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HAND-OUT IN LOGIC

By Catherine C. de la Cruz

Setember 20, 2013

CATEGORICAL SYLLOGISM

1. Categorical syllogism is an oral or written discourse showing the agreement or disagreement between twoterms on the basis of their respective relation to a common third term.

2. Categorical syllogismis a reasoning that shows the agreement or disagreement between two terms on the basisof their respective relation

3. Categorical syllogismis any argument in which, from two propositions called premises, we concluded a thirdproposition called the conclusion, which is so related to the premises taken jointly that if the premises are true,

the conclusion must also be true.

4. Categorical syllogismis a piece of deductive mediate inference which consists of three categorical propositions,the first two of which are premises and the third of which is the conclusion.

5. In the major premise, the major term is compared to the middle term6. In the minor premise, the minor term is compared to the middle term.7. The Principle of Reciprocal Identity states that If two terms agree with a third term, then these three terms are

identical with each other -

8. When three terms agree and are identical with each other, this falls under theprinciple ofReciprocal Identity9. The Principle of Reciprocal Non-Identity states that If two terms, one of which is identical with a third term

while the other is not, then the three terms are not identical with each other. -

10.When three terms are not identical with each other, ths falls under the Principle of Reciprocal Non-Identity11.The Dictum de Omni (The Law of All)states that What is affirmed of a given term may also be affirmed by every

term that comes under that term

12.The Dictum de Nullo (The Law of None)states that What is denied universally of a term is also denied of each ofall referents of that term

13.By the figure of syllogismwe mean that proper position of the middle term (M) with respect to the major term(P) and the minor term (S) in the premise.

14.Figure of syllogismis the proper arrangement of the middle term with respect to the major term and the minorterm in the premises.

15.By the mood of syllogism, we mean the proper arrangement of the premises according to quality and quantity(A, E, I, O).

16. The proper position of the premises according to the quality and quantity is mood of syllogismTHE EIGHT BASIC RULES OF CATEGORICAL SYLLOGISM ARE

Rule 1. The syllogism must contain three terms only.

Rule 2.No term can have a greater extension in the conclusion than it had in the premise

* Violation of Rule 2 of the basic rules of categorical syllogism is a commission of fallacy of the illicit major.

Rule 3. The middle term should not be found in the conclusion

Rule 4. The middle term must be universal at least once; however, it may be taken universally twice in the premises.

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* Violation of Rule 4 of the basic rules of categorical syllogism is a commission of n of fallacy of undistributed

middle.

Rule 5. Two affirmative premises cannot give a negative conclusion (meaning: only an affirmative conclusion can be

drawn from two affirmative premises)

Rule 6. From two negative premises, no conclusion can be inferred.

* Violation of Rule 6 of the basic rules of categorical syllogism is a commission of fallacy of two negative

premises

Rule 7. No conclusion can be drawn from two particular premises.*Violation of Rule 7 is commission of either fallacy of illicit major or fallacy of undistributed middle.

Rule 8. Conclusion must be particular, if one of the premises is particular, and negative, if one premise is negative

(conclusion follows the weaker side).

Note : Minor term (S)

Major term (P)

Middle term (M)

THE FOUR POSSIBLE POSITIONS OR ARRANGEMENTS WHICH GIVE RISE TO FOUR SYLLOGISTIC FIGURES ARE

Figure 1. The middle term is the subject of the major premise and the predicate of the minor premise.

M - P

S - M

____

S - P

Figure 2. The middle term (M) is the predicate of both premises

P - M

S - M

____

S - P

Figure 3. The middle term is the subject of both premises

M - P

M - S

____

S - P

Figure 4. The middle term is the predicate of the major premise and the subject of the minor premise

P - M

M - S

____

S - P

Note:

1. Categorical syllogism is not the same as categorical proposition because a syllogism consists of proposition.

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2. The minor premise comes second after the major premise.

3. The middle term should not be found in the conclusion.

4. The syllogism must contain three terms only.

5. From two negative premises, no conclusion can be inferred.

6. There can be no conclusion from two particular premises.

No conclusion can be drawn from two particular premises

Source: Teaching and Learning Logic by Jose R. Joven