In logic, the law of noncontradiction states, in the words of Aristotle, that "one cannot say of something that it is and that it is not in the same respect and at the same time". In the symbolism of propositional logic, this is expressed as: Logic, from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of criteria for the evaluation of arguments, although the exact definition of logic is a matter of controversy among philosophers. ... Media:Example. ... Propositional logic or sentential logic is the logic of propositions, sentences, or clauses. ...

According to Allan Bloom, "the earliest-known explicit statement of the principle of contradiction – the premise of philosophy and the foundation of rational discourse" – is given in Plato's Politeia (The Republic) where the character Socrates states, "It's plain that the same thing won't be willing at the same time to do or suffer opposites with respect to the same part and in relation to the same thing" (436B). Allan Bloom. ... Politeia (πολιτεία) is an Ancient Greek word with no single English translation. ... Plato. ... Socrates (Greek: , invariably anglicized assÉ”kɹətiːz, SÇ’cratÄ“s; 470?–399 BCE) was a ancient Greek philosopher who is widely credited for laying the foundation for Western philosophy. ...

According to Aristotle and Thomas Aquinas, this is a fundamental principle of thought, which can only be proved by showing the opponents of the principle to be themselves committed to it. Thus, Aristotle considers the case of someone who denies the principle in the strong way – holding that every proposition is both true and false – and asks why such a person goes on the Megara road to get to Megara from Athens, since on such a person's view it is just as true that any other road would get him to Megara. Media:Example. ... Saint Thomas Aquinas [Thomas of Aquin, or Aquino] (c. ... There were four classic laws of thought recognised in European thought of the seventeenth and eighteenth century, which held sway also during nineteenth century (while subject to greater debate). ...

See also

• Contradiction
• Law of excluded middle
• Law of identity
• Peirce's law
• Principle of bivalence
• Principle of explosion
• Road Runner Tactic

Broadly speaking, a contradiction is an incompatibility between two or more statements, ideas, or actions. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... In logic, the law of identity states that A = A. Any reflexive relation upholds the law of identity; when discussing equality, the fact that A is A is a tautology. ... Peirces law in logic is named after the philosopher and logician Charles Sanders Peirce. ... In logic, the principle of bivalence states that for any proposition P, either P is true or P is false. ... (A ∧ ¬A)→ B Ex falso quodlibet, also known as ex contradictione (sequitur) quodlibet or the principle of explosion is the rule of classical logic that states that anything follows from a contradiction. ... It has been suggested that this article or section be merged into Proof by contradiction. ...

External links

• Stanford Encyclopedia of Philosophy, Contradiction.