Inconsistency

Definition: The author asserts more than one proposition such that the propositions cannot all be true. In such a case, the propositions may be contradictories or they may be contraries. Examples: (i) Montreal is about 200 km from Ottawa, while Toronto is 400 km from Ottawa. Toronto is closer to Ottawa than Montreal. (ii) John is taller than Jake, and Jake is taller than Fred, while Fred is taller than John. Proof: Assume that one of the statements is true, and then use it as a premise to show that one of the other statements is false.