In my ethics class, I teach a section on moral methods—these are argument templates for ethical reasoning. One method, which is useful beyond ethics, is Logical Consistency. This method is based on a basic concept in logic, that of logical consistency. Two claims are consistent with each other when both can be true at the same time. For example, the claim “restricting freedom is sometimes acceptable” is consistent with the claim “restricting freedom is sometimes unacceptable.” This is because both claims could be true. Two claims are inconsistent when both cannot be true at the same time (but both could be false). For example, the claim “people should be free from government control” would seem to be inconsistent with the claim “the government should ban the teaching of critical race theory.” This is because while these claims cannot both be true at the same time, they could both be false.
Because of the nature of inconsistent claims, if someone makes inconsistent claims, then at least one of their claims must be false. The fact that two (or more) claims are inconsistent does not show which of them is false. The inconsistency just shows that. . .
News source: A Philosopher’s Blog