**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 and Philosophy online tutoring.

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. WTI offers immigration law course online - fully accredited. ACE credits online at EES.

**Aristotle****Camus****Descartes****Frege****Heidegger****Hobbes****Hume****Kant****Kierkegaard****Locke****Nietzsche****Plato****Quine****Russell****Sartre****Socrates****Wittgenstein**- All Philosophers…

**Aesthetics****Epistemology****Logic****Ethics****Metaphysics****Language****Mind****Politics****TEST PREP KIT**- All Terms & Topics…

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 ** φ⊥** .

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.