Självkonsekventa

Självkonsekventa is a Swedish term that translates to "self-consistent" in English. It is most commonly used in the context of logic and theoretical sciences, particularly in mathematics and physics. A system, theory, or statement is considered självkonsekventa if it does not contain any internal contradictions. This means that all its components or deductions logically follow from each other without violating established rules or axioms.

In mathematics, a set of axioms is självkonsekventa if no theorem can be proven that contradicts another theorem derived from the same axioms. This is a fundamental requirement for the validity of any mathematical system. For example, the axioms of Euclidean geometry are considered självkonsekventa because they form a coherent and non-contradictory framework for describing space.

In physics, the term is applied to theories that describe the universe. A self-consistent physical theory must adhere to its own internal logic and not produce paradoxical results when applied to different scenarios. For instance, Einstein's theory of general relativity is highly regarded for its självkonsekventa nature.

The concept of självkonsekventa is closely related to Gödel's incompleteness theorems, which demonstrate that for any sufficiently complex formal system, there will always be statements that are true but cannot be proven within the system itself, and that the system cannot prove its own consistency. Therefore, proving the självkonsekventa of a system can be a challenging, and sometimes impossible, task. Despite these limitations, the pursuit of självkonsekventa remains a cornerstone of scientific and logical inquiry, aiming for internal coherence and reliability in our understanding of the world and abstract concepts.