In traditional Aristotelian logic, consistency is a semantic concept meaning that two or more propositions are simultaneously true under some interpretation. In modern logic there's a syntactic definition that also fits the complex mathematical theories developed since Frege's Begriffsschrift (1879): a set of statements are called consistent with respect to a certain logical calculus (also called a logical system or a formal system), if no formula of the form 'P and not-P' is derivable from tho… (More on Inconsistency)