completeness
Intuitively, a logical system is complete if everything that we want can be derived in it. Thus a formalization of logic is complete if all logically valid forms of argument are derivable in the system; a system designed to codify mathematical reasoning is complete if all mathematical truths can be derived in it, and so on. Although put like this the notion seems to be entirely informal, more precise definitions can be given. A logical system is complete in the sense introduced by Gödel if and only if all valid well-formed formulae are theorems of the system. In a stronger sense a system is complete if for any well-formed formula A, either A is a theorem, or the system would become inconsistent if A were added as an axiom. See Gödel's theorem(<

Philosophy dictionary. . 2011.

Look at other dictionaries:

  • Completeness — Com*plete ness, n. The state of being complete. [1913 Webster] …   The Collaborative International Dictionary of English

  • completeness — index conclusion (outcome), entirety, fait accompli, finality, quorum, totality, whole Burton s Legal …   Law dictionary

  • Completeness — In general, an object is complete if nothing needs to be added to it. This notion is made more specific in various fields. Contents 1 Logical completeness 2 Mathematical completeness 3 Computing 4 …   Wikipedia

  • Completeness — (Roget s Thesaurus) < N PARAG:Completeness >N GRP: N 1 Sgm: N 1 completeness completeness &c. >Adj. Sgm: N 1 completion completion &c. 729 Sgm: N 1 integration integration Sgm: N 1 allness allness GRP: N 2 Sgm …   English dictionary for students

  • completeness — complete ► ADJECTIVE 1) having all the necessary or appropriate parts; entire. 2) having run its full course; finished. 3) to the greatest extent or degree; total. 4) skilled at every aspect of an activity: the complete footballer. 5) (complete… …   English terms dictionary

  • completeness — noun see complete I …   New Collegiate Dictionary

  • Completeness — Vollständigkeit ist eine Eigenschaft formaler Systeme bzw. Kalküle. Man unterscheidet semantische Vollständigkeit („Alles, was wahr ist, ist beweisbar.“), klassische Vollständigkeit („Eine der zwei Aussagen und ist stets beweisbar.“) und… …   Deutsch Wikipedia

  • completeness — See completely. * * * Concept of the adequacy of a formal system that is employed both in proof theory and in model theory (see logic). In proof theory, a formal system is said to be syntactically complete if and only if every closed sentence in… …   Universalium

  • completeness — noun the state or condition of being complete Ant: incompleteness …   Wiktionary

  • completeness — (Roget s Thesaurus II) noun The state of being entirely whole: entirety, integrity, oneness, totality, wholeness. See PART …   English dictionary for students

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