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adding formal logic definition
Another example is "If it [[rain]]s, it will rain."
Another example is "If it [[rain]]s, it will rain."
In formal [[logic]], the philosophical definition takes on a technical precision. Within a logical system such as [[proposition]]al [[calculus]] or [[intuitionistic logic]], a [[mathematical formula|formula]] φ is a tautology if it is its own [[proof]] (written symbolically as <math>\phi \vdash \phi</math>). This is equivalent to saying that φ is true under all truth assignments, or, by [[Gödel's completeness theorem]], that every collection of formulas containing φ is [[sound]].
== References ==
== References ==