Most logical systems are bivalent; that is, they admit only two truth-values. However, there is a fair amount of work done on non-bivalent systems of logic, especially intuitionist logic and relevance logic. In intuitionist logic, "true" and "false" are replaced with "proven true", "proven contradictory", and "not proven". In relevance logic, "neither true nor false" and "both true and false" are added to the standard two truth values. There is some debate about the value of these systems in philosophical circles, and Timothy Williamson claims to have a proof that any non-bivalent logic can be converted into a bivalent logic. | Most logical systems are bivalent; that is, they admit only two truth-values. However, there is a fair amount of work done on non-bivalent systems of logic, especially intuitionist logic and relevance logic. In intuitionist logic, "true" and "false" are replaced with "proven true", "proven contradictory", and "not proven". In relevance logic, "neither true nor false" and "both true and false" are added to the standard two truth values. There is some debate about the value of these systems in philosophical circles, and Timothy Williamson claims to have a proof that any non-bivalent logic can be converted into a bivalent logic. |