Completeness (Noun)
Meaning 1
The state of being complete and entire; having everything that is needed.
Classification
Nouns denoting natural processes.
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Meaning 2
(logic) an attribute of a logical system that is so constituted that a contradiction arises if any proposition is introduced that cannot be derived from the axioms of the system.
Classification
Nouns denoting attributes of people and objects.
Examples
- The formal system's completeness was proven by demonstrating that every proposition that was true in the model could be formally derived from the axioms.
- Gödel's incompleteness theorems showed that any sufficiently powerful logical system cannot be both complete and consistent.
- The completeness of a logical system is often seen as a desirable property, as it provides a high degree of confidence in the system's ability to produce consistent results.
- A complete logical system is one in which there are no truths that lie outside the system's formal structure.
- The concept of completeness is a central concern in the study of formal systems, as it bears directly on the system's ability to capture the full range of possibilities within its domain.