Varieties of Categorical Syllogism

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  • Topic: Logic, Syllogism, Disjunctive syllogism
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The previous chapter focused on the simple categorical syllogism. The present chapter deals with other varieties of categorical syllogism which in some arguments will prove useful in arriving at a conclusion. These varieties include the enthymeme, the epichereme, the polysyllogism, the sorites and the dilemma.

The Enthymeme

The enthymeme is an abbreviated or shortened type of categorical syllogism in that one of its premises or its conclusion is left unexpressed. Enthymemes are of three categories, distinguished on the basis of the missing [art of an argument.

1. Missing Major – enthymemes are of the missing major category when the major premise of an argument is not expressed. For example,

Africans are men,
Therefore, they are mortal beings.

2. Missing Minor – enthymemes belong to the missing minor category when the minor premise of an argument is omitted. For example,

Men are mortal beings,
Therefore, Africans are mortal beings.

3. Missing Conclusion – enthymemes whose conclusion is not expresses belong to the missing conclusion category. For example,

Men are mortal beings,
Therefore, Africans are men.

Enthymemes are categorical syllogism because of the presence of three syllogism terms. In the example for each category, above the syllogistic are men,” “Africans,” and “mortal beings.”

To check to which category an enthymeme belongs it will be helpful reconstruct in its full syllogistic form. Then, on the basis of the syllogistic term one can easily determine the category of an enthymeme. Using the example, above, its full syllogistic form is as follows:

Men are mortal beings,
but Africans are men;
therefore, they (Africans) are mortal beings.

The Epichereme

The epichireme is a type of categorical syllogism whose premise or premises are provided with proofs. The proof is often joined with the premise with a causal connective such as “for”, “because”, “since”, “due to”, and so on. For example,

Demagogues are persistent and aggressive because they are intensely-motivated, but because of their commitment to their cause communists are Demagogues, therefore, communists are persistent and aggressive.

In this example each premise has a proof. In the major premise the proof is “because they are intensely-motivated.” In the minor premise the proof is “because of their commitment to their cause.” Here are other examples:

1.Human beings will die because of their corruptible nature; but because of the presence of germs human beings are stalked with illnesses; therefore, anyone stalked with illnesses will die.

2. This city needs Darwin Selarda as mayor. Only a strong-hearted person can fight corruption. Only a man with keen business acumen can improve the economy. Only an upright person can bring back the dignity of the citizenry. Mr. Selarda has all these qualifications. Therefore, we must elect him as our next mayor.

The Polysyllogism

The polysyllogism is a chain of syllogisms which are constructed in a manner that the conclusion of the first syllogism serves as the premise of the next, and so on. The word “polysyllogism” is derived from the Greek word poly which means “many”. For the syllogism to be valid each individual syllogism must be valid by observing the rules of simple syllogism. Just one invalid individual syllogism in the series will render the whole chain of syllogism invalid. For example,

Animals are subject to death,
but men are animals,
therefore, men are subject to death,
but Asians are men,
therefore, Asians are subject to death,
but Filipinos are Asians,
therefore, Filipinos are subject to death
but Cebuanos are Filipinos,
Therefore, Cebuanos are subject to death,
But Sergio Osmeña is a Cebuano,
Therefore, Sergio Osmeña is subject to death.

The Sorites

The sorites is an abridged polysyllogism in which the intermediate conclusions are omitted. The word “sorites” is derived from the Greek word...
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