Vollständigkeitsprüfung

Vollständigkeit is a German philosophical concept that translates to "completeness." It generally refers to the idea that a system, set of knowledge, or argument is exhaustive and leaves no essential elements or possibilities unaccounted for. The concept can be applied in various domains, including logic, mathematics, and epistemology.

In logic and mathematics, Vollständigkeit often relates to the properties of formal systems. A system is considered complete if every true statement within its domain can be proven within the system. This means there are no true propositions that are undecidable by the system's rules. The incompleteness theorems, famously proven by Kurt Gödel, demonstrated that for any sufficiently powerful formal system, there will always be statements that are true but cannot be proven within that system, thus highlighting limitations to perfect completeness.

Epistemologically, Vollständigkeit can refer to a comprehensive understanding of a subject. A complete explanation or theory would ideally cover all relevant aspects, address all significant questions, and leave no room for ambiguity or further essential inquiry. However, achieving true epistemological completeness is often considered an unattainable ideal, as knowledge is constantly evolving and new questions and perspectives emerge. The pursuit of Vollständigkeit, therefore, often involves striving for a maximally thorough and coherent understanding, acknowledging that absolute completeness may be elusive.