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Concept
Trivialism
Summary
Trivialism 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 with 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 is 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.
Theoretical arguments and anecdotes have been offered for trivialism to contrast it with theories such as modal realism, dialetheism and paraconsistent logics.
Trivialism, as a term, is derived from the Latin word trivialis, meaning commonplace, in turn derived from the trivium, the three introductory educational topics (grammar, logic, and rhetoric) expected to be learned by all freemen. In logic, from this meaning, a "trivial" theory is something regarded as defective in the face of a 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 (∀).
A claim of trivialism may always apply its fundamental truth, otherwise known as a truth predicate:
The above would be read as a "proposition if and only if a true proposition", meaning that all propositions are believed to be inherently proven as true. Without consistent use of this concept, a claim of advocating trivialism may not be seen as genuine and complete trivialism; as to claim a proposition is true but deny it as probably true may be considered inconsistent with the assumed theory.
Luis Estrada-González in "Models of Possibilism and Trivialism" lists four types of trivialism through the concept of possible worlds, with a "world" being a possibility and "the actual world" being reality.
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