Valuable notes on Disjunctive-Categorical Syllogisms


This is a kind of mixed syllogism in which the major premise is a disjunctive proposition, whereas the minor premise and the conclusion are categorical propositions. A disjunctive proposition consists of two component propositions, which are called its disjuncts.

A disjunctive proposition is of the form “Either A is B or C is D” in which “either… or…” is understood in the weaker sense. A disjunctive proposition asserts that at least one of the disjuncts is true. It allows for the possibility that both disjuncts may be true.

In a disjunctive-categorical syllogism the major premise is a disjunctive proposition. The minor premise denies one of the two disjuncts of the major premise. From these two premises we draw the conclusion that the other disjunct of the major premise is true. Consider the following argument form.


Either A is B or C is D.

A is not B.

Therefore, C is D.

The following is a concrete example of disjunctive-categorical syllogism.


Either Rabi is telling the truth or Asok is innocent.

Rabi is not telling the truth.

Therefore, Asok is innocent.

This argument is valid. The form of this argument is Modus Tollendo Ponens, which means by denying one alternative we can affirm the other. In other words, the falsity of one of the alternatives implies the truth of the other. However, by affirming one we cannot deny the other alternative. For example, the following argument will be invalid.


Either students are intelligent or they are laborious.

The students are intelligent.

Therefore, students are not laborious.

Such a conclusion is obviously fallacious, since the major premise allows for the possibility that students can be both intelligent and laborious.

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