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Trivialism (from Latin trivialis, meaning "found everywhere") is the logical theory that all statements (also known as propositions) are true and that all contradictions of the form "p and not p" (e.g. the ball is red and not red) are true. In accordance to this, a trivialist is a person who believes everything is true.
In classical logic, trivialism is in direct violation of Aristotle's law of noncontradiction. In philosophy, trivialism may be considered by some to be the complete opposite of skepticism. Paraconsistent logics may use "the law of non-triviality" to abstain from trivialism in logical practices that involve true contradictions.
Trivialism, as a term, is derived from the Latin word trivialis, meaning something that can be found everywhere. From this, "" was used to suggest something was introductory or simple. In logic, from this meaning, a "trivial" theory is something regarded as defective in the face of complex phenomenon that needs to be completely represented. Thus, literally, the trivialist theory is something expressed in the simplest possible way.
In symbolic logic, trivialism may be expressed as the following:
The above would be read as "given any proposition, it is a true proposition" through universal quantification (∀).
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