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Completeness vs Consistency - What's the difference?

completeness | consistency |

In lang=en terms the difference between completeness and consistency

is that completeness is the property of a logical theory that whenever a wff is valid then it must also be a theorem. Symbolically, letting T represent a theory within logic L, this can be represented as the property that whenever T \vDash \phi is true, then T \vdash \phi must also be true, for any wff φ of logic L while consistency is freedom from contradiction; the state of a system of axioms such that none of the propositions deduced from them are mutually contradictory.

As nouns the difference between completeness and consistency

is that completeness is the state or condition of being complete while consistency is local coherence.

completeness

English

(wikipedia completeness)

Noun

(-)
  • the state or condition of being complete
  • (logic) The property of a logical theory that whenever a wff is valid then it must also be a theorem. Symbolically, letting T'' represent a theory within logic ''L'', this can be represented as the property that whenever T \vDash \phi is true, then T \vdash \phi must also be true, for any wff ''φ'' of logic ''L .
  • *
    • THEOREM 37°. (Gödel's completeness theorem 1930.) In the predicate calculus H'':
    (a) ''If'' \vDash F [''or even if'' \aleph_0-\vDash F], ''then'' \vdash F. ''If'' E_1, . . . , E_k \vDash F [''or even if'' E_1, . . . , E_k \ \aleph_0-\vDash F], ''then     E_1, . . . , E_k \vdash F.
    (b) [...]

    Synonyms

    *(state of being complete ): completion

    Antonyms

    * incompleteness

    consistency

    English

    (wikipedia consistency)

    Noun

    (consistencies)
  • Local coherence.
  • Correspondence or compatibility.
  • Reliability or uniformity; the quality of being consistent.
  • * Addison
    • That consistency of behaviour whereby he inflexibly pursues those measures which appear the most just.
  • The degree of viscosity of something.
  • *{{quote-magazine, year=2013, month=July-August, author= Stephen P. Lownie], [http://www.americanscientist.org/authors/detail/david-m-pelz David M. Pelz
    • , magazine=(American Scientist), title= Stents to Prevent Stroke , passage=As we age, the major arteries of our bodies frequently become thickened with plaque, a fatty material with an oatmeal-like consistency that builds up along the inner lining of blood vessels.}}
  • (logic) Freedom from contradiction; the state of a system of axioms such that none of the propositions deduced from them are mutually contradictory.
  • (obsolete) Firmness of constitution or character; substantiality; durability; persistency.
  • * South
    • His friendship is of a noble make and a lasting consistency .

    Antonyms

    * inconsistency

    Related terms

    * consist * consistence * consistent