For any proposition, either it is true or its negation is true. There is no third option.
The defining characteristic of formal logic is its indifference to truth in the empirical sense. Consider this classic syllogism: All glips are glorps. X is a glip. Therefore, X is a glorp. formal logic
Despite its power, formal logic is not a "truth machine" for the real world. In the 20th century, logicians like proved that within any sufficiently complex formal system, there are truths that cannot be proven using the rules of that system (Incompleteness Theorems). For any proposition, either it is true or