Mathematical truth

Truth is most often used to mean being in accord with fact or reality, or fidelity to an original or standard. Truth may also often be used in modern contexts to refer to an idea of "truth to self," or authenticity.

The commonly understood opposite of truth is falsehood, which, correspondingly, can also take on a logical, factual, or ethical meaning. The concept of truth is discussed and debated in several contexts, including philosophy, art, and religion. Many human activities depend upon the concept, where its nature as a concept is assumed rather than being a subject of discussion; these include most (but not all) of the sciences, law, journalism, and everyday life. Some philosophers view the concept of truth as basic, and unable to be explained in any terms that are more easily understood than the concept of truth itself. Commonly, truth is viewed as the correspondence of language or thought to an independent reality, in what is sometimes called the correspondence theory of truth.

Other philosophers take this common meaning to be secondary and derivative. According to Martin Heidegger, the original meaning and essence of truth in Ancient Greece was unconcealment, or the revealing or bringing of what was previously hidden into the open, as indicated by the original Greek term for truth, aletheia. On this view, the conception of truth as correctness is a later derivation from the concept's original essence, a development Heidegger traces to the Latin term veritas.

Pragmatists like C. S. Peirce take truth to have some manner of essential relation to human practices for inquiring into and discovering truth, with Peirce himself holding that truth is what human inquiry would find out on a matter, if our practice of inquiry were taken as far as it could profitably go: "The opinion which is fated to be ultimately agreed to by all who investigate, is what we mean by the truth..."

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