consistency in logic

Statement sets, such as arguments, can be true {consistency, logic} if and only if all statements are true. Sound arguments are consistent.

In consistent formal systems, no proposition can be both true and false, and propositions are either true or false. Logical consistency requires model or universe in which all sentences are true {consistency theorem}.

omega

Propositions can depend on variables. Propositions can be true for only some variable values {omega consistency, logic} and not true for others. Incompleteness theorem states that the proposition that formal system is omega consistent is not provable by the formal system.

contradiction

If statements are not consistent, at least one statement is false {contradiction}.

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Date Modified: 2022.0224