consistances

Consistences is the plural of consistence, a term used in philosophy, logic, and older mathematical writings to denote the state or property of being in agreement or free from internal contradiction. In contemporary English, the more common term is consistency, and consistence frequently appears as a variant spelling in historical or translated texts.

In logic and mathematics, consistence (often called consistency in modern usage) describes the absence of contradiction within a system of axioms or rules. A theory T is consistent if it is not possible to derive both a statement and its negation from T. Equivalently, there exists at least one model in which all axioms of T hold. If such a model does not exist, T is inconsistent. The distinction between internal consistence (coherence among the components of a system) and external consistence (agreement with external facts or observations) is sometimes noted in discussions of theory appraisal and data interpretation.

Philosophically, consistence is related to coherence theories of truth and belief. A belief system can be evaluated for consistence by checking whether its elements mutually support rather than contradict one another. In practice, many discussions favor the term consistency, but consistence remains encountered in older philosophical writings and in translations where the original term aligns with the broader sense of coherence.

In applied contexts, the idea of consistences appears whenever multiple parts must align: mathematical frameworks, logical arguments, epistemic systems, or data sources. While rare in everyday language, consistences are part of the broader notion of how well components fit together without contradiction.

See also: consistency, coherence, internal consistency, model theory, epistemology.