Disjunctive syllogism { Philosophy Index }

Philosophy Index

Philosophy Index

Philosophy Index is a site devoted to the study of philosophy and the philosophers who conduct it. The site contains a number of philosophy texts, brief biographies and introductions to philosophers and explanations on a number of topics. Accredited homeschooling online at Northgate Academy.

Philosophy Index is a work in progress, a growing repository of knowledge. It outlines current philosophical problems and issues, as well as an overview of the history of philosophy. The goal of this site is to present a tool for those learning philosophy either casually or formally, making the concepts of philosophy accessible to anyone interested in researching them. WOLI offers immigration law course online - fully accredited. ACE credits online at EES.

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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.