJOR TERM (P): MINOR TERM (S):
• compared to the • compared to the
middle term in a major middle term in a minor
premise premise
• more universal class
• less universal class
• predicate of the
conclusion • subject of the
conclusion

18. THREE TERMS
MIDDLE TERM:
term of comparison
appears twice in the premise but
NEVER in the conclusion

19. EXAMPLE
All fish (M) are sea creatues (P)
(Major Premise)
Every shark (S) s a fish (M)
(Minor Premise)
Therefore every shark (S) are sea
creatures (P)
(Conclusion)

20. EXERCISE
_________ All mammals (_) have lungs (_).
_________ All whales (_) have lungs (_).
_________ Therefore, all whales (_) are
mammals(_).

21. EXERCISE
A land and water dwellers are called
amphibians.
All salamanders are land and water
dwellers.
All salamanders are amphibians.

22. TO SUMMARIZE
All M is P – Major premise
All is S is M – Minor premise
Therefore, all S is P - Conclusion

23. General Axioms (Principles)
of the Syllogism
Prepared by:
Agnes Baculi, Rn
Geinah R. Quiñones, RN

24. 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. M agrees with P.
S is M. S agrees with M.
∴ S is P. ∴ S agrees with P.

25. Example:
A dog is an animal.
A hound is a dog.
∴ a hound is an animal.

26. 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.
P agrees with M.
S is not M. S does not agree with M.
∴ S is not P. ∴ S does not agree with P.

27. Example:
Nuclear-powered submarines are not commercial vessels.
All nuclear-powered submarines are warships.
∴ warships are not commercial vessels.

28. 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

29. 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.

30. 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.

31. Example:
All terriers are mammals.
Terriers are dogs.
Therefore, all dogs are mammals.
Mammals
Dogs
Terrier

32. 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.

33. 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.
Voters
Under
eighteen
Graduate years of
students
age

34. Eight General Syllogistic Rules
1. 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.

35. Eight General Syllogistic Rules
5. 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.

36. Rule 1: There must be only three
terms in the syllogism.
-Minor Term (S)
-Major Term (P)
-Middle Term (M)

37. 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.

38. Example:
All academicians are egotists.
Susan is someone who works in a university.
Therefore, Susan is an egotist.

39. Fallacy of Ambiguous Middle
Sound travels very fast.
His knowledge of law is sound.
Therefore, his knowledge of law travels
very fast.

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

41. Fallacy of Illicit Process
a) Fallacy of Illicit Major
b) Fallacy of Illicit Minor

42. 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.

43. Example:
All Texans are Americans.
No Californians are Texans.
Therefore, no Californians are Americans.

44. Mu Pp
A- All Texans are Americans.
Su Mu
E- No Californians are Texans.
Su Pu
E- Therefore, no Californians are Americans.

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

46. Example:
All animal rights activists are vegans.
All animal rights activists are humans.
Therefore, all humans are vegans.

47. 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.

48. Rule 3: The middle term must not
appear in the conclusion.
All tables have four legs
All dogs have four legs
Therefore all dogs and tables have four legs.

49. 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.

50. Example:
Contradictories are opposites.
Black and white are opposites.
∴ black and white are contradictories.

51. Pu Mp
Contradictories are opposites.
Su Mp
Black and white are opposites.
Su Pp
∴ black and white are contradictories.

52. Fallacy of Undistributed Middle
Arises when the middle term is not
used at least once as universal in the
premises.

53. 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).

54. EXAMPLE
Every carnivore is a meat-eater.
(affirmative)
A lion is a carnivore.
(affirmative)
Therefore, a Lion is a meat-eater.
(affirmative)

55. RULES ON PREMISES
6. 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)

56. FALLACY OF TWO NEGATIVES
No vegetables are fruits.
(negative)
All tomatoes are not vegetables.
(negative)
Therefore, all tomatoes are not fruits.
(negative)

57. 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.

58. FALLACY OF ILLICIT MINOR
All Spartans are Greek.
Some warriors are Spartans.
(particular)
Therefore, all warriors are Greek.

59. EXAMPLE
All Spartans are Greek.
Some warriors are Spartans.
Therefore, some warriors are Greek.

60. 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

61. EXAMPLE
No cube is round.
(negative)
A box is a cube.
Therefore a box is not round.
(negative)

62. RULES ON PREMISES
8. 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

63. THREE POSSIBILITIES
a) 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.

64. 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

65. FALLACY OF ILLICIT MAJOR
Some priests are Dominicans.
Some teachers are not priests.
Therefore, some teachers are not
Dominicans.

66. FALLACY OF UNDISTRIBUTED
MIDDLE
Some elephants are big.
Some boys are big.
Therefore some boys are elephants.

67. Figures and Moods of the
Categorical Syllogism

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

69. 4 Syllogistic Figures
1st M-p p-M M-p p-M
Premise
2nd s-M s-M M-s M-s
Premise
Figure 1 2 3 4

70. Figure 1: The middle term is the
subject of the major premise and
the predicate of the minor premise
Some people are difficult to get along with.
M-p
All Americans are people.
s-M
Therefore, some Americans are difficult to get
S-P along with.

71. Figure 2: The middle term is the
predicate of both premises.
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.

72. Mood
Proper arrangement of the premises
according to quantity and quality.
AAAA EEEE IIII OOOO
AEIO AEIO AEIO AEIO

73. 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

74. 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.

75. 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.