Categorical Syllogism

CATEGORICAL SYLLOGISM Just as the verbal expression of the IDEA is the TERM, and that of the JUDGMENT is the PROPOSITION, so the verbal expression of DEDUCTIVE REASONING is called ARGUMENTATION. ARGUMENTATION is a discourse which logically deduces one proposition from other propositions. ARGUMENTATION takes the form of a SYLLOGISM. A SYLLOGISM is defined as any argumentation in which, from two propositions called the PREMISES, we conclude a third proposition called the CONCLUSION, which is so related to the premises jointly, that if the premises are true, the conclusion must also be true.

A SYLLOGISM derives its name from the kinds of propositions composing the syllogism. A SYLLOGISM is called CATEGORICAL if all the propositions composing the syllogism are CATEGORICAL PROPOSITIONS ( the predicate is affirmed or denied of the subject outright without any condition ). Example: All fathers are male parents. No true sportsman is a cheater. A SYLLOGISM is called HYPOTHETICAL if all the propositions composing the syllogism are HYPOTHETICAL PROPOSITIONS ( two propositions united into one, where one can only be true if the other is false or vice-versa ). Example: If it rains, then the ground is wet.

You cannot be a saint and a sinner at the same time. A matter is either in motion or at rest. ELEMENTS OF CATEGORICAL SYLLOGISM MATERIAL FORMAL PROXIMATE REMOTE ( 3 categorical propositions) ( 3 univocal terms S, M, P ) M P Major Every body is a substance.

Premises S M Minor Every man is a body. CONSISTENCY S P Conclusion Therefore Every man is a substance. I. MATERIAL ELEMENTS are the terms and propositions composing the syllogism. A. PROXIMATE ELEMENTS – are the three categorical propositions. . PREMISES – are the first two propositions from which a third proposition is concluded and which lead us to the new truth. 1. 1 MAJOR PREMISE – the first proposition in which the major term (P) appears. 1. 2 MINOR PPREMISE – the second proposition in which the minor term (S) appears. 2. CONCLUSION – the third proposition which is concluded from the premises and which expresses the new truth. B. REMOTE ELEMENTS – are the three univocal terms 1.

MAJOR TERM (P) – it always appears either as subject or predicate in the major premise, and always as predicate of the conclusion. 2. MINOR TERM (S) – it always appears either as subject or predicate in the minor premise, and always as the subject of the conclusion. 3. MIDDLE TERM – the term that serves as a medium through which the major term(P) and the minor term(S) are united in the affirmative syllogism and separated in the negative syllogism.

It must appear as subject or as predicate in the major and minor premises but must never in the conclusion. II. FORMAL ELEMENT S– is the proper and orderly arrangement of terms and propositions in the premises necessary to produce a valid conclusion. A. SYLLOGISTIC FIGURE – is the proper arrangement of “M” with respect to the “S” and the “P” in the premises. Fig. 1 Fig. Fig. 3 Fig. 4 ( sub – pre ) ( pre – pre ) ( sub – sub ) ( pre – sub ) M P P M M P P M S M S M M S M S . : S P . S P . : S P . : S P In Fig. 1 ( sub – pre ), the M is the subject of the major premise and the predicate of the minor premise. Example: All crimes are punishable by law. M P All murders are crimes. S M . : All murders are punishable by law. .: S P In Fig. 2 ( pre – pre ), the M is the predicate of both major and minor premises.

Example: Every animal is with senses. P M No stone is with senses. S M . : No stone is an animal. .: S P In Fig. 3 ( sub – sub ), the M is the subject of both premises. Example: All bodies are material. M P All bodies are substances. M S . : Some substances are material. : S P In Fig. 4 ( pre – sub ), the M is the predicate of the major premise and the subject of the minor premise. Example: Some bodies are plants. P M All plants are living objects. M S . : Some living objects are bodies. .: S P B. SYLLOGISTIC MOOD – is the proper and orderly arrangement of the premises according to quantity ( universal or particular ) and quality ( affirmative or negative ).

Theoretically, the following combinations of MOODS are possible in the construction of premises in each of the four syllogistic figures. A A A A E E E E I I I I O O O O A E I O A E I O A E I O A E I O RULES OF THE CATEGORICAL SYLLOGISM 1. ONLY THREE UNIVOCAL TERMS MUST APPEAR IN THE SYLLOGISM. fallacy of equivocation or fallacy of four terms Example: All minerals are substances.

A ruler has 12 inches. All material beings are organisms. Marcos is a ruler. .: ________________________. .: Marcos has 12 inches. 2. THE MAJOR TERM NOR THE MINOR TERM CANNOT BE UNIVERSAL IN THE CONCLUSION IF IT WAS PARTICULAR IN THE PREMISE. note: the following symbols will used M – middle term + – affirmative proposition P – major term – – negative proposition S – minor term Examples: All hammers are tools. M + pP No chisels are hammers. uS – uM fallacy of illicit major term . : No chisels are tools. .: uS – uP All birds have wings. uM + pP All birds are animals. uM + pS fallacy of illicit minor term . : All animals have wings. .: uS + pP 3. THE MIDDLE TERM MUST NOT BE USED IN THE CONCLUSION.

Example: Socrates is a philosopher. Socrates is poor. fallacy of misplaced middle term . : Socrates is a poor philosopher. 4. THE MIDDLE TERM MUST BE USED AT LEAST ONCE AS A UNIVERSAL IN THE PREMISES. Example: All Ilocanos are Filipinos. uP + pM All Batanguenos are Filipinos. uS + pM fallacy of undistributed middle term . : All Batanguenos are Ilocanos. .:uS + pP 5. IF BOTH PREMISES ARE AFFIRMATIVE, THE CONCLUSION IS AFFIRMATIVE.

Example: Every money is a currency. Every peso bill is a money. fallacy of a negative conclusion drawn from affirmative premises . : No peso bill is a currency. 6. BOTH PREMISES MUST NOT BE NEGATIVE, ONE AT LEAST MUST BE AFFIRMATIVE. Example: A cat is not a dog. A pussycat is not a dog. fallacy of negative premises . : A pussycat is not a cat. 7. IF ONE PREMISE IS NEGATIVE, THE CONCLUSION IS NEGATIVE. Example: All rebels are terrorists. Some students are not terrorists. allacy of affirmative conclusion drawn from a negative premise . : Some students are rebels. 8. IF ONE PREMISE IS PARTICULAR, THE CONCLUSION IS PARTICULAR. Example: All roses are flowers. Some roses are fragrant. fallacy of universal conclusion drawn from a particular premise . : All fragrant are flowers. 9. NO CONCLUSION CAN BE DRAWN FROM TWO PARTICULAR PREMISES. Example: Some men are old people. Some old people are women. fallacy of two particular premises . : Some women are men.