trueconditionally

Trueconditionally is a neologism used in logic and philosophy of language to denote a proposition whose truth value is determined by a specified condition. A statement P is true conditionally on a condition C if P is true in all cases where C holds, while its truth in cases where C does not hold is not fixed by C.

From a semantic viewpoint, P is true conditionally on C if, in all accessible worlds where C is true, P is true. This differs from material implication (C → P) in standard logic, which is true whenever C is false or P is true, whereas trueconditionally emphasizes the dependence of P's truth on C's truth. The notion is used to capture context-dependence and contingency in natural-language semantics, where some statements reliably hold only under certain circumstances.

Examples help illustrate the idea. The server is online is true conditionally on the network being up; if the network is up, the statement is true, whereas if the network is down, the truth of the statement is not determined by this condition. The store is open is true conditionally on today being a weekday during business hours; if it is a weekday in business hours, the statement is true, but outside that window the condition does not force a truth value.

Relation to contextual truth, contingency, and presupposition is widely discussed. Some critics note that trueconditional terminology can blur distinctions with counterfactuals or other conditional-logical notions, so careful use is advised in formal work.

See also contextualism, contextual truth, conditionalization, presupposition.