selvkonsistent

Selvkonsistent, or self-consistent, describes a system, model, or theory that is internally coherent. A self-consistent theory is one whose axioms and derived statements do not contain contradictions; it does not prove both a proposition and its negation. In formal logic, a set of sentences is self-consistent if it does not entail a contradiction. For first-order theories strong enough to express arithmetic, Gödel's incompleteness theorems show that if such a theory is consistent, it cannot prove its own consistency. Therefore, self-consistency is not something that can be demonstrated within the theory itself; it is usually established by external (meta-theoretical) arguments or by exhibiting a model.

In practice, self-consistency also appears in mathematical and computational methods, such as self-consistent field methods in quantum chemistry, where orbitals are determined iteratively until the computed field matches the input. In databases and distributed systems, self-consistency refers to states that agree with one another according to a chosen consistency model.

The term is often contrasted with inconsistent or paraconsistent approaches, where contradictions can exist without trivialization, or with external criteria for consistency that are not verifiable inside the theory itself. The concept provides a standard for assessing the reliability and coherence of a theoretical framework, a model’s assumptions, or a computational method.