Trivialism
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| - | '''Dialetheism''' is the view that some [[statement (logic)|statements]] can be both true and false simultaneously. More precisely, it is the belief that there can be a true statement whose [[negation]] is also true. Such statements are called "true [[contradiction]]s", ''dialetheia'', or [[nondualism]]s. | ||
| - | Dialetheism is not a [[formal system|system of formal logic]]; instead, it is a thesis about [[truth]] that influences the construction of a formal logic, often based on pre-existing systems. Introducing dialetheism has various [[logical consequence|consequences]], depending on the theory into which it is introduced. A common myth is that, in traditional systems of logic (e.g., [[classical logic]] and [[intuitionistic logic]]), every statement becomes false if a contradiction is true; this means that such systems are, mistakenly, thought to become [[trivialism|trivial]] when dialetheism is included as an axiom. Other logical systems do not [[principle of explosion|explode]] in this manner when contradictions are introduced; such contradiction-tolerant systems are known as [[paraconsistent logic]]s. | + | '''Trivialism''' is the [[logical theory]] that all [[Statement (logic)|statements]] (also known as [[propositions]]) are [[truth value|true]] and that all [[contradiction]]s 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. |
| - | [[Graham Priest]] defines dialetheism as the view that there are true contradictions. JC Beall is another advocate; his position differs from Priest's in advocating constructive (methodological) [[deflationism]] regarding the truth predicate. | + | 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 logic]]s may use "the law of non-triviality" to abstain from trivialism in logical practices that involve true contradictions. |
| - | ==See also== | + | Theoretical arguments and anecdotes have been offered for trivialism to contrast it with theories such as [[modal realism]] (possibilism), [[dialetheism]] and paraconsistent logics. |
| - | *[[Problem of future contingents]] | + | |
| - | *[[Gottfried Wilhelm Leibniz|Leibniz]]'s [[compossibility]] | + | |
| - | *[[Liar paradox]] | + | |
| - | *[[Doublethink]] | + | |
| - | *[[Trivialism]] | + | |
| + | ==See also== | ||
| + | * [[Discordianism]] | ||
| + | * [[Doublethink]] | ||
| + | * [[Factual relativism]] | ||
| + | * [[Fatalism]] | ||
| + | * [[Anekantavada]] | ||
| + | * [[Syādvāda]] | ||
| + | * [[Law of excluded middle]] | ||
| + | * [[Laws of thought]] | ||
| + | * [[Monism]] | ||
| + | * [[Moral relativism]] | ||
| + | * [[Principle of bivalence]] | ||
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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 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.
Theoretical arguments and anecdotes have been offered for trivialism to contrast it with theories such as modal realism (possibilism), dialetheism and paraconsistent logics.
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See also
- Discordianism
- Doublethink
- Factual relativism
- Fatalism
- Anekantavada
- Syādvāda
- Law of excluded middle
- Laws of thought
- Monism
- Moral relativism
- Principle of bivalence
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