Contradiction { 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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Contradiction

In propositional logic, a contradiction is a formula which implies two opposing conclusions. A contradiction is always false, and any contradictory formula implies its own negation.

The symbol ⊥ is used to indicate a contradiction. We may formally indicate that a formula φ is contradictory by φimplies .

We may easily show that the formula (P ∧ ¬P) is a contradiction by means of a truth table:

P P ∧ ¬P
T F
F F

Contradictions are often used in formal proofs to demonstrate that the true valuation of a specific proposition or formula leads to a contradiction, and that, therefore, it is false and its negation is true. This method is known as reductio ad absurdum (reduction to absurdity), or proof by contradiction.

The negation of a contradiction is, itself, a tautology.