Notes on Categorical Syllogism

SIMPLY PUT, CATEGORICAL SYLLOGISM is the kind of argument being studied in Traditional Aristotelian Logic. This is a form of deductive argument that consists of a major premise, a minor premise, and a conclusion. Certain rules govern proper syllogistic reasoning that if any of the rules are violated, a formal fallacy has been committed, making the argument invalid.

Example of Categorical Syllogism:         

All Filipinos are hospitable persons.

All Ilocanos are Filipinos.

Therefore, all Ilocanos are hospitable persons.

Composition of a Categorical Syllogism:

I.Three (3) categorical statements: major premise, minor premise, &conclusion.

II. Three (3) terms:

         1) the major term (P) – the predicate of the conclusion

         2) the minor term (S) – the subject of the conclusion

         3) the middle term (M) – the term found in both premises

Distribution of Terms:

(The professor would explain in the classroom how the subject and predicate term in each type of statement is distributed. The following is a summary of the distribution of each term in each type of proposition.)

A statement (All S are P):             S is Distributed & P is Undistributed

E statement (No S are P):              S is Distributed & P is Distributed

I statement (Some S are P):          S is Undistributed & P is Undistributed

O statement (Some S are not P):  S is Undistributed & P is Distributed

Rules Governing Syllogistic Reasoning:

1. There must be three and only three terms to be used in the same meaning throughout the argument. Violation of this rule results in committing the “Fallacy of Four (4) Terms”.

e.g. All stars are heavenly bodies. Jessica Alba is a star. Therefore, Jessica Alba is a heavenly body.

 (Note: Some students claim that it could have been valid if the conclusion is, “Therefore, Jessica Alba has a heavenly body.” The claim, of course, is not correct.)

2. The Middle term must be distributed at least once (otherwise, “Fallacy of Undistributed Middle Term” is committed).

e.g. All priests are men. Rico is a man. Therefore, Rico is a priest.

3. If a term is distributed in the conclusion, then it must also be distributed in the premise (lest, the argument is guilty of “Fallacy of Undistributed Major/Minor Term”)

e.g. A few boxers are college graduates. Most boxers are rich persons. Therefore, all rich persons are college graduates.

e.g. All metals are electric conductors. Mercury is a metal. Therefore, Mercury is not an electric conductor.

4. Two negative premises are not allowed. (They make an argument guilty of “Fallacy of Exclusive Terms”)

e.g. No horses are dogs. No dogs are cats. Therefore, no cats are horses.

5. One negative premise is allowed if and only if the conclusion is negative. (Else, the syllogism commits the “Fallacy of drawing an affirmative conclusion from a negative premise”).

e.g. A cat is a mammal. Garfield is not a mammal. Therefore, Garfield is a cat.

Sample Quiz:

Determine the validity of the following syllogisms. If the syllogism is invalid, state the fallacy committed.

1. A dog is a mammal. Blackie is not a mammal. Therefore, Blackie is not a dog.

2. A ruler is 12 inches long. Gloria is a ruler. Therefore, Gloria is 12 inches long.

3. Many Filipinos are brown. Many Filipinos are hospitable persons. Therefore, many hospitable persons are brown.

4. No priests are nuns. Some Jamaicans are not nuns. Therefore, some Jamaicans are not priests.

5. All metals are elements. Gold is a metal. Therefore, gold is an element.

6. Only men are priests. Ted is a man. Therefore, Ted is a priest.

7. All criminal lawyers are bad persons. All lawyers who specialize in Criminal Law are criminal lawyers. Therefore, all lawyers who specialize in Criminal Law are bad persons.

8. None but Americans are members of the club. Peter is an American. Therefore, Peter is a member of the club.

9. All utts are pitts. All pitts are mits. Therefore, all mitts are utts.

10. All except varsity players are academic scholars. Some students are varsity players. Therefore, some students are not academic scholars.

11. Some students are SSS scholars. All students are hardworking persons. Therefore, some hardworking persons are SSS scholars.

12. No animals are rational creatures. Some rational creatures are Republicans. Therefore, some Republicans are not animals.

13. Apples are sweet. Some fruits are apples. Therefore, some fruits are sweet.

14. All priests are men. Rene is not a man. Therefore, Rene is not a priest.

15. All Filipinos are brown persons. All Filipinos are Asians. Therefore, some Asians are brown persons.