Philosophy Index

Disjunctive syllogism

A disjunctive syllogism (modus tollendo ponens) is a valid argument form in logic.

The form of the disjunctive syllogism is: "P or Q, not P, therefore Q" It may also be written as:

P ∨ Q, ¬P infers Q

P and Q may represent any proposition, or any other formula (using Greek letters to represent formulas rather than propositions, we may also express modus tollens as α → β, ¬β infers ¬α).

Examples of disjunctive syllogisms

The following are examples of the disjunctive syllogism argument form:

The cake has either chocolate or vanilla frosting.
The cake does not have vanilla frosting.
Therefore, the cake has chocolate frosting.

Either the Sun orbits the Earth, or the Earth orbits the Sun.
The Sun does not orbit the Earth.
Therefore, the Earth orbits the Sun.