Categorical Syllogism

I. Definition II. Three categorical propositions III. General Rules 1) Number of terms in the syllogism. 2) How to determine the three terms in the syllogism. 3) Distribution of the major and minor terms in the syllogism. 4) Distribution of the major and minor terms in the syllogism. 5) The quality of the premises. 6) The quality of the premises. 7) The quality of the premises. 8) The quantity of the premises. 9) The quantity of the premises. IV. Figure 1) SUB-PRE (Subject-predicate) 2) PRE-PRE (Predicate-predicate) 3) SUB-SUB (Subject-subject) 4) PRE-SUB (Predicate-subject) V. Moods 1) SUB-PRE (AA, AI, EA, EI) (AAA) 2) PRE-PRE (AE, AO,EA, EI) (AEE) 3) SUB-SUB (AA, AI, EA, EI, IA, OA) (AAI) 4) PRE-SUB (AA, AE, EA, EI, IA) (EAO)

Categorical Syllogism

I. Definition

Syllogism is a mediate inference because the agreement or disagreement between two ideas or propositions is known through the mediation of a third idea or proposition. It is a process of reasoning or inference where one can determine the agreement or disagreement between two ideas with the third idea and from which deductively/inductively form a conclusion.

II. Three categorical propositions

1) Major Premise- is the predicate of the conclusion and is also found in the major premise.. 2) Minor Premise- is the subject of the conclusion and appear in the minor premise. 3) Conclusion- is the third statement in the syllogism and usually introduced therefore. Example: Animals are corporeal. (major premise) Dogs are animals. (minor premise) Therefore, Dogs are corporeal. (conclusion)

III. General Rules

1) There must be only three terms in the syllogism; the major, middle, and minor terms. Violation of this is called fallacy of 4, 5 or 6 terms. Example: All birds are animals. Tweety is a bird. Tweety is an animal. 2) The major term (T) is the predicate of the conclusion and should appear in the first premise; the minor term (t) is the subject of the conclusion and should be found in the second premise and the middle term (M) is found in both premises but in the conclusion.
Example:
Diamonds are precious. But diamonds are stones. Stones are precious.

3) The major and minor terms should not be universal in the conclusion if they are not universal in the premises. Violation of this rule is called fallacy of illicit major/minor.
Example:
All teachers are nice. Bernard is a teacher. Bernard is nice. 4) The middle term must be universal at least once. Violation of this rule is called undistributed middle.
Example:
All athletes are sickly. But no healthy are sickly. No sickly are athletes.

5) If both premises are affirmative, the conclusion must be affirmative. Violation of this commits the fallacy of drawing a negative premise from affirmative premises.
Example:
All sins are detestable. But some pretense is sin. Some pretense is detestable.

6) If a premise is affirmative and the other is negative, the conclusion must be negative. Violation of this commits the fallacy of drawing an affirmative conclusion from negative premise.
Example:
A man is two-legged. But a horse is not a two-legged. A horse is not a man.

7) If both premises are negative, no conclusion possible. Violation of this commits the fallacy of exclusive premises. Any negative premise denies inclusion. Hence, one cannot assert any relationship between the major and minor term.
Example:
Every immaterial is not mortal. But human soul is not material. Human soul is not mortal.

8) At least one premise must be universal. To violate this rule is to commit the fallacy of either illicit major, undistributed middle or two negative premises.
Example:
All Russians are communists. Some atheists are Russians. Some atheists are communists.

9) If one premise is particular and the other is universal, the conclusion must be particular. To violate this rule is to commit the fallacy of either illicit major, illicit minor or undistributed middle.
Example:
No Americans are small. Some Filipinos are Americans. Some Filipinos are not small.

IV. Figures

Figures refers to the arrangement of middle term in the syllogism. So middle term becomes the basis of the arrangement to the other terms.

1) SUB-PRE (Subject-predicate) The syllogism is known to have a sub-pre figure if the middle term is the subject of the first premise and the predicate of the second premise. Example: All cheaters are immoral people. No angels are cheaters. Some angels are not immoral people. 2) PRE-PRE (Predicate-predicate) The middle term is the predicate of both premises.
Example:
Some lawyers are liars. All politicians are liars. Some politicians are lawyers.

3) SUB-SUB (Subject-subject) The middle term is the subject of both premises.
Example:
All lawyers are professionals. Some lawyers are professors. Some professors are professional.

4) PRE-SUB (Predicate-subject) The middle term is the predicate of the first premise and the subject of the second premise. Example: All lawyers are professionals. Some professionals are businessmen. Some businessmen are lawyers. V. Moods

Moods refers to the arrangement of propositions or premises in the syllogism according to the quality and quantity combined (categorical symbols).

1) SUB-PRE (AA, AI, EA, EI) (AAA) a) The major premise must be universal. b) The minor premise must be affirmative.
Example:
All fruits are sweet. A All apples are fruits. A Al apples are sweet. A

2) PRE-PRE (AE, AO,EA, EI) (AEE) a) The major premise must be universal. b) One premise must be negative.
Example:
All brutes are mortals. A No angels are mortals. E Angels are not brutes. E

3) SUB-SUB (AA, AI, EA, EI, IA, OA) (AAI) a) The minor premise must be affirmative. b) The conclusion must be particular.
Example:
All brutes are irrationals. A All brutes are mortals. A All irrationals are mortals. A

4) PRE-SUB (AA, AE, EA, EI, IA) (EAO) a) If the major premise is universal, the minor premise must be affirmative. b) If the minor premise is particular, the conclusion must be negative. c) If a premise and the conclusion is negative, the minor premise must be universal.
Example:
All grass-eaters are not carnivorous. E Some carnivorous are animals. I Some animals are not grass-eaters. O

References:

Bauzon, Priciliano (2002) Logic for Filipinos. 2nd ed. Mandaluyong City: National Bookstore. (ASL, 160, B328, 2002)

Copi, Irving M. and Carl Cohen. (2005) Introduction to Logic. 12th ed. USAA: Prentice Hall. (ASL, 160, C791, 2005)

Hurley, Patrick. (2000) A Concise Introduction to Logic. 7th ed. USA: Wadsworth. (ASL, 160, H939, 2000)

Meer, Thelma Q. (2004) Basics of Logic. Philippines: Trinitas Pub. Inc. (ASL, 160, M471, 2004)

Nery, Ma. Imelda Pastrana Nabor. (2003) Logic with Ethics and Values Education. Quezon City: Katha Pub. Co. Inc. (ASL, 160, N359, 2003)

Olaguer, Raymundo Julio et al. (2007) Logic: The Art of Reasoning. 2nd ed. Manila: Libro Filipino. (ASL, 160, OI1, 2007)

University of the Cordilleras
College of Arts and Sciences

Introduction to Philosophy and Logic
A128 2:35-4:00 MWF (S110)

CATEGORICAL
SYLLOGISM

GROUP 1

Leader: Dioquino, Kathlene A. Secretary: Maglaya, Crichelle Treasurer: Tayaban, Sarah Researchers: Salvador, Jovy
Baggao, Jobelle
Sernande, Katrina Reporters: Abibico, Rizalina
Vicente, Joralyn Lois
Alumno, Joan Leigh Tinaya, Jasper

Submitted to: Mr. Manuel M. Ocaña Jr.